Elements

Elements Machine readable text Euclid J. L. Heiberg Perseus Project, Tufts University Gregory Crane Prepared under the supervision of Lisa Cerrato William Merrill Elli Mylonas David Smith The National Science Foundation Trustees of Tufts University Medford, MA Perseus Project

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You credit Perseus, as follows, whenever you use the document: Text provided by Perseus Digital Library, with funding from The National Science Foundation. Original version available for viewing and download at http://www.perseus.tufts.edu/hopper/. You leave this availability statement intact. You use it for non-commercial purposes only. You offer Perseus any modifications you make. Euclid Euclidis Elementa J. L. Heiberg Leipzig Teubner 1883-1888 Greek 12/1/97 DASed. $Log: euc.elem_gk.xml,v $ Revision 1.2 2011-09-07 13:56:14 rsingh04 adding rend=displayNum to lb tags Revision 1.1 2011-01-04 05:42:34 gcrane base sdl file Revision 1.1 2009/11/23 18:46:53 rsingh04 moved more xml files around based on copyright status Revision 1.4 2009/01/16 20:00:04 rsingh04 fixed some more entities and chunking Revision 1.3 2009/01/15 21:58:10 rsingh04 lots of cleanup to chunking schemes, entities, head tags, etc Revision 1.2 2005/08/01 21:17:14 packel removed stray item tags Revision 1.1 2005/07/25 14:33:11 packel Converted to XML Revision 1.11 2004/06/02 19:16:22 lcerrato missing div for 7.20; added without checking source Revision 1.10 2004/01/20 17:22:06 dasmith Made DIV types explicit on all elements, since the inheritance behavior didn't survive XML conversion. Revision 1.9 2003/08/29 19:04:45 lcerrato changed TEI header to reflect correct edition Revision 1.8 2003/07/01 22:16:08 yorkc Updated texts to TEI P4 and Perseus P4 extensions; minor cleanup (esp. character encodings and typos.) Revision 1.7 2000/10/17 17:40:32 lcerrato fixed numeration problem at book 7 definitions Revision 1.6 2000/03/04 20:34:30 dasmith Added separate funder entity to TEI header. Revision 1.5 2000/02/11 00:51:31 dasmith Type all DIVs properly. Write refsDecl that works for whole document. Revision 1.4 2000/02/10 20:58:15 dasmith Added refsDecl for definitions, etc. Revision 1.3 1997/12/01 23:05:36 textgod Tagged points and line segments as NUMs. Revision 1.2 1997/12/01 22:51:02 textgod New header.

shmei=o/n e)stin, ou(= me/ros ou)qe/n.

grammh\ de\ mh=kos a)plate/s.

grammh=s de\ pe/rata shmei=a.

eu)qei=a grammh/ e)stin, h(/tis e)c i)/sou toi=s e)f' e(auth=s shmei/ois kei=tai.

e)pifa/neia de/ e)stin, o(\ mh=kos kai\ pla/tos mo/non e)/xei.

e)pifanei/as de\ pe/rata grammai/.

e)pi/pedos e)pifa/neia/ e)stin, h(/tis e)c i)/sou tai=s e)f' e(auth=s eu)qei/ais kei=tai.

e)pi/pedos de\ gwni/a e)sti\n h( e)n e)pipe/dw| du/o grammw=n a(ptome/nwn a)llh/lwn kai\ mh\ e)p' eu)qei/as keime/nwn pro\s a)llh/las tw=n grammw=n kli/sis.

o(/tan de\ ai( perie/xousai th\n gwni/an grammai\ eu)qei=ai w)=sin, eu)qu/grammos kalei=tai h( gwni/a.

o(/tan de\ eu)qei=a e)p' eu)qei=an staqei=sa ta\s e)fech=s gwni/as i)/sas a)llh/lais poih=|, o)rqh\ e(kate/ra tw=n i)/swn gwniw=n e)sti, kai\ h( e)festhkui=a eu)qei=a ka/qetos kalei=tai, e)f' h(\n e)fe/sthken.

a)mblei=a gwni/a e)sti\n h( mei/zwn o)rqh=s.

o)cei=a de\ h( e)la/sswn o)rqh=s.

o(/ros e)sti/n, o(/ tino/s e)sti pe/ras.

sxh=ma/ e)sti to\ u(po/ tinos h)/ tinwn o(/rwn periexo/menon.

ku/klos e)sti\ sxh=ma e)pi/pedon u(po\ mia=s grammh=s periexo/menon ~~h(\ kalei=tai perife/reia~~, pro\s h(\n a)f' e(no\s shmei/ou tw=n e)nto\s tou= sxh/matos keime/nwn pa=sai ai( prospi/ptousai eu)qei=ai ~~pro\s th\n tou= ku/klou perife/reian~~ i)/sai a)llh/lais ei)si/n.

ke/ntron de\ tou= ku/klou to\ shmei=on kalei=tai.

dia/metros de\ tou= ku/klou e)sti\n eu)qei=a/ tis dia\ tou= ke/ntrou h)gme/nh kai\ peratoume/nh e)f' e(ka/tera ta\ me/rh u(po\ th=s tou= ku/klou periferei/as, h(/tis kai\ di/xa te/mnei to\n ku/klon.

h(miku/klion de/ e)sti to\ periexo/menon sxh=ma u(po/ te th=s diame/trou kai\ th=s a)polambanome/nhs u(p' au)th=s periferei/as. ke/ntron de\ tou= h(mikukli/ou to\ au)to/, o(\ kai\ tou= ku/klou e)sti/n.

sxh/mata eu)qu/gramma/ e)sti ta\ u(po\ eu)qeiw=n periexo/mena, tri/pleura me\n ta\ u(po\ triw=n, tetra/pleura de\ ta\ u(po\ tessa/rwn, polu/pleura de\ ta\ u(po\ pleio/nwn h)\ tessa/rwn eu)qeiw=n periexo/mena.

tw=n de\ tripleu/rwn sxhma/twn i)so/pleuron me\n tri/gwno/n e)sti to\ ta\s trei=s i)/sas e)/xon pleura/s, i)soskele\s de\ to\ ta\s du/o mo/nas i)/sas e)/xon pleura/s, skalhno\n de\ to\ ta\s trei=s a)ni/sous e)/xon pleura/s.

e)/ti de\ tw=n tripleu/rwn sxhma/twn o)rqogw/nion me\n tri/gwno/n e)sti to\ e)/xon o)rqh\n gwni/an, a)mblugw/nion de\ to\ e)/xon a)mblei=an gwni/an, o)cugw/nion de\ to\ ta\s trei=s o)cei/as e)/xon gwni/as.

tw=n de\ tetrapleu/rwn sxhma/twn tetra/gwnon me/n e)stin, o(\ i)so/pleuro/n te/ e)sti kai\ o)rqogw/nion, e(tero/mhkes de/, o(\ o)rqogw/nion me/n, ou)k i)so/pleuron de/, r(o/mbos de/, o(\ i)so/pleuron me/n, ou)k o)rqogw/nion de/, r(omboeide\s de\ to\ ta\s a)penanti/on pleura/s te kai\ gwni/as i)/sas a)llh/lais e)/xon, o(\ ou)/te i)so/pleuro/n e)stin ou)/te o)rqogw/nion: ta\ de\ para\ tau=ta tetra/pleura trape/zia kalei/sqw.

para/llhloi/ ei)sin eu)qei=ai, ai(/tines e)n tw=| au)tw=| e)pipe/dw| ou)=sai kai\ e)kballo/menai ei)s a)/peiron e)f' e(ka/tera ta\ me/rh e)pi\ mhde/tera sumpi/ptousin a)llh/lais.

*)hith/sqw a)po\ panto\s shmei/ou e)pi\ pa=n shmei=on eu)qei=an grammh\n a)gagei=n.

kai\ peperasme/nhn eu)qei=an kata\ to\ sunexe\s e)p' eu)qei/as e)kbalei=n.

kai\ panti\ ke/ntrw| kai\ diasth/mati ku/klon gra/fesqai.

kai\ pa/sas ta\s o)rqa\s gwni/as i)/sas a)llh/lais ei)=nai.

kai\ e)a\n ei)s du/o eu)qei/as eu)qei=a e)mpi/ptousa ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh gwni/as du/o o)rqw=n e)la/ssonas poih=|, e)kballome/nas ta\s du/o eu)qei/as e)p' a)/peiron sumpi/ptein, e)f' a(\ me/rh ei)si\n ai( tw=n du/o o)rqw=n e)la/ssones.

ta\ tw=| au)tw=| i)/sa kai\ a)llh/lois e)sti\n i)/sa.

kai\ e)a\n i)/sois i)/sa prosteqh=|, ta\ o(/la e)sti\n i)/sa.

kai\ e)a\n a)po\ i)/swn i)/sa a)faireqh=|, ta\ kataleipo/mena/ e)stin i)/sa.

~~kai\ e)a\n a)ni/sois i)/sa prosteqh=|, ta\ o(/la e)sti\n a)/nisa.~~

~~kai\ ta\ tou= au)tou= dipla/sia i)/sa a)llh/lois e)sti/n.~~

~~kai\ ta\ tou= au)tou= h(mi/sh i)/sa a)llh/lois e)sti/n.~~

kai\ ta\ e)farmo/zonta e)p' a)/llhla i)/sa a)llh/lois e)sti/n.

kai\ to\ o(/lon tou= me/rous mei=zon ~~e)stin~~.

kai\ du/o eu)qei=ai xwri/on ou) perie/xousin.

e)pi\ th=s doqei/shs eu)qei/as peperasme/nhs tri/gwnon i)so/pleuron susth/sasqai.

e)/stw h( doqei=sa eu)qei=a peperasme/nh h( *a*b.

dei= dh\ e)pi\ th=s *a*b eu)qei/as tri/gwnon i)so/pleuron susth/sasqai.

oi( ku/kloi, e)pi\ ta\ *a, *b shmei=a e)pezeu/xqwsan eu)qei=ai ai( *g*a, *g*b.

kai\ e)pei\ to\ *a shmei=on ke/ntron e)sti\ tou= *g*d*b ku/klou, i)/sh e)sti\n h( *a*g th=| *a*b: pa/lin, e)pei\ to\ *b shmei=on ke/ntron e)sti\ tou= *g*a*e ku/klou, i)/sh e)sti\n h( *b*g th=| *b*a. e)dei/xqh de\ kai\ h( *g*a th=| *a*b i)/sh: e(kate/ra a)/ra tw=n *g*a, *g*b th=| *a*b e)sti\n i)/sh. ta\ de\ tw=| au)tw=| i)/sa kai\ a)llh/lois e)sti\n i)/sa: kai\ h( *g*a a)/ra th=| *g*b e)sti\n i)/sh: ai( trei=s a)/ra ai( *g*a, *a*b, *b*g i)/sai a)llh/lais ei)si/n.

i)so/pleuron a)/ra e)sti\ to\ *a*b*g tri/gwnon, kai\ sune/statai e)pi\ th=s doqei/shs eu)qei/as peperasme/nhs th=s *a*b.

*)epi\ th=s doqei/shs a)/ra eu)qei/as peperasme/nhs tri/gwnon i)so/pleuron sune/statai: o(/per e)/dei poih=sai.

e)pezeu/xqw ga\r a)po\ tou= *a shmei/ou e)pi\ to\ *b shmei=on eu)qei=a h( *a*b, kai\ sunesta/tw e)p' au)th=s tri/gwnon i)so/pleuron to\ *d*a*b, kai\ e)kbeblh/sqwsan e)p' eu)qei/as tai=s *d*a, *d*b eu)qei=ai ai( *a*e, *b*z, kai\ ke/ntrw| me\n tw=| *b diasth/mati de\ tw=| *b*g ku/klos gegra/fqw o( *g*h*q, kai\ pa/lin ke/ntrw| tw=| *d kai\ diasth/mati tw=| *d*h ku/klos gegra/fqw o( *h*k*l.

e)pei\ ou)=n to\ *b shmei=on ke/ntron

du/o doqeisw=n eu)qeiw=n a)ni/swn a)po\ th=s mei/zonos th=| e)la/ssoni i)/shn eu)qei=an a)felei=n.

e)/stwsan ai( doqei=sai du/o eu)qei=ai

a)/nisoi ai( *a*b, *g, w(=n mei/zwn e)/stw h( *a*b: dei= dh\ a)po\ th=s mei/zonos th=s *a*b th=| e)la/ssoni th=| *g i)/shn eu)qei=an a)felei=n.

kai\ e)pei\ to\ *a shmei=on ke/ntron e)sti\ tou= *d*e*z ku/klou, i)/sh e)sti\n h( *a*e th=| *a*d: a)lla\ kai\ h( *g th=| *a*d e)stin i)/sh. e(kate/ra a)/ra tw=n *a*e, *g th=| *a*d e)stin i)/sh: w(/ste kai\ h( *a*e th=| *g e)stin i)/sh.

du/o a)/ra doqeisw=n eu)qeiw=n a)ni/swn tw=n *a*b, *g a)po\ th=s mei/zonos th=s *a*b th=| e)la/ssoni th=| *g i)/sh a)fh/|rhtai h( *a*e: o(/per e)/dei poih=sai.

e)/stw du/o tri/gwna ta\ *a*b*g, *d*e*z ta\s du/o pleura\s ta\s *a*b, *a*g tai=s dusi\ pleurai=s tai=s *d*e, *d*z i)/sas e)/xonta e(kate/ran e(kate/ra| th\n me\n *a*b th=| *d*e th\n de\ *a*g th=| *d*z kai\ gwni/an th\n u(po\ *b*a*g gwni/a| th=| u(po\ *e*d*z i)/shn. le/gw, o(/ti kai\ ba/sis h( *b*g ba/sei th=| *e*z i)/sh e)sti/n, kai\ to\ *a*b*g tri/gwnon tw=| *d*e*z trigw/nw| i)/son e)/stai, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin, h( me\n u(po\ *a*b*g th=| u(po\ *d*e*z, h( de\ u(po\ *a*g*b th=| u(po\ *d*z*e.

*)efarmozome/nou ga\r tou= *a*b*g trigw/nou e)pi\ to\ *d*e*z tri/gwnon kai\ tiqeme/nou tou= me\n *a shmei/ou e)pi\ to\ *d shmei=on th=s de\ *a*b eu)qei/as e)pi\ th\n *d*e, e)farmo/sei kai\ to\ *b shmei=on e)pi\ to\ *e dia\ to\ i)/shn ei)=nai th\n *a*b th=| *d*e: e)farmosa/shs dh\ th=s *a*b e)pi\ th\n *d*e e)farmo/sei kai\ h( *a*g eu)qei=a e)pi\ th\n *d*z dia\ to\ i)/shn ei)=nai th\n u(po\ *b*a*g gwni/an th=| u(po\ *e*d*z: w(/ste kai\ to\ *g shmei=on e)pi\ to\ *z shmei=on e)farmo/sei dia\ to\ i)/shn pa/lin ei)=nai th\n *a*g th=| *d*z. a)lla\ mh\n kai\ to\ *b e)pi\ to\ *e e)fhrmo/kei: w(/ste ba/sis h( *b*g e)pi\ ba/sin th\n *e*z e)farmo/sei. ei) ga\r tou= me\n *b e)pi\ to\ *e e)farmo/santos tou= de\ *g e)pi\ to\ *z h( *b*g ba/sis e)pi\ th\n *e*z ou)k e)farmo/sei, du/o eu)qei=ai xwri/on perie/cousin: o(/per e)sti\n a)du/naton. e)farmo/sei a)/ra h( *b*g ba/sis e)pi\ th\n *e*z kai\ i)/sh au)th=| e)/stai: w(/ste kai\ o(/lon to\ *a*b*g tri/gwnon e)pi\ o(/lon to\ *d*e*z tri/gwnon e)farmo/sei kai\ i)/son au)tw=| e)/stai, kai\ ai( loipai\ gwni/ai e)pi\ ta\s loipa\s gwni/as e)farmo/sousi kai\ i)/sai au)tai=s e)/sontai, h( me\n u(po\ *a*b*g th=| u(po\ *d*e*z h( de\ u(po\ *a*g*b th=| u(po\ *d*z*e.

e)a\n a)/ra du/o tri/gwna ta\s du/o pleura\s ~~tai=s~~ du/o pleurai=s i)/sas e)/xh| e(kate/ran e(kate/ra| kai\ th\n gwni/an th=| gwni/a| i)/shn e)/xh| th\n u(po\ tw=n i)/swn eu)qeiw=n periexome/nhn, kai\ th\n ba/sin th=| ba/sei i)/shn e(/cei, kai\ to\ tri/gwnon tw=| trigw/nw| i)/son e)/stai, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: o(/per e)/dei dei=cai.

tw=n i)soskelw=n trigw/nwn ai( pro\s th=| ba/sei gwni/ai i)/sai a)llh/lais ei)si/n, kai\ prosekblhqeisw=n tw=n i)/swn eu)qeiw=n ai( u(po\ th\n ba/sin gwni/ai i)/sai a)llh/lais e)/sontai.

e)/stw tri/gwnon i)soskele\s to\ *a*b*g i)/shn e)/xon th\n *a*b pleura\n th=| *a*g pleura=|, kai\ prosekbeblh/sqwsan e)p'

eu)qei/as tai=s *a*b, *a*g eu)qei=ai ai( *b*d, *g*e: le/gw, o(/ti h( me\n u(po\ *a*b*g gwni/a th=| u(po\ *a*g*b i)/sh e)sti/n, h( de\ u(po\ *g*b*d th=| u(po\ *b*g*e.

ei)lh/fqw ga\r e)pi\ th=s *b*d tuxo\n shmei=on to\ *z, kai\ a)fh|rh/sqw a)po\ th=s mei/zonos th=s *a*e th=| e)la/ssoni th=| *a*z i)/sh h( *a*h, kai\ e)pezeu/xqwsan ai( *z*g, *h*b eu)qei=ai.

e)pei\ ou)=n i)/sh e)sti\n h( me\n *a*z th=| *a*h h( de\ *a*b th=| *a*g, du/o dh\ ai( *z*a, *a*g dusi\ tai=s *h*a, *a*b i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/an koinh\n perie/xousi th\n u(po\ *z*a*h: ba/sis a)/ra h( *z*g ba/sei th=| *h*b i)/sh e)sti/n, kai\ to\ *a*z*g tri/gwnon tw=| *a*h*b trigw/nw| i)/son e)/stai, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin, h( me\n u(po\ *a*g*z th=| u(po\ *a*b*h, h( de\ u(po\ *a*z*g th=| u(po\ *a*h*b. kai\ e)pei\ o(/lh h( *a*z o(/lh| th=| *a*h e)stin i)/sh, w(=n h( *a*b th=| *a*g e)stin i)/sh, loiph\ a)/ra h( *b*z loiph=| th=| *g*h e)stin i)/sh. e)dei/xqh de\ kai\ h( *z*g th=| *h*b i)/sh: du/o dh\ ai( *b*z, *z*g dusi\ tai=s *g*h, *h*b i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *b*z*g gwni/a| th=| u(po\ *g*h*b i)/sh, kai\ ba/sis au)tw=n koinh\ h( *b*g: kai\ to\ *b*z*g a)/ra tri/gwnon tw=| *g*h*b trigw/nw| i)/son e)/stai, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra e)sti\n h( me\n u(po\ *z*b*g th=| u(po\ *h*g*b h( de\ u(po\ *b*g*z th=| u(po\ *g*b*h. e)pei\ ou)=n o(/lh h( u(po\ *a*b*h gwni/a o(/lh| th=| u(po\ *a*g*z gwni/a| e)dei/xqh i)/sh, w(=n h( u(po\ *g*b*h th=| u(po\ *b*g*z i)/sh, loiph\ a)/ra h( u(po\ *a*b*g loiph=| th=| u(po\ *a*g*b e)stin i)/sh: kai/ ei)si pro\s th=| ba/sei tou= *a*b*g trigw/nou. e)dei/xqh de\ kai\ h( u(po\ *z*b*g th=| u(po\ *h*g*b i)/sh: kai/ ei)sin u(po\ th\n ba/sin.

tw=n a)/ra i)soskelw=n trigw/nwn ai( pro\s th=| ba/sei gwni/ai i)/sai a)llh/lais ei)si/n, kai\ prosekblhqeisw=n tw=n i)/swn eu)qeiw=n ai( u(po\ th\n ba/sin gwni/ai i)/sai a)llh/lais e)/sontai: o(/per e)/dei dei=cai.

e)a\n trigw/nou ai( du/o gwni/ai i)/sai a)llh/lais w)=sin, kai\ ai( u(po\ ta\s i)/sas gwni/ais u(potei/nousai pleurai\ i)/sai a)llh/lais e)/sontai.

e)/stw tri/gwnon to\ *a*b*g i)/shn e)/xon th\n u(po\ *a*b*g gwni/an th=| u(po\ *a*g*b gwni/a|: le/gw, o(/ti kai\ pleura\ h( *a*b pleura=| th=| *a*g e)stin i)/sh.

ei) ga\r a)/niso/s e)stin h( *a*b th=| *a*g, h( e(te/ra au)tw=n mei/zwn e)sti/n. e)/stw mei/zwn h( *a*b, kai\ a)fh|rh/sqw a)po\ th=s mei/zonos th=s *a*b th=| e)la/ttoni th=| *a*g i)/sh h( *d*b, kai\ e)pezeu/xqw h( *d*g.

e)pei\ ou)=n i)/sh e)sti\n h( *d*b th=| *a*g koinh\ de\ h( *b*g, du/o dh\ ai( *d*b, *b*g du/o tai=s *a*g, *g*b i)/sai ei)si\n e(kate/ra e(kate/ra|, kai\ gwni/a h( u(po\ *d*b*g gwni/a| th=| u(po\ *a*g*b e)stin i)/sh: ba/sis a)/ra h( *d*g ba/sei th=| *a*b i)/sh e)sti/n, kai\ to\ *d*b*g tri/gwnon tw=| *a*g*b trigw/nw| i)/son e)/stai, to\ e)/lasson tw=| mei/zoni: o(/per a)/topon: ou)k a)/ra a)/niso/s e)stin h( *a*b th=| *a*g: i)/sh a)/ra.

e)a\n a)/ra trigw/nou ai( du/o gwni/ai i)/sai a)llh/lais w)=sin, kai\ ai( u(po\ ta\s i)/sas gwni/as u(potei/nousai pleurai\ i)/sai a)llh/lais e)/sontai: o(/per e)/dei dei=cai.

e)pi\ th=s au)th=s eu)qei/as du/o tai=s au)tai=s eu)qei/ais a)/llai du/o eu)qei=ai i)/sai e(kate/ra e(kate/ra| ou) sustaqh/sontai pro\s a)/llw| kai\ a)/llw| shmei/w| e)pi\ ta\ au)ta\ me/rh ta\ au)ta\ pe/rata e)/xousai tai=s e)c a)rxh=s eu)qei/ais.

ta\ au)ta\ me/rh ta\ au)ta\ pe/rata e)/xousai, w(/ste i)/shn ei)=nai th\n me\n *g*a th=| *d*a to\ au)to\ pe/ras e)/xousan au)th=| to\ *a, th\n de\ *g*b th=| *d*b to\ au)to\ pe/ras e)/xousan au)th=| to\ *b, kai\ e)pezeu/xqw h( *g*d.

e)pei\ ou)=n i)/sh e)sti\n h( *a*g th=| *a*d, i)/sh e)sti\ kai\ gwni/a h( u(po\ *a*g*d th=| u(po\ *a*d*g: mei/zwn a)/ra h( u(po\ *a*d*g th=s u(po\ *d*g*b: pollw=| a)/ra h( u(po\ *g*d*b mei/zwn e)sti\ th=s u(po\ *d*g*b. pa/lin e)pei\ i)/sh e)sti\n h( *g*b th=| *d*b, i)/sh e)sti\ kai\ gwni/a h( u(po\ *g*d*b gwni/a| th=| u(po\ *d*g*b. e)dei/xqh de\ au)th=s kai\ pollw=| mei/zwn: o(/per e)sti\n a)du/naton.

ou)k a)/ra e)pi\ th=s au)th=s eu)qei/as du/o tai=s au)tai=s eu)qei/ais a)/llai du/o eu)qei=ai i)/sai e(kate/ra e(kate/ra| sustaqh/sontai pro\s a)/llw| kai\ a)/llw| shmei/w| e)pi\ ta\ au)ta\ me/rh ta\ au)ta\ pe/rata e)/xousai tai=s e)c a)rxh=s eu)qei/ais: o(/per e)/dei dei=cai.

e)/stw du/o tri/gwna ta\ *a*b*g, *d*e*z ta\s du/o pleura\s ta\s *a*b, *a*g tai=s du/o pleurai=s tai=s *d*e, *d*z i)/sas e)/xonta

*)efarmozome/nou ga\r tou= *a*b*g trigw/nou e)pi\ to\ *d*e*z tri/gwnon kai\ tiqeme/nou tou= me\n *b shmei/ou e)pi\ to\ *e shmei=on th=s de\ *b*g eu)qei/as e)pi\ th\n *e*z e)farmo/sei kai\ to\ *g shmei=on e)pi\ to\ *z dia\ to\ i)/shn ei)=nai th\n *b*g th=| *e*z: e)farmosa/shs dh\ th=s *b*g e)pi\ th\n *e*z e)farmo/sousi kai\ ai( *b*a, *g*a e)pi\ ta\s *e*d, *d*z. ei) ga\r ba/sis me\n h( *b*g e)pi\ ba/sin th\n *e*z e)farmo/sei, ai( de\ *b*a, *a*g pleurai\ e)pi\ ta\s *e*d, *d*z ou)k e)farmo/sousin a)lla\ paralla/cousin w(s ai( *e*h, *h*z, sustaqh/sontai e)pi\ th=s au)th=s eu)qei/as du/o tai=s au)tai=s eu)qei/ais a)/llai du/o eu)qei=ai i)/sai e(kate/ra e(kate/ra| pro\s a)/llw| kai\ a)/llw| shmei/w| e)pi\ ta\ au)ta\ me/rh ta\ au)ta\ pe/rata e)/xousai. ou) suni/stantai de/: ou)k a)/ra e)farmozome/nhs th=s *b*g ba/sews e)pi\ th\n *e*z ba/sin ou)k e)farmo/sousi kai\ ai( *b*a, *a*g pleurai\ e)pi\ ta\s *e*d, *d*z. e)farmo/sousin a)/ra: w(/ste kai\ gwni/a h( u(po\ *b*a*g e)pi\ gwni/an th\n u(po\ *e*d*z e)farmo/sei kai\ i)/sh au)th=| e)/stai.

th\n doqei=san gwni/an eu)qu/grammon di/xa temei=n.

e)/stw h( doqei=sa gwni/a eu)qu/grammos h( u(po\ *b*a*g. dei= dh\ au)th\n di/xa temei=n.

ei)lh/fqw e)pi\ th=s *a*b tuxo\n shmei=on to\ *d, kai\ a)fh|rh/sqw a)po\ th=s *a*g th=| *a*d i)/sh h( *a*e, kai\ e)pezeu/xqw h( *d*e, kai\ sunesta/tw e)pi\ th=s *d*e tri/gwnon i)so/pleuron to\ *d*e*z, kai\ e)pezeu/xqw h( *a*z: le/gw, o(/ti h( u(po\ *b*a*g gwni/a di/xa te/tmhtai u(po\ th=s *a*z eu)qei/as.

e)pei\ ga\r i)/sh e)sti\n h( *a*d th=| *a*e, koinh\ de\ h( *a*z, du/o dh\ ai( *d*a, *a*z dusi\ tai=s *e*a, *a*z

i)/sai ei)si\n e(kate/ra e(kate/ra|. kai\ ba/sis h( *d*z ba/sei th=| *e*z i)/sh e)sti/n: gwni/a a)/ra h( u(po\ *d*a*z gwni/a| th=| u(po\ *e*a*z i)/sh e)sti/n.

h( a)/ra doqei=sa gwni/a eu)qu/grammos h( u(po\ *b*a*g di/xa te/tmhtai u(po\ th=s *a*z eu)qei/as: o(/per e)/dei poih=sai.

th\n doqei=san eu)qei=an peperasme/nhn di/xa temei=n.

e)/stw h( doqei=sa eu)qei=a peperasme/nh h( *a*b: dei= dh\ th\n *a*b eu)qei=an peperasme/nhn di/xa temei=n.

sunesta/tw e)p' au)th=s tri/gwnon i)so/pleuron to\ *a*b*g, kai\ tetmh/sqw h( u(po\ *a*g*b gwni/a di/xa th=| *g*d eu)qei/a|: le/gw, o(/ti h( *a*b eu)qei=a di/xa te/tmhtai kata\ to\ *d shmei=on.

e)pei\ ga\r i)/sh e)sti\n h( *a*g th=| *g*b, koinh\ de\ h( *g*d, du/o dh\ ai( *a*g, *g*d du/o tai=s *b*g, *g*d i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *a*g*d gwni/a| th=| u(po\ *b*g*d i)/sh e)sti/n: ba/sis a)/ra h( *a*d ba/sei th=| *b*d i)/sh e)sti/n.

h( a)/ra doqei=sa eu)qei=a peperasme/nh h( *a*b di/xa te/tmhtai kata\ to\ *d: o(/per e)/dei poih=sai.

th=| doqei/sh| eu)qei/a| a)po\ tou= pro\s au)th=| doqe/ntos shmei/ou pro\s o)rqa\s gwni/as eu)qei=an grammh\n a)gagei=n.

e)/stw h( me\n doqei=sa eu)qei=a h( *a*b to\ de\ doqe\n shmei=on e)p' au)th=s to\ *g: dei= dh\ a)po\ tou= *g shmei/ou th=| *a*b eu)qei/a| pro\s o)rqa\s gwni/as eu)qei=an grammh\n a)gagei=n.

tou= pro\s au)th=| doqe/ntos shmei/ou tou= *g pro\s o)rqa\s gwni/as eu)qei=a grammh\ h)=ktai h( *z*g.

e)pei\ ga\r i)/sh e)sti\n h( *d*g th=| *g*e, koinh\ de\ h( *g*z, du/o dh\ ai( *d*g, *g*z dusi\ tai=s *e*g, *g*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ ba/sis h( *d*z ba/sei th=| *z*e i)/sh e)sti/n: gwni/a a)/ra h( u(po\ *d*g*z gwni/a| th=| u(po\ *e*g*z i)/sh e)sti/n: kai/ ei)sin e)fech=s. o(/tan de\ eu)qei=a e)p' eu)qei=an staqei=sa ta\s e)fech=s gwni/as i)/sas a)llh/lais poih=|, o)rqh\ e(kate/ra tw=n i)/swn gwniw=n e)stin: o)rqh\ a)/ra e)sti\n e(kate/ra tw=n u(po\ *d*g*z, *z*g*e.

e)pi\ th\n doqei=san eu)qei=an a)/peiron a)po\ tou= doqe/ntos shmei/ou, o(\ mh/ e)stin e)p' au)th=s, ka/qeton eu)qei=an grammh\n a)gagei=n.

e)/stw h( me\n doqei=sa eu)qei=a a)/peiros h( *a*b to\ de\ doqe\n shmei=on, o(\ mh/ e)stin e)p' au)th=s, to\ *g: dei= dh\ e)pi\ th\n doqei=san eu)qei=an a)/peiron th\n *a*b a)po\ tou= doqe/ntos shmei/ou tou= *g, o(\ mh/ e)stin e)p' au)th=s, ka/qeton eu)qei=an grammh\n a)gagei=n.

ei)lh/fqw ga\r e)pi\ ta\ e(/tera me/rh th=s *a*b eu)qei/as tuxo\n shmei=on to\ *d, kai\ ke/ntrw| me\n tw=| *g diasth/mati de\ tw=| *g*d ku/klos gegra/fqw o( *e*z*h, kai\ tetmh/sqw h( *e*h

eu)qei=a di/xa kata\ to\ *q, kai\ e)pezeu/xqwsan ai( *g*h, *g*q, *g*e eu)qei=ai: le/gw, o(/ti e)pi\ th\n doqei=san eu)qei=an a)/peiron th\n *a*b a)po\ tou= doqe/ntos shmei/ou tou= *g, o(\ mh/ e)stin e)p' au)th=s, ka/qetos h)=ktai h( *g*q.

e)pei\ ga\r i)/sh e)sti\n h( *h*q th=| *q*e, koinh\ de\ h( *q*g, du/o dh\ ai( *h*q, *q*g du/o tai=s *e*q, *q*g i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ ba/sis h( *g*h ba/sei th=| *g*e e)stin i)/sh: gwni/a a)/ra h( u(po\ *g*q*h gwni/a| th=| u(po\ *e*q*g e)stin i)/sh. kai/ ei)sin e)fech=s. o(/tan de\ eu)qei=a e)p' eu)qei=an staqei=sa ta\s e)fech=s gwni/as i)/sas a)llh/lais poih=|, o)rqh\ e(kate/ra tw=n i)/swn gwniw=n e)stin, kai\ h( e)festhkui=a eu)qei=a ka/qetos kalei=tai e)f' h(\n e)fe/sthken.

e)pi\ th\n doqei=san a)/ra eu)qei=an a)/peiron th\n *a*b a)po\ tou= doqe/ntos shmei/ou tou= *g, o(\ mh/ e)stin e)p' au)th=s, ka/qetos h)=ktai h( *g*q: o(/per e)/dei poih=sai.

e)a\n eu)qei=a e)p' eu)qei=an staqei=sa gwni/as poih=|, h)/toi du/o o)rqa\s h)\ dusi\n o)rqai=s i)/sas poih/sei.

eu)qei=a ga/r tis h( *a*b e)p' eu)qei=an th\n *g*d staqei=sa gwni/as poiei/tw ta\s u(po\ *g*b*a, *a*b*d: le/gw, o(/ti ai( u(po\ *g*b*a, *a*b*d gwni/ai h)/toi du/o o)rqai/

ei)sin h)\ dusi\n o)rqai=s i)/sai.

ei) me\n ou)=n i)/sh e)sti\n h( u(po\ *g*b*a th=| u(po\ *a*b*d, du/o o)rqai/ ei)sin. ei) de\ ou)/, h)/xqw a)po\ tou= *b shmei/ou th=| *g*d ~~eu)qei/a|~~ pro\s o)rqa\s h( *b*e: ai( a)/ra u(po\ *g*b*e, *e*b*d du/o o)rqai/ ei)sin: kai\ e)pei\ h( u(po\ *g*b*e dusi\ tai=s u(po\ *g*b*a, *a*b*e i)/sh e)sti/n, koinh\ proskei/sqw h( u(po\ *e*b*d: ai( a)/ra u(po\ *g*b*e, *e*b*d trisi\ tai=s u(po\ *g*b*a, *a*b*e, *e*b*d i)/sai ei)si/n. pa/lin, e)pei\ h( u(po\ *d*b*a dusi\ tai=s u(po\ *d*b*e, *e*b*a i)/sh e)sti/n, koinh\ proskei/sqw h( u(po\ *a*b*g: ai( a)/ra u(po\ *d*b*a, *a*b*g trisi\ tai=s u(po\ *d*b*e, *e*b*a, *a*b*g i)/sai ei)si/n. e)dei/xqhsan de\ kai\ ai( u(po\ *g*b*e, *e*b*d trisi\ tai=s au)tai=s i)/sai: ta\ de\ tw=| au)tw=| i)/sa kai\ a)llh/lois e)sti\n i)/sa: kai\ ai( u(po\ *g*b*e, *e*b*d a)/ra tai=s u(po\ *d*b*a, *a*b*g i)/sai ei)si/n: a)lla\ ai( u(po\ *g*b*e, *e*b*d du/o o)rqai/ ei)sin: kai\ ai( u(po\ *d*b*a, *a*b*g a)/ra dusi\n o)rqai=s i)/sai ei)si/n.

e)a\n a)/ra eu)qei=a e)p' eu)qei=an staqei=sa gwni/as poih=|, h)/toi du/o o)rqa\s h)\ dusi\n o)rqai=s i)/sas poih/sei: o(/per e)/dei dei=cai.

e)a\n pro/s tini eu)qei/a| kai\ tw=| pro\s au)th=| shmei/w| du/o eu)qei=ai mh\ e)pi\ ta\ au)ta\ me/rh kei/menai ta\s e)fech=s gwni/as dusi\n o)rqai=s i)/sas poiw=sin, e)p' eu)qei/as e)/sontai a)llh/lais ai( eu)qei=ai.

kei/menai ta\s e)fech=s gwni/as ta\s u(po\ *a*b*g, *a*b*d du/o o)rqai=s i)/sas poiei/twsan: le/gw, o(/ti e)p' eu)qei/as e)sti\ th=| *g*b h( *b*d.

ei) ga\r mh/ e)sti th=| *b*g e)p' eu)qei/as h( *b*d, e)/stw th=| *g*b e)p' eu)qei/as h( *b*e.

e)pei\ ou)=n eu)qei=a h( *a*b e)p' eu)qei=an th\n *g*b*e e)fe/sthken, ai( a)/ra u(po\ *a*b*g, *a*b*e gwni/ai du/o o)rqai=s i)/sai ei)si/n: ei)si\ de\ kai\ ai( u(po\ *a*b*g, *a*b*d du/o o)rqai=s i)/sai: ai( a)/ra u(po\ *g*b*a, *a*b*e tai=s u(po\ *g*b*a, *a*b*d i)/sai ei)si/n. koinh\ a)fh|rh/sqw h( u(po\ *g*b*a: loiph\ a)/ra h( u(po\ *a*b*e loiph=| th=| u(po\ *a*b*d e)stin i)/sh, h( e)la/sswn th=| mei/zoni: o(/per e)sti\n a)du/naton. ou)k a)/ra e)p' eu)qei/as e)sti\n h( *b*e th=| *g*b. o(moi/ws dh\ dei/comen, o(/ti ou)de\ a)/llh tis plh\n th=s *b*d: e)p' eu)qei/as a)/ra e)sti\n h( *g*b th=| *b*d.

e)a\n a)/ra pro/s tini eu)qei/a| kai\ tw=| pro\s au)th=| shmei/w| du/o eu)qei=ai mh\ e)pi\ ta\ au)ta\ me/rh kei/menai ta\s e)fech=s gwni/as dusi\n o)rqai=s i)/sas poiw=sin, e)p' eu)qei/as e)/sontai a)llh/lais ai( eu)qei=ai: o(/per e)/dei dei=cai.

e)a\n du/o eu)qei=ai te/mnwsin a)llh/las, ta\s kata\ korufh\n gwni/as i)/sas a)llh/lais poiou=sin.

du/o ga\r eu)qei=ai ai( *a*b, *g*d temne/twsan a)llh/las kata\ to\ *e shmei=on: le/gw, o(/ti i)/sh e)sti\n h( me\n u(po\ *a*e*g gwni/a th=| u(po\ *d*e*b, h( de\ u(po\ *g*e*b th=| u(po\ *a*e*d.

e)pei\ ga\r eu)qei=a h( *a*e e)p' eu)qei=an

th\n *g*d e)fe/sthke gwni/as poiou=sa ta\s u(po\ *g*e*a, *a*e*d, ai( a)/ra u(po\ *g*e*a, *a*e*d gwni/ai dusi\n o)rqai=s i)/sai ei)si/n. pa/lin, e)pei\ eu)qei=a h( *d*e e)p' eu)qei=an th\n *a*b e)fe/sthke gwni/as poiou=sa ta\s u(po\ *a*e*d, *d*e*b, ai( a)/ra u(po\ *a*e*d, *d*e*b gwni/ai dusi\n o)rqai=s i)/sai ei)si/n. e)dei/xqhsan de\ kai\ ai( u(po\ *g*e*a, *a*e*d dusi\n o)rqai=s i)/sai: ai( a)/ra u(po\ *g*e*a, *a*e*d tai=s u(po\ *a*e*d, *d*e*b i)/sai ei)si/n. koinh\ a)fh|rh/sqw h( u(po\ *a*e*d: loiph\ a)/ra h( u(po\ *g*e*a loiph=| th=| u(po\ *b*e*d i)/sh e)sti/n: o(moi/ws dh\ deixqh/setai, o(/ti kai\ ai( u(po\ *g*e*b, *d*e*a i)/sai ei)si/n.

e)a\n a)/ra du/o eu)qei=ai te/mnwsin a)llh/las, ta\s kata\ korufh\n gwni/as i)/sas a)llh/lais poiou=sin: o(/per e)/dei dei=cai.

*po/risma

~~e)k dh\ tou/tou fanero\n o(/ti, e)a\n du/o eu)qei=ai te/mnwsin a)llh/las, ta\s pro\s th=| tomh=| gwni/as te/trasin o)rqai=s i)/sas poih/sousin.~~

panto\s trigw/nou mia=s tw=n pleurw=n prosekblhqei/shs h( e)kto\s gwni/a e(kate/ras tw=n e)nto\s kai\ a)penanti/on gwniw=n mei/zwn e)sti/n.

e)/stw tri/gwnon to\ *a*b*g, kai\ prosekbeblh/sqw au)tou= mi/a pleura\ h( *b*g e)pi\ to\ *d: le/gw, o(/ti h( e)kto\s gwni/a h( u(po\ *a*g*d mei/zwn e)sti\n e(kate/ras tw=n

e)nto\s kai\ a)penanti/on tw=n u(po\ *g*b*a, *b*a*g gwniw=n.

tetmh/sqw h( *a*g di/xa kata\ to\ *e, kai\ e)pizeuxqei=sa h( *b*e e)kbeblh/sqw e)p' eu)qei/as e)pi\ to\ *z, kai\ kei/sqw th=| *b*e i)/sh h( *e*z, kai\ e)pezeu/xqw h( *z*g, kai\ dih/xqw h( *a*g e)pi\ to\ *h.

e)pei\ ou)=n i)/sh e)sti\n h( me\n *a*e th=| *e*g, h( de\ *b*e th=| *e*z, du/o dh\ ai( *a*e, *e*b dusi\ tai=s *g*e, *e*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *a*e*b gwni/a| th=| u(po\ *z*e*g i)/sh e)sti/n: kata\ korufh\n ga/r: ba/sis a)/ra h( *a*b ba/sei th=| *z*g i)/sh e)sti/n, kai\ to\ *a*b*e tri/gwnon tw=| *z*e*g trigw/nw| e)sti\n i)/son, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai ei)si\n e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra e)sti\n h( u(po\ *b*a*e th=| u(po\ *e*g*z. mei/zwn de/ e)stin h( u(po\ *e*g*d th=s u(po\ *e*g*z: mei/zwn a)/ra h( u(po\ *a*g*d th=s u(po\ *b*a*e. o(moi/ws dh\ th=s *b*g tetmhme/nhs di/xa deixqh/setai kai\ h( u(po\ *b*g*h, toute/stin h( u(po\ *a*g*d, mei/zwn kai\ th=s u(po\ *a*b*g.

panto\s a)/ra trigw/nou mia=s tw=n pleurw=n prosekblhqei/shs h( e)kto\s gwni/a e(kate/ras tw=n e)nto\s kai\ a)penanti/on gwniw=n mei/zwn e)sti/n: o(/per e)/dei dei=cai.

panto\s trigw/nou ai( du/o gwni/ai du/o o)rqw=n e)la/ssone/s ei)si pa/nth| metalambano/menai.

e)/stw tri/gwnon to\ *a*b*g: le/gw, o(/ti tou= *a*b*g trigw/nou

ai( du/o gwni/ai du/o o)rqw=n e)la/ttone/s ei)si pa/nth| metalambano/menai.

*)ekbeblh/sqw ga\r h( *b*g e)pi\ to\ *d.

kai\ e)pei\ trigw/nou tou= *a*b*g e)kto/s e)sti gwni/a h( u(po\ *a*g*d, mei/zwn e)sti\ th=s e)nto\s kai\ a)penanti/on th=s u(po\ *a*b*g. koinh\ proskei/sqw h( u(po\ *a*g*b: ai( a)/ra u(po\ *a*g*d, *a*g*b tw=n u(po\ *a*b*g, *b*g*a mei/zone/s ei)sin. a)ll' ai( u(po\ *a*g*d, *a*g*b du/o o)rqai=s i)/sai ei)si/n: ai( a)/ra u(po\ *a*b*g, *b*g*a du/o o)rqw=n e)la/ssone/s ei)sin. o(moi/ws dh\ dei/comen, o(/ti kai\ ai( u(po\ *b*a*g, *a*g*b du/o o)rqw=n e)la/ssone/s ei)si kai\ e)/ti ai( u(po\ *g*a*b, *a*b*g.

panto\s a)/ra trigw/nou ai( du/o gwni/ai du/o o)rqw=n e)la/ssone/s ei)si pa/nth| metalambano/menai: o(/per e)/dei dei=cai.

panto\s trigw/nou h( mei/zwn pleura\ th\n mei/zona gwni/an u(potei/nei.

e)/stw ga\r tri/gwnon to\ *a*b*g mei/zona e)/xon th\n *a*g pleura\n th=s *a*b: le/gw, o(/ti kai\ gwni/a h( u(po\ *a*b*g mei/zwn e)sti\ th=s u(po\ *b*g*a.

e)pei\ ga\r mei/zwn e)sti\n h( *a*g th=s *a*b, kei/sqw th=| *a*b i)/sh h( *a*d, kai\ e)pezeu/xqw h( *b*d.

kai\ e)pei\ trigw/nou tou= *b*g*d e)kto/s e)sti gwni/a h( u(po\ *a*d*b, mei/zwn e)sti\ th=s e)nto\s kai\

a)penanti/on th=s u(po\ *d*g*b: i)/sh de\ h( u(po\ *a*d*b th=| u(po\ *a*b*d, e)pei\ kai\ pleura\ h( *a*b th=| *a*d e)stin i)/sh: mei/zwn a)/ra kai\ h( u(po\ *a*b*d th=s u(po\ *a*g*b: pollw=| a)/ra h( u(po\ *a*b*g mei/zwn e)sti\ th=s u(po\ *a*g*b.

panto\s a)/ra trigw/nou h( mei/zwn pleura\ th\n mei/zona gwni/an u(potei/nei: o(/per e)/dei dei=cai.

panto\s trigw/nou u(po\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei.

e)/stw tri/gwnon to\ *a*b*g mei/zona e)/xon

th\n u(po\ *a*b*g gwni/an th=s u(po\ *b*g*a: le/gw, o(/ti kai\ pleura\ h( *a*g pleura=s th=s *a*b mei/zwn e)sti/n.

ei) ga\r mh/, h)/toi i)/sh e)sti\n h( *a*g th=| *a*b h)\ e)la/sswn: i)/sh me\n ou)=n ou)k e)/stin h( *a*g th=| *a*b: i)/sh ga\r a)\n h)=n kai\ gwni/a h( u(po\ *a*b*g th=| u(po\ *a*g*b: ou)k e)/sti de/: ou)k a)/ra i)/sh e)sti\n h( *a*g th=| *a*b. ou)de\ mh\n e)la/sswn e)sti\n h( *a*g th=s *a*b: e)la/sswn ga\r a)\n h)=n kai\ gwni/a h( u(po\ *a*b*g th=s u(po\ *a*g*b: ou)k e)/sti de/: ou)k a)/ra e)la/sswn e)sti\n h( *a*g th=s *a*b. e)dei/xqh de/, o(/ti ou)de\ i)/sh e)sti/n. mei/zwn a)/ra e)sti\n h( *a*g th=s *a*b.

panto\s a)/ra trigw/nou u(po\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei: o(/per e)/dei dei=cai.

panto\s trigw/nou ai( du/o pleurai\ th=s loiph=s mei/zone/s ei)si pa/nth| metalambano/menai.

e)/stw ga\r tri/gwnon to\ *a*b*g: le/gw, o(/ti tou= *a*b*g trigw/nou ai( du/o pleurai\ th=s loiph=s mei/zone/s ei)si pa/nth| metalambano/menai, ai( me\n *b*a, *a*g th=s *b*g, ai( de\ *a*b, *b*g th=s *a*g, ai( de\ *b*g, *g*a th=s *a*b.

dih/xqw ga\r h( *b*a e)pi\ to\ *d shmei=on, kai\ kei/sqw th=| *g*a i)/sh h( *a*d, kai\ e)pezeu/xqw h( *d*g.

e)pei\ ou)=n i)/sh e)sti\n h( *d*a th=| *a*g, i)/sh e)sti\ kai\ gwni/a h( u(po\ *a*d*g th=| u(po\ *a*g*d: mei/zwn a)/ra h( u(po\ *b*g*d th=s u(po\ *a*d*g: kai\ e)pei\ tri/gwno/n e)sti to\ *d*g*b mei/zona e)/xon th\n u(po\ *b*g*d gwni/an th=s u(po\ *b*d*g, u(po\ de\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei, h( *d*b a)/ra th=s *b*g e)sti mei/zwn. i)/sh de\ h( *d*a th=| *a*g: mei/zones a)/ra ai( *b*a, *a*g th=s *b*g: o(moi/ws dh\ dei/comen, o(/ti kai\ ai( me\n *a*b, *b*g th=s *g*a mei/zone/s ei)sin, ai( de\ *b*g, *g*a th=s *a*b.

panto\s a)/ra trigw/nou ai( du/o pleurai\ th=s loiph=s mei/zone/s ei)si pa/nth| metalambano/menai: o(/per e)/dei dei=cai.

e)a\n trigw/nou e)pi\ mia=s tw=n pleurw=n a)po\ tw=n pera/twn du/o eu)qei=ai e)nto\s sustaqw=sin, ai( sustaqei=sai tw=n loipw=n tou= trigw/nou du/o pleurw=n e)la/ttones me\n e)/sontai, mei/zona de\ gwni/an perie/cousin.

trigw/nou ga\r tou= *a*b*g e)pi\ mia=s tw=n pleurw=n th=s *b*g a)po\ tw=n pera/twn tw=n *b, *g du/o eu)qei=ai e)nto\s sunesta/twsan ai( *b*d, *d*g: le/gw, o(/ti ai( *b*d, *d*g tw=n loipw=n tou= trigw/nou du/o pleurw=n tw=n *b*a, *a*g e)la/ssones me/n ei)sin, mei/zona de\ gwni/an perie/xousi th\n u(po\ *b*d*g th=s u(po\ *b*a*g.

dih/xqw ga\r h( *b*d e)pi\ to\ *e. kai\ e)pei\ panto\s trigw/nou ai( du/o pleurai\ th=s loiph=s mei/zone/s ei)sin, tou= *a*b*e a)/ra trigw/nou ai( du/o pleurai\ ai( *a*b, *a*e th=s *b*e mei/zone/s ei)sin: koinh\ proskei/sqw h( *e*g: ai( a)/ra *b*a, *a*g tw=n *b*e, *e*g mei/zone/s ei)sin. pa/lin, e)pei\ tou= *g*e*d trigw/nou

ai( du/o pleurai\ ai( *g*e, *e*d th=s *g*d mei/zone/s ei)sin, koinh\ proskei/sqw h( *d*b: ai( *g*e, *e*b a)/ra tw=n *g*d, *d*b mei/zone/s ei)sin. a)lla\ tw=n *b*e, *e*g mei/zones e)dei/xqhsan ai( *b*a, *a*g: pollw=| a)/ra ai( *b*a, *a*g tw=n *b*d, *d*g mei/zone/s ei)sin.

pa/lin, e)pei\ panto\s trigw/nou h( e)kto\s gwni/a th=s e)nto\s kai\ a)penanti/on mei/zwn e)sti/n, tou= *g*d*e a)/ra trigw/nou h( e)kto\s gwni/a h( u(po\ *b*d*g mei/zwn e)sti\ th=s u(po\ *g*e*d. dia\ tau)ta\ toi/nun kai\ tou= *a*b*e trigw/nou h( e)kto\s gwni/a h( u(po\ *g*e*b mei/zwn e)sti\ th=s u(po\ *b*a*g. a)lla\ th=s u(po\ *g*e*b mei/zwn e)dei/xqh h( u(po\ *b*d*g: pollw=| a)/ra h( u(po\ *b*d*g mei/zwn e)sti\ th=s u(po\ *b*a*g.

e)a\n a)/ra trigw/nou e)pi\ mia=s tw=n pleurw=n a)po\ tw=n pera/twn du/o eu)qei=ai e)nto\s sustaqw=sin, ai( sustaqei=sai tw=n loipw=n tou= trigw/nou du/o pleurw=n e)la/ttones me/n ei)sin, mei/zona de\ gwni/an perie/xousin: o(/per e)/dei dei=cai.

e)k triw=n eu)qeiw=n, ai(/ ei)sin i)/sai trisi\ tai=s doqei/sais ~~eu)qei/ais~~, tri/gwnon susth/sasqai: dei= de\ ta\s du/o th=s loiph=s mei/zonas ei)=nai pa/nth| metalambanome/nas ~~dia\ to\ kai\ panto\s trigw/nou ta\s du/o pleura\s th=s loiph=s mei/zonas ei)=nai pa/nth| metalambanome/nas~~.

e)/stwsan ai( doqei=sai trei=s eu)qei=ai ai( *a, *b, *g, w(=n ai( du/o th=s loiph=s mei/zones e)/stwsan pa/nth| metalambano/menai, ai( me\n *a, *b th=s *g, ai( de\ *a, *g th=s *b, kai\ e)/ti ai( *b, *g th=s *a: dei= dh\ e)k tw=n i)/swn tai=s *a, *b, *g tri/gwnon susth/sasqai.

*)ekkei/sqw tis eu)qei=a h( *d*e peperasme/nh me\n kata\ to\ *d a)/peiros de\ kata\ to\ *e, kai\ kei/sqw th=| me\n *a i)/sh h( *d*z, th=| de\ *b i)/sh h( *z*h, th=| de\ *g i)/sh h( *h*q: kai\ ke/ntrw| me\n tw=| *z, diasth/mati de\ tw=| *z*d ku/klos gegra/fqw o( *d*k*l: pa/lin ke/ntrw| me\n tw=| *h, diasth/mati de\ tw=| *h*q ku/klos gegra/fqw o( *k*l*q, kai\ e)pezeu/xqwsan ai( *k*z, *k*h: le/gw, o(/ti e)k triw=n eu)qeiw=n tw=n i)/swn tai=s *a, *b, *g tri/gwnon sune/statai to\ *k*z*h.

e)pei\ ga\r to\ *z shmei=on ke/ntron e)sti\ tou= *d*k*l ku/klou, i)/sh e)sti\n h( *z*d th=| *z*k: a)lla\ h( *z*d th=| *a e)stin i)/sh. kai\ h( *k*z a)/ra th=| *a e)stin i)/sh. pa/lin, e)pei\ to\ *h shmei=on ke/ntron e)sti\ tou= *l*k*q ku/klou, i)/sh e)sti\n h( *h*q th=| *h*k: a)lla\ h( *h*q th=| *g e)stin i)/sh: kai\ h( *k*h a)/ra th=| *g e)stin i)/sh. e)sti\ de\ kai\ h( *z*h th=| *b i)/sh: ai( trei=s a)/ra eu)qei=ai ai( *k*z, *z*h, *h*k trisi\ tai=s *a, *b, *g i)/sai ei)si/n.

e)k triw=n a)/ra eu)qeiw=n tw=n *k*z, *z*h, *h*k, ai(/ ei)sin i)/sai trisi\ tai=s doqei/sais eu)qei/ais tai=s *a, *b, *g, tri/gwnon sune/statai to\ *k*z*h: o(/per e)/dei poih=sai.

e)/stw h( me\n doqei=sa eu)qei=a h( *a*b, to\ de\ pro\s au)th=| shmei=on to\ *a, h( de\ doqei=sa gwni/a eu)qu/grammos h( u(po\

ei)lh/fqw e)f' e(kate/ras tw=n *g*d, *g*e tuxo/nta shmei=a ta\ *d, *e, kai\ e)pezeu/xqw h( *d*e: kai\ e)k triw=n eu)qeiw=n, ai(/ ei)sin i)/sai trisi\ tai=s *g*d, *d*e, *g*e, tri/gwnon sunesta/tw to\ *a*z*h, w(/ste i)/shn ei)=nai th\n me\n *g*d th=| *a*z, th\n de\ *g*e th=| *a*h, kai\ e)/ti th\n *d*e th=| *z*h.

e)pei\ ou)=n du/o ai( *d*g, *g*e du/o tai=s *z*a, *a*h i)/sai ei)si\n e(kate/ra e(kate/ra|, kai\ ba/sis h( *d*e ba/sei th=| *z*h i)/sh, gwni/a a)/ra h( u(po\ *d*g*e gwni/a| th=| u(po\ *z*a*h e)stin i)/sh.

e)a\n du/o tri/gwna ta\s du/o pleura\s ~~tai=s~~ du/o pleurai=s i)/sas e)/xh| e(kate/ran e(kate/ra|, th\n de\ gwni/an th=s gwni/as mei/zona e)/xh| th\n u(po\ tw=n i)/swn eu)qeiw=n periexome/nhn, kai\ th\n ba/sin th=s ba/sews mei/zona e(/cei.

e)/stw du/o tri/gwna ta\ *a*b*g, *d*e*z ta\s du/o pleura\s ta\s *a*b, *a*g tai=s du/o pleurai=s tai=s *d*e, *d*z i)/sas e)/xonta e(kate/ran e(kate/ra|, th\n me\n *a*b th=| *d*e th\n de\ *a*g th=| *d*z, h( de\ pro\s tw=| *a gwni/a th=s pro\s tw=| *d gwni/as mei/zwn e)/stw: le/gw, o(/ti kai\ ba/sis h( *b*g ba/sews th=s *e*z mei/zwn e)sti/n.

e)pei\ ou)=n i)/sh e)sti\n h( me\n *a*b th=| *d*e, h( de\ *a*g th=| *d*h, du/o dh\ ai( *b*a, *a*g dusi\ tai=s *e*d, *d*h i)/sai ei)si\n e(kate/ra

e(kate/ra|: kai\ gwni/a h( u(po\ *b*a*g gwni/a| th=| u(po\ *e*d*h i)/sh: ba/sis a)/ra h( *b*g ba/sei th=| *e*h e)stin i)/sh. pa/lin, e)pei\ i)/sh e)sti\n h( *d*z th=| *d*h, i)/sh e)sti\ kai\ h( u(po\ *d*h*z gwni/a th=| u(po\ *d*z*h: mei/zwn a)/ra h( u(po\ *d*z*h th=s u(po\ *e*h*z: pollw=| a)/ra mei/zwn e)sti\n h( u(po\ *e*z*h th=s u(po\ *e*h*z. kai\ e)pei\ tri/gwno/n e)sti to\ *e*z*h mei/zona e)/xon th\n u(po\ *e*z*h gwni/an th=s u(po\ *e*h*z, u(po\ de\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei, mei/zwn a)/ra kai\ pleura\ h( *e*h th=s *e*z. i)/sh de\ h( *e*h th=| *b*g: mei/zwn a)/ra kai\ h( *b*g th=s *e*z.

e)a\n a)/ra du/o tri/gwna ta\s du/o pleura\s dusi\ pleurai=s i)/sas e)/xh| e(kate/ran e(kate/ra|, th\n de\ gwni/an th=s gwni/as mei/zona e)/xh| th\n u(po\ tw=n i)/swn eu)qeiw=n periexome/nhn, kai\ th\n ba/sin th=s ba/sews mei/zona e(/cei: o(/per e)/dei dei=cai.

e)a\n du/o tri/gwna ta\s du/o pleura\s dusi\ pleurai=s i)/sas e)/xh| e(kate/ran e(kate/ra|, th\n de\ ba/sin th=s ba/sews mei/zona e)/xh|, kai\ th\n gwni/an th=s gwni/as mei/zona e(/cei th\n u(po\ tw=n i)/swn eu)qeiw=n periexome/nhn.

e)/stw du/o tri/gwna ta\ *a*b*g, *d*e*z ta\s du/o pleura\s ta\s *a*b, *a*g tai=s du/o pleurai=s tai=s *d*e, *d*z i)/sas e)/xonta e(kate/ran e(kate/ra|, th\n me\n *a*b th=|

*d*e, th\n de\ *a*g th=| *d*z: ba/sis de\ h( *b*g ba/sews th=s *e*z mei/zwn e)/stw: le/gw, o(/ti kai\ gwni/a h( u(po\ *b*a*g gwni/as th=s u(po\ *e*d*z mei/zwn e)sti/n:

ei) ga\r mh/, h)/toi i)/sh e)sti\n au)th=| h)\ e)la/sswn: i)/sh me\n ou)=n ou)k e)/stin h( u(po\ *b*a*g th=| u(po\ *e*d*z: i)/sh ga\r a)\n h)=n kai\ ba/sis h( *b*g ba/sei th=| *e*z: ou)k e)/sti de/. ou)k a)/ra i)/sh e)sti\ gwni/a h( u(po\ *b*a*g th=| u(po\ *e*d*z: ou)de\ mh\n e)la/sswn e)sti\n h( u(po\ *b*a*g th=s u(po\ *e*d*z: e)la/sswn ga\r a)\n h)=n kai\ ba/sis h( *b*g ba/sews th=s *e*z: ou)k e)/sti de/: ou)k a)/ra e)la/sswn e)sti\n h( u(po\ *b*a*g gwni/a th=s u(po\ *e*d*z. e)dei/xqh de\ o(/ti ou)de\ i)/sh: mei/zwn a)/ra e)sti\n h( u(po\ *b*a*g th=s u(po\ *e*d*z.

e)a\n a)/ra du/o tri/gwna ta\s du/o pleura\s dusi\ pleurai=s i)/sas e)/xh| e(kate/ran e(ka/tera|, th\n de\ ba/sin th=s ba/sews mei/zona e)/xh|, kai\ th\n gwni/an th=s gwni/as mei/zona e(/cei th\n u(po\ tw=n i)/swn eu)qeiw=n periexome/nhn: o(/per e)/dei dei=cai.

e)/stw du/o tri/gwna ta\ *a*b*g, *d*e*z ta\s du/o gwni/as ta\s u(po\ *a*b*g, *b*g*a dusi\ tai=s u(po\ *d*e*z, *e*z*d i)/sas e)/xonta

ei) ga\r a)/niso/s e)stin h( *a*b th=| *d*e, mi/a au)tw=n mei/zwn e)sti/n. e)/stw mei/zwn h( *a*b, kai\ kei/sqw th=| *d*e i)/sh h( *b*h, kai\ e)pezeu/xqw h( *h*g.

e)pei\ ou)=n i)/sh e)sti\n h( me\n *b*h th=| *d*e, h( de\ *b*g th=| *e*z, du/o dh\ ai( *b*h, *b*g dusi\ tai=s *d*e, *e*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *h*b*g gwni/a| th=| u(po\ *d*e*z i)/sh e)sti/n: ba/sis a)/ra h( *h*g ba/sei th=| *d*z i)/sh e)sti/n, kai\ to\ *h*b*g tri/gwnon tw=| *d*e*z trigw/nw| i)/son e)sti/n, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra h( u(po\ *h*g*b gwni/a th=| u(po\ *d*z*e. a)lla\ h( u(po\ *d*z*e th=| u(po\ *b*g*a u(po/keitai i)/sh: kai\ h( u(po\ *b*g*h a)/ra th=| u(po\ *b*g*a i)/sh e)sti/n, h( e)la/sswn th=| mei/zoni: o(/per a)du/naton. ou)k a)/ra a)/niso/s e)stin h( *a*b th=| *d*e. i)/sh a)/ra. e)/sti de\ kai\ h( *b*g th=| *e*z i)/sh: du/o dh\ ai( *a*b, *b*g dusi\ tai=s *d*e, *e*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *a*b*g gwni/a| th=| u(po\ *d*e*z e)stin i)/sh: ba/sis a)/ra h( *a*g ba/sei th=| *d*z i)/sh e)sti/n, kai\ loiph\ gwni/a h( u(po\ *b*a*g th=| loiph=| gwni/a| th=| u(po\ *e*d*z i)/sh e)sti/n.

a)lla\ dh\ pa/lin e)/stwsan ai( u(po\ ta\s i)/sas gwni/as pleurai\ u(potei/nousai i)/sai, w(s h( *a*b th=| *d*e: le/gw pa/lin, o(/ti kai\ ai( loipai\ pleurai\ tai=s loipai=s pleurai=s i)/sai e)/sontai, h( me\n *a*g th=| *d*z, h( de\ *b*g th=| *e*z kai\ e)/ti h( loiph\ gwni/a h( u(po\ *b*a*g th=| loiph=| gwni/a| th=| u(po\ *e*d*z i)/sh e)sti/n.

ei) ga\r a)/niso/s e)stin h( *b*g th=| *e*z, mi/a au)tw=n mei/zwn e)sti/n. e)/stw mei/zwn, ei) dunato/n, h( *b*g, kai\ kei/sqw th=| *e*z i)/sh h( *b*q, kai\ e)pezeu/xqw h( *a*q. kai\ e)pei\ i)/sh e)sti\n h( me\n *b*q th=| *e*z h( de\ *a*b th=| *d*e, du/o dh\ ai( *a*b, *b*q dusi\ tai=s *d*e, *e*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/as i)/sas perie/xousin: ba/sis a)/ra h( *a*q ba/sei th=| *d*z i)/sh e)sti/n, kai\ to\ *a*b*q tri/gwnon tw=| *d*e*z trigw/nw| i)/son e)sti/n, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra e)sti\n h( u(po\ *b*q*a gwni/a th=| u(po\ *e*z*d. a)lla\ h( u(po\ *e*z*d th=| u(po\ *b*g*a e)stin i)/sh: trigw/nou dh\ tou= *a*q*g h( e)kto\s gwni/a h( u(po\ *b*q*a i)/sh e)sti\ th=| e)nto\s kai\ a)penanti/on th=| u(po\ *b*g*a: o(/per a)du/naton. ou)k a)/ra a)/niso/s e)stin h( *b*g th=| *e*z: i)/sh a)/ra. e)sti\ de\ kai\ h( *a*b th=| *d*e i)/sh. du/o dh\ ai( *a*b, *b*g du/o tai=s *d*e, *e*z i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/as i)/sas perie/xousi: ba/sis a)/ra h( *a*g ba/sei th=| *d*z i)/sh e)sti/n, kai\ to\ *a*b*g tri/gwnon tw=| *d*e*z trigw/nw| i)/son kai\ loiph\ gwni/a h( u(po\ *b*a*g th=| loiph=| gwni/a| th=| u(po\ *e*d*z i)/sh.

e)a\n a)/ra du/o tri/gwna ta\s du/o gwni/as dusi\ gwni/ais i)/sas e)/xh| e(kate/ran e(kate/ra| kai\ mi/an pleura\n mia=| pleura=| i)/shn h)/toi th\n pro\s tai=s i)/sais gwni/ais, h)\ th\n u(potei/nousan u(po\ mi/an tw=n i)/swn gwniw=n, kai\ ta\s loipa\s pleura\s tai=s loipai=s pleurai=s i)/sas e(/cei kai\ th\n loiph\n gwni/an th=| loiph=| gwni/a|: o(/per e)/dei dei=cai.

e)a\n ei)s du/o eu)qei/as eu)qei=a e)mpi/ptousa ta\s e)nalla\c gwni/as i)/sas a)llh/lais poih=|, para/llhloi e)/sontai a)llh/lais ai( eu)qei=ai.

ei)s ga\r du/o eu)qei/as ta\s *a*b, *g*d eu)qei=a e)mpi/ptousa h( *e*z ta\s e)nalla\c gwni/as ta\s u(po\ *a*e*z, *e*z*d i)/sas a)llh/lais poiei/tw: le/gw, o(/ti para/llhlo/s e)stin h( *a*b th=| *g*d.

ei) ga\r mh/, e)kballo/menai ai( *a*b, *g*d sumpesou=ntai h)/toi e)pi\ ta\ *b, *d me/rh h)\ e)pi\ ta\ *a, *g. e)kbeblh/sqwsan kai\

sumpipte/twsan e)pi\ ta\ *b, *d me/rh kata\ to\ *h. trigw/nou dh\ tou= *h*e*z h( e)kto\s gwni/a h( u(po\ *a*e*z i)/sh e)sti\ th=| e)nto\s kai\ a)penanti/on th=| u(po\ *e*z*h: o(/per e)sti\n a)du/naton: ou)k a)/ra ai( *a*b, *g*d e)kballo/menai sumpesou=ntai e)pi\ ta\ *b, *d me/rh. o(moi/ws dh\ deixqh/setai, o(/ti ou)de\ e)pi\ ta\ *a, *g: ai( de\ e)pi\ mhde/tera ta\ me/rh sumpi/ptousai para/llhloi/ ei)sin: para/llhlos a)/ra e)sti\n h( *a*b th=| *g*d.

e)a\n a)/ra ei)s du/o eu)qei/as eu)qei=a e)mpi/ptousa ta\s e)nalla\c gwni/as i)/sas a)llh/lais poih=|, para/llhloi e)/sontai ai( eu)qei=ai: o(/per e)/dei dei=cai.

e)a\n ei)s du/o eu)qei/as eu)qei=a e)mpi/ptousa th\n e)kto\s gwni/an th=| e)nto\s kai\ a)penanti/on kai\ e)pi\ ta\ au)ta\ me/rh i)/shn poih=| h)\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh dusi\n o)rqai=s i)/sas, para/llhloi e)/sontai a)llh/lais ai( eu)qei=ai.

ei)s ga\r du/o eu)qei/as ta\s *a*b, *g*d eu)qei=a e)mpi/ptousa h( *e*z th\n e)kto\s gwni/an th\n u(po\ *e*h*b th=| e)nto\s kai\ a)penanti/on gwni/a| th=| u(po\ *h*q*d i)/shn poiei/tw h)\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh ta\s u(po\ *b*h*q, *h*q*d dusi\n o)rqai=s i)/sas: le/gw, o(/ti para/llhlo/s e)stin h( *a*b th=| *g*d.

e)pei\ ga\r i)/sh e)sti\n h( u(po\ *e*h*b th=| u(po\ *h*q*d, a)lla\ h( u(po\ *e*h*b th=| u(po\ *a*h*q e)stin i)/sh, kai\ h( u(po\ *a*h*q a)/ra th=| u(po\ *h*q*d e)stin i)/sh: kai/ ei)sin e)nalla/c: para/llhlos a)/ra e)sti\n h( *a*b th=| *g*d.

pa/lin, e)pei\ ai( u(po\ *b*h*q, *h*q*d du/o o)rqai=s i)/sai ei)si/n,

ei)si\ de\ kai\ ai( u(po\ *a*h*q, *b*h*q dusi\n o)rqai=s i)/sai, ai( a)/ra u(po\ *a*h*q, *b*h*q tai=s u(po\ *b*h*q, *h*q*d i)/sai ei)si/n: koinh\ a)fh|rh/sqw h( u(po\ *b*h*q: loiph\ a)/ra h( u(po\ *a*h*q loiph=| th=| u(po\ *h*q*d e)stin i)/sh: kai/ ei)sin e)nalla/c: para/llhlos a)/ra e)sti\n h( *a*b th=| *g*d.

e)a\n a)/ra ei)s du/o eu)qei/as eu)qei=a e)mpi/ptousa th\n e)kto\s gwni/an th=| e)nto\s kai\ a)penanti/on kai\ e)pi\ ta\ au)ta\ me/rh i)/shn poih=| h)\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh dusi\n o)rqai=s i)/sas, para/llhloi e)/sontai ai( eu)qei=ai: o(/per e)/dei dei=cai.

h( ei)s ta\s parallh/lous eu)qei/as eu)qei=a e)mpi/ptousa ta/s te e)nalla\c gwni/as i)/sas a)llh/lais poiei= kai\ th\n e)kto\s th=| e)nto\s kai\ a)penanti/on i)/shn kai\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh dusi\n o)rqai=s i)/sas.

ei)s ga\r parallh/lous eu)qei/as ta\s *a*b, *g*d eu)qei=a e)mpipte/tw h( *e*z: le/gw, o(/ti ta\s e)nalla\c gwni/as ta\s u(po\ *a*h*q, *h*q*d i)/sas poiei= kai\ th\n e)kto\s gwni/an th\n u(po\ *e*h*b th=| e)nto\s kai\ a)penanti/on th=| u(po\ *h*q*d i)/shn kai\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh ta\s u(po\

*b*h*q, *h*q*d dusi\n o)rqai=s i)/sas.

ei) ga\r a)/niso/s e)stin h( u(po\ *a*h*q th=| u(po\ *h*q*d, mi/a au)tw=n mei/zwn e)sti/n. e)/stw mei/zwn h( u(po\ *a*h*q: koinh\ proskei/sqw h( u(po\ *b*h*q: ai( a)/ra u(po\ *a*h*q, *b*h*q tw=n u(po\ *b*h*q, *h*q*d mei/zone/s ei)sin. a)lla\ ai( u(po\ *a*h*q, *b*h*q dusi\n o)rqai=s i)/sai ei)si/n. ~~kai\~~ ai( a)/ra u(po\ *b*h*q, *h*q*d du/o o)rqw=n e)la/ssone/s ei)sin. ai( de\ a)p' e)lasso/nwn h)\ du/o o)rqw=n e)kballo/menai ei)s a)/peiron sumpi/ptousin: ai( a)/ra *a*b, *g*d e)kballo/menai ei)s a)/peiron sumpesou=ntai: ou) sumpi/ptousi de\ dia\ to\ parallh/lous au)ta\s u(pokei=sqai: ou)k a)/ra a)/niso/s e)stin h( u(po\ *a*h*q th=| u(po\ *h*q*d: i)/sh a)/ra. a)lla\ h( u(po\ *a*h*q th=| u(po\ *e*h*b e)stin i)/sh: kai\ h( u(po\ *e*h*b a)/ra th=| u(po\ *h*q*d e)stin i)/sh. koinh\ proskei/sqw h( u(po\ *b*h*q: ai( a)/ra u(po\ *e*h*b, *b*h*q tai=s u(po\ *b*h*q, *h*q*d i)/sai ei)si/n. a)lla\ ai( u(po\ *e*h*b, *b*h*q du/o o)rqai=s i)/sai ei)si/n: kai\ ai( u(po\ *b*h*q, *h*q*d a)/ra du/o o)rqai=s i)/sai ei)si/n.

h( a)/ra ei)s ta\s parallh/lous eu)qei/as eu)qei=a e)mpi/ptousa ta/s te e)nalla\c gwni/as i)/sas a)llh/lais poiei= kai\ th\n e)kto\s th=| e)nto\s kai\ a)penanti/on i)/shn kai\ ta\s e)nto\s kai\ e)pi\ ta\ au)ta\ me/rh dusi\n o)rqai=s i)/sas: o(/per e)/dei dei=cai.

ai( th=| au)th=| eu)qei/a| para/llhloi kai\ a)llh/lais ei)si\ para/llhloi.

e)/stw e(kate/ra tw=n *a*b, *g*d th=| *e*z para/llhlos: le/gw, o(/ti kai\ h( *a*b th=| *g*d e)sti para/llhlos.

e)mpipte/tw ga\r ei)s au)ta\s eu)qei=a h( *h*k.

kai\ e)pei\ ei)s parallh/lous eu)qei/as ta\s *a*b, *e*z eu)qei=a e)mpe/ptwken h( *h*k, i)/sh a)/ra h( u(po\ *a*h*k th=| u(po\ *h*q*z. pa/lin, e)pei\ ei)s parallh/lous eu)qei/as ta\s *e*z, *g*d eu)qei=a e)mpe/ptwken h( *h*k, i)/sh e)sti\n h( u(po\ *h*q*z th=| u(po\ *h*k*d. e)dei/xqh de\ kai\ h( u(po\ *a*h*k th=| u(po\ *h*q*z i)/sh. kai\ h( u(po\ *a*h*k a)/ra th=| u(po\ *h*k*d e)stin i)/sh:

kai/ ei)sin e)nalla/c. para/llhlos a)/ra e)sti\n h( *a*b th=| *g*d.

*ai( a)/ra th=| au)th=| eu)qei/a| para/llhloi kai\ a)llh/lais ei)si\ para/llhloi: o(/per e)/dei dei=cai.

dia\ tou= doqe/ntos shmei/ou th=| doqei/sh| eu)qei/a| para/llhlon eu)qei=an grammh\n a)gagei=n.

e)/stw to\ me\n doqe\n shmei=on to\ *a, h( de\ doqei=sa eu)qei=a h( *b*g: dei= dh\ dia\ tou= *a shmei/ou th=|

*b*g eu)qei/a| para/llhlon eu)qei=an grammh\n a)gagei=n.

kai\ e)pei\ ei)s du/o eu)qei/as ta\s *b*g, *e*z eu)qei=a e)mpi/ptousa h( *a*d ta\s e)nalla\c gwni/as ta\s u(po\ *e*a*d, *a*d*g i)/sas a)llh/lais pepoi/hken, para/llhlos a)/ra e)sti\n h( *e*a*z th=| *b*g.

dia\ tou= doqe/ntos a)/ra shmei/ou tou= *a th=| doqei/sh| eu)qei/a| th=| *b*g para/llhlos eu)qei=a grammh\ h)=ktai h( *e*a*z: o(/per e)/dei poih=sai.

panto\s trigw/nou mia=s tw=n pleurw=n prosekblhqei/shs h( e)kto\s gwni/a dusi\ tai=s e)nto\s kai\ a)penanti/on i)/sh e)sti/n, kai\ ai( e)nto\s tou= trigw/nou trei=s gwni/ai dusi\n o)rqai=s i)/sai ei)si/n.

e)/stw tri/gwnon to\ *a*b*g, kai\ prosekbeblh/sqw au)tou= mi/a pleura\ h( *b*g e)pi\ to\ *d: le/gw, o(/ti h( e)kto\s gwni/a h(

u(po\ *a*g*d i)/sh e)sti\ dusi\ tai=s e)nto\s kai\ a)penanti/on tai=s u(po\ *g*a*b, *a*b*g, kai\ ai( e)nto\s tou= trigw/nou trei=s gwni/ai ai( u(po\ *a*b*g, *b*g*a, *g*a*b dusi\n o)rqai=s i)/sai ei)si/n.

h)/xqw ga\r dia\ tou= *g shmei/ou th=| *a*b eu)qei/a| para/llhlos h( *g*e.

kai\ e)pei\ para/llhlo/s e)stin h( *a*b th=| *g*e, kai\ ei)s au)ta\s e)mpe/ptwken h( *a*g, ai( e)nalla\c gwni/ai ai( u(po\ *b*a*g, *a*g*e i)/sai a)llh/lais ei)si/n. pa/lin, e)pei\ para/llhlo/s e)stin h( *a*b th=| *g*e, kai\ ei)s au)ta\s e)mpe/ptwken eu)qei=a h( *b*d, h( e)kto\s gwni/a h( u(po\ *e*g*d i)/sh e)sti\ th=| e)nto\s kai\ a)penanti/on th=| u(po\ *a*b*g. e)dei/xqh de\ kai\ h( u(po\ *a*g*e th=| u(po\ *b*a*g i)/sh: o(/lh a)/ra h( u(po\ *a*g*d gwni/a i)/sh e)sti\ dusi\ tai=s e)nto\s kai\ a)penanti/on tai=s u(po\ *b*a*g, *a*b*g.

koinh\ proskei/sqw h( u(po\ *a*g*b: ai( a)/ra u(po\ *a*g*d, *a*g*b trisi\ tai=s u(po\ *a*b*g, *b*g*a, *g*a*b i)/sai ei)si/n. a)ll' ai( u(po\ *a*g*d, *a*g*b dusi\n o)rqai=s i)/sai ei)si/n: kai\ ai( u(po\ *a*g*b, *g*b*a, *g*a*b a)/ra dusi/n o)rqai=s i)/sai ei)si/n.

panto\s a)/ra trigw/nou mia=s tw=n pleurw=n prosekblhqei/shs h( e)kto\s gwni/a dusi\ tai=s e)nto\s kai\ a)penanti/on i)/sh e)sti/n, kai\ ai( e)nto\s tou= trigw/nou trei=s gwni/ai dusi\n o)rqai=s i)/sai ei)si/n: o(/per e)/dei dei=cai.

ai( ta\s i)/sas te kai\ parallh/lous e)pi\ ta\ au)ta\ me/rh e)pizeugnu/ousai eu)qei=ai kai\ au)tai\ i)/sai te kai\ para/llhloi/ ei)sin.

e)/stwsan i)/sai te kai\ para/llhloi

ai( *a*b, *g*d, kai\ e)pizeugnu/twsan au)ta\s e)pi\ ta\ au)ta\ me/rh eu)qei=ai ai( *a*g, *b*d: le/gw, o(/ti kai\ ai( *a*g, *b*d i)/sai te kai\ para/llhloi/ ei)sin.

e)pezeu/xqw h( *b*g. kai\ e)pei\ para/llhlo/s e)stin h( *a*b th=| *g*d, kai\ ei)s au)ta\s e)mpe/ptwken h( *b*g, ai( e)nalla\c gwni/ai ai( u(po\ *a*b*g, *b*g*d i)/sai a)llh/lais ei)si/n. kai\ e)pei\ i)/sh e)sti\n h( *a*b th=| *g*d koinh\ de\ h( *b*g, du/o dh\ ai( *a*b, *b*g du/o tai=s *b*g, *g*d i)/sai ei)si/n: kai\ gwni/a h( u(po\ *a*b*g gwni/a| th=| u(po\ *b*g*d i)/sh: ba/sis a)/ra h( *a*g ba/sei th=| *b*d e)stin i)/sh, kai\ to\ *a*b*g tri/gwnon tw=| *b*g*d trigw/nw| i)/son e)sti/n, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai e(kate/ra e(kate/ra|, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra h( u(po\ *a*g*b gwni/a th=| u(po\ *g*b*d. kai\ e)pei\ ei)s du/o eu)qei/as ta\s *a*g, *b*d eu)qei=a e)mpi/ptousa h( *b*g ta\s e)nalla\c gwni/as i)/sas a)llh/lais pepoi/hken, para/llhlos a)/ra e)sti\n h( *a*g th=| *b*d. e)dei/xqh de\ au)th=| kai\ i)/sh.

ai( a)/ra ta\s i)/sas te kai\ parallh/lous e)pi\ ta\ au)ta\ me/rh e)pizeugnu/ousai eu)qei=ai kai\ au)tai\ i)/sai te kai\ para/llhloi/ ei)sin: o(/per e)/dei dei=cai.

tw=n parallhlogra/mmwn xwri/wn ai( a)penanti/on pleurai/ te kai\ gwni/ai i)/sai a)llh/lais ei)si/n, kai\ h( dia/metros au)ta\ di/xa te/mnei.

e)/stw parallhlo/grammon xwri/on to\ *a*g*d*b, dia/metros de\ au)tou= h( *b*g: le/gw, o(/ti tou= *a*g*d*b parallhlogra/mmou ai( a)penanti/on pleurai/ te kai\ gwni/ai i)/sai a)llh/lais ei)si/n, kai\ h( *b*g dia/metros

au)to\ di/xa te/mnei.

e)pei\ ga\r para/llhlo/s e)stin h( *a*b th=| *g*d, kai\ ei)s au)ta\s e)mpe/ptwken eu)qei=a h( *b*g, ai( e)nalla\c gwni/ai ai( u(po\ *a*b*g, *b*g*d i)/sai a)llh/lais ei)si/n. pa/lin, e)pei\ para/llhlo/s e)stin h( *a*g th=| *b*d, kai\ ei)s au)ta\s e)mpe/ptwken h( *b*g, ai( e)nalla\c gwni/ai ai( u(po\ *a*g*b, *g*b*d i)/sai a)llh/lais ei)si/n. du/o dh\ tri/gwna/ e)sti ta\ *a*b*g, *b*g*d ta\s du/o gwni/as ta\s u(po\ *a*b*g, *b*g*a dusi\ tai=s u(po\ *b*g*d, *g*b*d i)/sas e)/xonta e(kate/ran e(kate/ra| kai\ mi/an pleura\n mia=| pleura=| i)/shn th\n pro\s tai=s i)/sais gwni/ais koinh\n au)tw=n th\n *b*g: kai\ ta\s loipa\s a)/ra pleura\s tai=s loipai=s i)/sas e(/cei e(kate/ran e(kate/ra| kai\ th\n loiph\n gwni/an th=| loiph=| gwni/a|: i)/sh a)/ra h( me\n *a*b pleura\ th=| *g*d, h( de\ *a*g th=| *b*d, kai\ e)/ti i)/sh e)sti\n h( u(po\ *b*a*g gwni/a th=| u(po\ *g*d*b. kai\ e)pei\ i)/sh e)sti\n h( me\n u(po\ *a*b*g gwni/a th=| u(po\ *b*g*d, h( de\ u(po\ *g*b*d th=| u(po\ *a*g*b, o(/lh a)/ra h( u(po\ *a*b*d o(/lh| th=| u(po\ *a*g*d e)stin i)/sh. e)dei/xqh de\ kai\ h( u(po\ *b*a*g th=| u(po\ *g*d*b i)/sh.

tw=n a)/ra parallhlogra/mmwn xwri/wn ai( a)penanti/on pleurai/ te kai\ gwni/ai i)/sai a)llh/lais ei)si/n.

le/gw dh/, o(/ti kai\ h( dia/metros au)ta\ di/xa te/mnei. e)pei\ ga\r i)/sh e)sti\n h( *a*b th=| *g*d, koinh\ de\ h( *b*g, du/o dh\ ai( *a*b, *b*g dusi\ tai=s *g*d, *b*g i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *a*b*g gwni/a| th=| u(po\ *b*g*d i)/sh. kai\ ba/sis a)/ra h( *a*g th=| *d*b i)/sh. kai\ to\ *a*b*g ~~a)/ra~~ tri/gwnon tw=| *b*g*d trigw/nw| i)/son e)sti/n.

h( a)/ra *b*g dia/metros di/xa te/mnei to\ *a*b*g*d parallhlo/grammon: o(/per e)/dei dei=cai.

ta\ parallhlo/gramma ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n.

e)/stw parallhlo/gramma ta\ *a*b*g*d, *e*b*g*z e)pi\ th=s au)th=s ba/sews th=s *b*g kai\ e)n tai=s au)tai=s parallh/lois tai=s *a*z, *b*g: le/gw, o(/ti i)/son e)sti\ to\ *a*b*g*d tw=| *e*b*g*z parallhlogra/mmw|.

ta\ a)/ra parallhlo/gramma ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

ta\ parallhlo/gramma ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n.

e)/stw parallhlo/gramma ta\ *a*b*g*d, *e*z*h*q e)pi\ i)/swn ba/sewn o)/nta tw=n *b*g, *z*h

kai\ e)n tai=s au)tai=s parallh/lois tai=s *a*q, *b*h: le/gw, o(/ti i)/son e)sti\ to\ *a*b*g*d parallhlo/grammon tw=| *e*z*h*q.

e)pezeu/xqwsan ga\r ai( *b*e, *g*q. kai\ e)pei\ i)/sh e)sti\n h( *b*g th=| *z*h, a)lla\ h( *z*h th=| *e*q e)stin i)/sh, kai\ h( *b*g a)/ra th=| *e*q e)stin i)/sh. ei)si\ de\ kai\ para/llhloi. kai\ e)pizeugnu/ousin au)ta\s ai( *e*b, *q*g: ai( de\ ta\s i)/sas te kai\ parallh/lous e)pi\ ta\ au)ta\ me/rh e)pizeugnu/ousai i)/sai te kai\ para/llhloi/ ei)si: ~~kai\ ai( *e*b, *q*g a)/ra i)/sai te/ ei)si kai\ para/llhloi~~. parallhlo/grammon a)/ra e)sti\ to\ *e*b*g*q. kai/ e)stin i)/son tw=| *a*b*g*d: ba/sin te ga\r au)tw=| th\n au)th\n e)/xei th\n *b*g, kai\ e)n tai=s au)tai=s parallh/lois e)sti\n au)tw=| tai=s *b*g, *a*q. dia\ ta\ au)ta\ dh\ kai\ to\ *e*z*h*q tw=| au)tw=| tw=| *e*b*g*q e)stin i)/son: w(/ste kai\ to\ *a*b*g*d parallhlo/grammon tw=| *e*z*h*q e)stin i)/son.

ta\ a)/ra parallhlo/gramma ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

ta\ tri/gwna ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n.

e)/stw tri/gwna ta\ *a*b*g, *d*b*g e)pi\ th=s au)th=s ba/sews

th=s *b*g kai\ e)n tai=s au)tai=s parallh/lois tai=s *a*d, *b*g: le/gw, o(/ti i)/son e)sti\ to\ *a*b*g tri/gwnon tw=| *d*b*g trigw/nw|.

*)ekbeblh/sqw h( *a*d e)f' e(ka/tera ta\ me/rh e)pi\ ta\ *e, *z, kai\ dia\ me\n tou= *b th=| *g*a para/llhlos h)/xqw h( *b*e, dia\ de\ tou= *g th=| *b*d para/llhlos h)/xqw h( *g*z. parallhlo/grammon a)/ra e)sti\n e(ka/teron tw=n *e*b*g*a, *d*b*g*z: kai/ ei)sin i)/sa: e)pi/ te ga\r th=s au)th=s ba/sew/s ei)si th=s *b*g kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*g, *e*z: kai/ e)sti tou= me\n *e*b*g*a parallhlogra/mmou h(/misu to\ *a*b*g tri/gwnon: h( ga\r *a*b dia/metros au)to\ di/xa te/mnei: tou= de\ *d*b*g*z parallhlogra/mmou h(/misu to\ *d*b*g tri/gwnon: h( ga\r *d*g dia/metros au)to\ di/xa te/mnei. ~~ta\ de\ tw=n i)/swn h(mi/sh i)/sa a)llh/lois e)sti/n~~. i)/son a)/ra e)sti\ to\ *a*b*g tri/gwnon tw=| *d*b*g trigw/nw|.

ta\ a)/ra tri/gwna ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

ta\ tri/gwna ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n.

e)/stw tri/gwna ta\ *a*b*g,

*d*e*z e)pi\ i)/swn ba/sewn tw=n *b*g, *e*z kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*z, *a*d: le/gw, o(/ti i)/son e)sti\ to\ *a*b*g tri/gwnon tw=| *d*e*z trigw/nw|.

*)ekbeblh/sqw ga\r h( *a*d e)f' e(ka/tera ta\ me/rh e)pi\ ta\ *h, q, kai\ dia\ me\n tou= *b th=| *g*a para/llhlos h)/xqw h( *b*h, dia\ de\ tou= *z th=| *d*e para/llhlos h)/xqw h( *z*q. parallhlo/grammon a)/ra e)sti\n e(ka/teron tw=n *h*b*g*a, *d*e*z*q: kai\ i)/son to\ *h*b*g*a tw=| *d*e*z*q: e)pi/ te ga\r i)/swn ba/sew/n ei)si tw=n *b*g, *e*z kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*z, *h*q: kai/ e)sti tou= me\n *h*b*g*a parallhlogra/mmou h(/misu to\ *a*b*g tri/gwnon. h( ga\r *a*b dia/metros au)to\ di/xa te/mnei: tou= de\ *d*e*z*q parallhlogra/mmou h(/misu to\ *z*e*d tri/gwnon: h( ga\r *d*z dia/metros au)to\ di/xa te/mnei: ~~ta\ de\ tw=n i)/swn h(mi/sh i)/sa a)llh/lois e)sti/n~~. i)/son a)/ra e)sti\ to\ *a*b*g tri/gwnon tw=| *d*e*z trigw/nw|.

ta\ a)/ra tri/gwna ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)n tai=s au)tai=s parallh/lois i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

ta\ i)/sa tri/gwna ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)pi\ ta\ au)ta\ me/rh kai\ e)n tai=s au)tai=s parallh/lois e)sti/n.

e)/stw i)/sa tri/gwna ta\ *a*b*g, *d*b*g e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)pi\ ta\ au)ta\ me/rh th=s *b*g: le/gw, o(/ti kai\ e)n tai=s au)tai=s parallh/lois e)sti/n.

e)pezeu/xqw ga\r h( *a*d: le/gw, o(/ti para/llhlo/s e)stin h( *a*d th=| *b*g.

ei) ga\r mh/, h)/xqw dia\ tou= *a shmei/ou th=| *b*g eu)qei/a| para/llhlos h( *a*e, kai\ e)pezeu/xqw h( *e*g. i)/son a)/ra e)sti\ to\ *a*b*g tri/gwnon tw=| *e*b*g trigw/nw|: e)pi/

te ga\r th=s au)th=s ba/sew/s e)stin au)tw=| th=s *b*g kai\ e)n tai=s au)tai=s parallh/lois. a)lla\ to\ *a*b*g tw=| *d*b*g e)stin i)/son: kai\ to\ *d*b*g a)/ra tw=| *e*b*g i)/son e)sti\ to\ mei=zon tw=| e)la/ssoni: o(/per e)sti\n a)du/naton: ou)k a)/ra para/llhlo/s e)stin h( *a*e th=| *b*g. o(moi/ws dh\ dei/comen, o(/ti ou)d' a)/llh tis plh\n th=s *a*d: h( *a*d a)/ra th=| *b*g e)sti para/llhlos.

ta\ a)/ra i)/sa tri/gwna ta\ e)pi\ th=s au)th=s ba/sews o)/nta kai\ e)pi\ ta\ au)ta\ me/rh kai\ e)n tai=s au)tai=s parallh/lois e)sti/n: o(/per e)/dei dei=cai.

ta\ i)/sa tri/gwna ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)pi\ ta\ au)ta\ me/rh kai\ e)n tai=s au)tai=s parallh/lois e)sti/n.

e)/stw i)/sa tri/gwna ta\ *a*b*g, *g*d*e e)pi\ i)/swn ba/sewn tw=n *b*g, *g*e kai\ e)pi\ ta\ au)ta\ me/rh. le/gw, o(/ti kai\ e)n tai=s au)tai=s parallh/lois e)sti/n.

e)pezeu/xqw ga\r h( *a*d: le/gw, o(/ti para/llhlo/s e)stin h( *a*d th=| *b*e.

ei) ga\r mh/, h)/xqw dia\ tou= *a th=| *b*e para/llhlos h( *a*z, kai\ e)pezeu/xqw h( *z*e. i)/son a)/ra e)sti\ to\ *a*b*g tri/gwnon tw=| *z*g*e trigw/nw|: e)pi/ te ga\r i)/swn ba/sew/n ei)si tw=n *b*g, *g*e kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*e, *a*z. a)lla\ to\ *a*b*g tri/gwnon i)/son e)sti\ tw=| *d*g*e ~~trigw/nw|~~: kai\ to\ *d*g*e a)/ra ~~tri/gwnon~~ i)/son e)sti\ tw=| *z*g*e trigw/nw| to\ mei=zon tw=| e)la/ssoni: o(/per e)sti\n a)du/naton: ou)k a)/ra para/llhlos h( *a*z th=| *b*e. o(moi/ws dh\ dei/comen, o(/ti ou)d' a)/llh tis plh\n th=s *a*d: h( *a*d a)/ra th=| *b*e e)sti para/llhlos.

ta\ a)/ra i)/sa tri/gwna ta\ e)pi\ i)/swn ba/sewn o)/nta kai\ e)pi\ ta\ au)ta\ me/rh kai\ e)n tai=s au)tai=s parallh/lois e)sti/n: o(/per e)/dei dei=cai.

e)a\n parallhlo/grammon trigw/nw| ba/sin te e)/xh| th\n au)th\n kai\ e)n tai=s au)tai=s parallh/lois h)=|, dipla/sio/n e)sti to\ parallhlo/grammon tou= trigw/nou.

parallhlo/grammon ga\r to\ *a*b*g*d trigw/nw| tw=| *e*b*g ba/sin te e)xe/tw th\n au)th\n th\n *b*g kai\ e)n tai=s au)tai=s parallh/lois e)/stw tai=s *b*g, *a*e: le/gw, o(/ti dipla/sio/n e)sti to\ *a*b*g*d parallhlo/grammon tou=

*b*e*g trigw/nou.

e)pezeu/xqw ga\r h( *a*g. i)/son dh/ e)sti to\ *a*b*g tri/gwnon tw=| *e*b*g trigw/nw|: e)pi/ te ga\r th=s au)th=s ba/sew/s e)stin au)tw=| th=s *b*g kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*g, *a*e. a)lla\ to\ *a*b*g*d parallhlo/grammon dipla/sio/n e)sti tou= *a*b*g trigw/nou: h( ga\r *a*g dia/metros au)to\ di/xa te/mnei: w(/ste to\ *a*b*g*d parallhlo/grammon kai\ tou= *e*b*g trigw/nou e)sti\ dipla/sion.

e)a\n a)/ra parallhlo/grammon trigw/nw| ba/sin te e)/xh| th\n au)th\n kai\ e)n tai=s au)tai=s parallh/lois h)=|, dipla/sio/n e)sti to\ parallhlo/grammon tou= trigw/nou: o(/per e)/dei dei=cai.

tetmh/sqw h( *b*g di/xa kata\ to\ *e, kai\ e)pezeu/xqw h( *a*e, kai\ sunesta/tw pro\s th=| *e*g eu)qei/a| kai\ tw=| pro\s au)th=|

shmei/w| tw=| *e th=| *d gwni/a| i)/sh h( u(po\ *g*e*z, kai\ dia\ me\n tou= *a th=| *e*g para/llhlos h)/xqw h( *a*h, dia\ de\ tou= *g th=| *e*z para/llhlos h)/xqw h( *g*h: parallhlo/grammon a)/ra e)sti\ to\ *z*e*g*h. kai\ e)pei\ i)/sh e)sti\n h( *b*e th=| *e*g, i)/son e)sti\ kai\ to\ *a*b*e tri/gwnon tw=| *a*e*g trigw/nw|: e)pi/ te ga\r i)/swn ba/sew/n ei)si tw=n *b*e, *e*g kai\ e)n tai=s au)tai=s parallh/lois tai=s *b*g, *a*h: dipla/sion a)/ra e)sti\ to\ *a*b*g tri/gwnon tou= *a*e*g trigw/nou. e)/sti de\ kai\ to\ *z*e*g*h parallhlo/grammon dipla/sion tou= *a*e*g trigw/nou: ba/sin te ga\r au)tw=| th\n au)th\n e)/xei kai\ e)n tai=s au)tai=s e)stin au)tw=| parallh/lois: i)/son a)/ra e)sti\ to\ *z*e*g*h parallhlo/grammon tw=| *a*b*g trigw/nw|. kai\ e)/xei th\n u(po\ *g*e*z gwni/an i)/shn th=| doqei/sh| th=| *d.

tw=| a)/ra doqe/nti trigw/nw| tw=| *a*b*g i)/son parallhlo/grammon sune/statai to\ *z*e*g*h e)n gwni/a| th=| u(po\ *g*e*z, h(/tis e)sti\n i)/sh th=| *d: o(/per e)/dei poih=sai.

panto\s parallhlogra/mmou tw=n peri\ th\n dia/metron parallhlogra/mmwn ta\ paraplhrw/mata i)/sa a)llh/lois e)sti/n.

e)/stw parallhlo/grammon to\ *a*b*g*d, dia/metros de\ au)tou= h( *a*g, peri\ de\ th\n *a*g parallhlo/gramma me\n e)/stw ta\ *z*q, *z*h, ta\ de\ lego/mena paraplhrw/mata

ta\ *b*k, *k*d: le/gw, o(/ti i)/son e)sti\ to\ *b*k paraplh/rwma tw=| *k*d paraplhrw/mati.

e)pei\ ga\r parallhlo/grammo/n e)sti to\ *a*b*g*d, dia/metros de\ au)tou= h( *a*g, i)/son e)sti\ to\ *a*b*g tri/gwnon tw=| *a*g*d trigw/nw|. pa/lin, e)pei\ parallhlo/grammo/n e)sti to\ *e*q, dia/metros de\ au)tou= e)stin h( *a*k, i)/son e)sti\ to\ *a*e*k tri/gwnon tw=| *a*q*k trigw/nw|. dia\ ta\ au)ta\ dh\ kai\ to\ *k*z*g tri/gwnon tw=| *k*h*g e)stin i)/son. e)pei\ ou)=n to\ me\n *a*e*k tri/gwnon tw=| *a*q*k trigw/nw| e)sti\n i)/son, to\ de\ *k*z*g tw=| *k*h*g, to\ *a*e*k tri/gwnon meta\ tou= *k*h*g i)/son e)sti\ tw=| *a*q*k trigw/nw| meta\ tou= *k*z*g: e)/sti de\ kai\ o(/lon to\ *a*b*g tri/gwnon o(/lw| tw=| *a*d*g i)/son: loipo\n a)/ra to\ *b*k paraplh/rwma loipw=| tw=| *k*d paraplhrw/mati/ e)stin i)/son.

panto\s a)/ra parallhlogra/mmou xwri/ou tw=n peri\ th\n dia/metron parallhlogra/mmwn ta\ paraplhrw/mata i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

e)/stw h( me\n doqei=sa eu)qei=a h( *a*b, to\ de\ doqe\n tri/gw

non to\ *g, h( de\ doqei=sa gwni/a eu)qu/grammos h( *d: dei= dh\ para\ th\n doqei=san eu)qei=an th\n *a*b tw=| doqe/nti trigw/nw| tw=| *g i)/son parallhlo/grammon parabalei=n e)n i)/sh| th=| *d gwni/a|.

sunesta/tw tw=| *g trigw/nw| i)/son parallhlo/grammon to\ *b*e*z*h e)n gwni/a| th=| u(po\ *e*b*h, h(/ e)stin i)/sh th=| *d: kai\ kei/sqw w(/ste e)p' eu)qei/as ei)=nai th\n *b*e th=| *a*b, kai\ dih/xqw h( *z*h e)pi\ to\ *q, kai\ dia\ tou= *a o(pote/ra| tw=n *b*h, *e*z para/llhlos h)/xqw h( *a*q, kai\ e)pezeu/xqw h( *q*b. kai\ e)pei\ ei)s parallh/lous ta\s *a*q, *e*z eu)qei=a e)ne/pesen h( *q*z, ai( a)/ra u(po\ *a*q*z, *q*z*e gwni/ai dusi\n o)rqai=s ei)sin i)/sai. ai( a)/ra u(po\ *b*q*h, *h*z*e du/o o)rqw=n e)la/ssone/s ei)sin: ai( de\ a)po\ e)lasso/nwn h)\ du/o o)rqw=n ei)s a)/peiron e)kballo/menai sumpi/ptousin: ai( *q*b, *z*e a)/ra e)kballo/menai sumpesou=ntai. e)kbeblh/sqwsan kai\ sumpipte/twsan kata\ to\ *k, kai\ dia\ tou= *k shmei/ou o(pote/ra| tw=n *e*a, *z*q para/llhlos h)/xqw h( *k*l, kai\ e)kbeblh/sqwsan ai( *q*a, *h*b e)pi\ ta\ *l, *m shmei=a. parallhlo/grammon a)/ra e)sti\ to\ *q*l*k*z, dia/metros de\ au)tou= h( *q*k, peri\ de\ th\n *q*k parallhlo/gramma me\n ta\ *a*h, *m*e, ta\ de\ lego/mena paraplhrw/mata ta\ *l*b, *b*z: i)/son a)/ra e)sti\ to\ *l*b tw=| *b*z. a)lla\ to\ *b*z tw=| *g trigw/nw| e)sti\n i)/son: kai\ to\ *l*b a)/ra tw=| *g e)stin i)/son. kai\ e)pei\ i)/sh e)sti\n h( u(po\ *h*b*e gwni/a th=| u(po\ *a*b*m, a)lla\ h( u(po\ *h*b*e th=| *d e)stin i)/sh, kai\ h( u(po\ *a*b*m a)/ra th=| *d gwni/a| e)sti\n i)/sh.

e)pezeu/xqw h( *d*b, kai\ sunesta/tw tw=| *a*b*d trigw/nw| i)/son parallhlo/grammon to\ *z*q e)n th=| u(po\ *q*k*z gwni/a|, h(/ e)stin i)/sh th=| *e: kai\ parabeblh/sqw para\ th\n *h*q eu)qei=an tw=| *d*b*g trigw/nw| i)/son parallhlo/grammon to\ *h*m e)n th=| u(po\ *h*q*m gwni/a|, h(/ e)stin i)/sh th=| *e. kai\ e)pei\ h( *e gwni/a e(kate/ra| tw=n u(po\ *q*k*z, *h*q*m e)stin i)/sh, kai\ h( u(po\ *q*k*z a)/ra th=| u(po\ *h*q*m e)stin i)/sh. koinh\ proskei/sqw h( u(po\ *k*q*h: ai( a)/ra u(po\ *z*k*q, *k*q*h tai=s u(po\ *k*q*h, *h*q*m i)/sai ei)si/n. a)ll' ai( u(po\ *z*k*q, *k*q*h dusi\n o)rqai=s i)/sai ei)si/n: kai\ ai( u(po\ *k*q*h, *h*q*m a)/ra du/o o)rqai=s i)/sai ei)si/n. pro\s dh/ tini eu)qei/a| th=| *h*q kai\ tw=| pro\s au)th=| shmei/w| tw=| *q du/o eu)qei=ai ai( *k*q, *q*m mh\ e)pi\ ta\ au)ta\ me/rh kei/menai ta\s e)fech=s gwni/as du/o o)rqai=s i)/sas poiou=sin: e)p' eu)qei/as a)/ra e)sti\n h( *k*q th=| *q*m: kai\ e)pei\ ei)s parallh/lous ta\s *k*m, *z*h eu)qei=a e)ne/pesen h( *q*h, ai( e)nalla\c gwni/ai ai( u(po\ *m*q*h, *q*h*z i)/sai a)llh/lais ei)si/n. koinh\ proskei/sqw h( u(po\ *q*h*l: ai( a)/ra u(po\ *m*q*h, *q*h*l tai=s u(po\ *q*h*z, *q*h*l i)/sai ei)si/n. a)ll' ai( u(po\ *m*q*h, *q*h*l du/o o)rqai=s i)/sai ei)si/n: kai\ ai( u(po\ *q*h*z, *q*h*l a)/ra du/o o)rqai=s i)/sai ei)si/n: e)p' eu)qei/as a)/ra e)sti\n h( *z*h th=| *h*l. kai\ e)pei\ h( *z*k th=| *q*h i)/sh te kai\ para/llhlo/s e)stin, a)lla\ kai\ h( *q*h th=| *m*l, kai\ h( *k*z a)/ra th=| *m*l i)/sh te kai\ para/llhlo/s e)stin: kai\ e)pizeugnu/ousin au)ta\s eu)qei=ai ai( *k*m, *z*l: kai\ ai( *k*m, *z*l a)/ra i)/sai te kai\ para/llhloi/ ei)sin: parallhlo/grammon a)/ra e)sti\ to\ *k*z*l*m. kai\ e)pei\ i)/son e)sti\ to\ me\n *a*b*d tri/gwnon tw=| *z*q parallhlogra/mmw|, to\ de\ *d*b*g tw=| *h*m, o(/lon a)/ra to\ *a*b*g*d eu)qu/grammon o(/lw| tw=| *k*z*l*m parallhlogra/mmw| e)sti\n i)/son.

tw=| a)/ra doqe/nti eu)qugra/mmw| tw=| *a*b*g*d i)/son parallhlo/grammon sune/statai to\ *k*z*l*m e)n gwni/a| th=| u(po\ *z*k*m, h(/ e)stin i)/sh th=| doqei/sh| th=| *e: o(/per e)/dei poih=sai.

a)po\ th=s doqei/shs eu)qei/as tetra/gwnon a)nagra/yai.

e)/stw h( doqei=sa eu)qei=a h( *a*b: dei= dh\ a)po\ th=s *a*b eu)qei/as tetra/gwnon a)nagra/yai.

h)/xqw th=| *a*b eu)qei/a| a)po\ tou= pro\s au)th=| shmei/ou tou= a pro\s o)rqa\s h( *a*g, kai\ kei/sqw th=| *a*b i)/sh h( *a*d: kai\

dia\ me\n tou= *d shmei/ou th=| *a*b para/llhlos h)/xqw h( *d*e, dia\ de\ tou= *b shmei/ou th=| *a*d para/llhlos h)/xqw h( *b*e. parallhlo/grammon a)/ra e)sti\ to\ *a*d*e*b: i)/sh a)/ra e)sti\n h( me\n *a*b th=| *d*e, h( de\ *a*d th=| *b*e. a)lla\ h( *a*b th=| *a*d e)stin i)/sh: ai( te/ssares a)/ra ai( *b*a, *a*d, *d*e, *e*b i)/sai a)llh/lais ei)si/n: i)so/pleuron a)/ra e)sti\ to\ *a*d*e*b parallhlo/grammon. le/gw dh/, o(/ti kai\ o)rqogw/nion. e)pei\ ga\r ei)s parallh/lous ta\s *a*b, *d*e eu)qei=a e)ne/pesen h( *a*d, ai( a)/ra u(po\ *b*a*d, *a*d*e gwni/ai du/o o)rqai=s i)/sai ei)si/n. o)rqh\ de\ h( u(po\ *b*a*d: o)rqh\ a)/ra kai\ h( u(po\ *a*d*e. tw=n de\ parallhlogra/mmwn xwri/wn ai( a)penanti/on pleurai/ te kai\ gwni/ai i)/sai a)llh/lais ei)si/n: o)rqh\ a)/ra kai\ e(kate/ra tw=n a)penanti/on tw=n u(po\ *a*b*e, *b*e*d gwniw=n: o)rqogw/nion a)/ra e)sti\ to\ *a*d*e*b. e)dei/xqh de\ kai\ i)so/pleuron.

tetra/gwnon a)/ra e)sti/n: kai/ e)stin a)po\ th=s *a*b eu)qei/as a)nagegramme/non: o(/per e)/dei poih=sai.

e)n toi=s o)rqogwni/ois trigw/nois to\ a)po\ th=s th\n o)rqh\n gwni/an u(poteinou/shs pleura=s tetra/gwnon i)/son e)sti\ toi=s a)po\ tw=n th\n o)rqh\n gwni/an periexousw=n pleurw=n tetragw/nois.

e)/stw tri/gwnon o)rqogw/nion to\ *a*b*g o)rqh\n e)/xon th\n u(po\ *b*a*g gwni/an: le/gw, o(/ti to\ a)po\ th=s *b*g tetra/gwnon i)/son e)sti\ toi=s a)po\ tw=n *b*a, *a*g tetragw/nois.

*)anagegra/fqw ga\r a)po\ me\n th=s *b*g tetra/gwnon to\ *b*d*e*g, a)po\ de\ tw=n *b*a, *a*g ta\ *h*b, *q*g, kai\ dia\ tou= a o(pote/ra| tw=n *b*d, *g*e para/llhlos h)/xqw h( *a*l: kai\ e)pezeu/xqwsan ai( *a*d, *z*g. kai\ e)pei\ o)rqh/ e)stin e(kate/ra tw=n u(po\ *b*a*g, *b*a*h gwniw=n, pro\s dh/ tini eu)qei/a| th=| *b*a kai\ tw=| pro\s au)th=| shmei/w| tw=| *a du/o eu)qei=ai ai( *a*g, *a*h mh\ e)pi\ ta\ au)ta\ me/rh kei/menai ta\s e)fech=s gwni/as dusi\n o)rqai=s i)/sas poiou=sin: e)p' eu)qei/as a)/ra e)sti\n h( *g*a th=| *a*h. dia\ ta\ au)ta\ dh\ kai\ h( *b*a th=| *a*q e)stin e)p' eu)qei/as. kai\ e)pei\ i)/sh e)sti\n h( u(po\ *d*b*g gwni/a th=| u(po\ *z*b*a: o)rqh\ ga\r e(kate/ra: koinh\ proskei/sqw h( u(po\ *a*b*g: o(/lh a)/ra h( u(po\ *d*b*a o(/lh| th=| u(po\ *z*b*g e)stin i)/sh. kai\ e)pei\ i)/sh e)sti\n h( me\n *d*b th=| *b*g, h( de\ *z*b th=| *b*a, du/o dh\ ai( *d*b, *b*a du/o tai=s *z*b, *b*g i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\

gwni/a h( u(po\ *d*b*a gwni/a| th=| u(po\ *z*b*g i)/sh: ba/sis a)/ra h( *a*d ba/sei th=| *z*g ~~e)stin~~ i)/sh, kai\ to\ *a*b*d tri/gwnon tw=| *z*b*g trigw/nw| e)sti\n i)/son: kai\ ~~e)sti\~~ tou= me\n *a*b*d trigw/nou dipla/sion to\ *b*l parallhlo/grammon: ba/sin te ga\r th\n au)th\n e)/xousi th\n *b*d kai\ e)n tai=s au)tai=s ei)si parallh/lois tai=s *b*d, *a*l: tou= de\ *z*b*g trigw/nou dipla/sion to\ *h*b tetra/gwnon: ba/sin te ga\r pa/lin th\n au)th\n e)/xousi th\n *z*b kai\ e)n tai=s au)tai=s ei)si parallh/lois tai=s *z*b, *h*g. ~~ta\ de\ tw=n i)/swn dipla/sia i)/sa a)llh/lois e)sti/n:~~ i)/son a)/ra e)sti\ kai\ to\ *b*l parallhlo/grammon tw=| *h*b tetragw/nw|. o(moi/ws dh\ e)pizeugnume/nwn tw=n *a*e, *b*k deixqh/setai kai\ to\ *g*l parallhlo/grammon i)/son tw=| *q*g tetragw/nw|: o(/lon a)/ra to\ *b*d*e*g tetra/gwnon dusi\ toi=s *h*b, *q*g tetragw/nois i)/son e)sti/n. kai/ e)sti to\ me\n *b*d*e*g tetra/gwnon a)po\ th=s *b*g a)nagrafe/n, ta\ de\ *h*b, *q*g a)po\ tw=n *b*a, *a*g. to\ a)/ra a)po\ th=s *b*g pleura=s tetra/gwnon i)/son e)sti\ toi=s a)po\ tw=n *b*a, *a*g pleurw=n tetragw/nois.

e)n a)/ra toi=s o)rqogwni/ois trigw/nois to\ a)po\ th=s th\n o)rqh\n gwni/an u(poteinou/shs pleura=s tetra/gwnon i)/son e)sti\ toi=s a)po\ tw=n th\n o)rqh\n ~~gwni/an~~ periexousw=n pleurw=n tetragw/nois: o(/per e)/dei dei=cai.

e)a\n trigw/nou to\ a)po\ mia=s tw=n pleurw=n tetra/gwnon i)/son h)=| toi=s a)po\ tw=n loipw=n tou= trigw/nou du/o pleurw=n tetragw/nois, h( periexome/nh gwni/a u(po\ tw=n loipw=n tou= trigw/nou du/o pleurw=n o)rqh/ e)stin.

trigw/nou ga\r tou= *a*b*g to\ a)po\ mia=s th=s *b*g pleura=s tetra/gwnon i)/son e)/stw toi=s a)po\ tw=n *b*a, *a*g pleurw=n tetragw/nois: le/gw, o(/ti o)rqh/ e)stin h( u(po\ *b*a*g gwni/a.

h)/xqw ga\r a)po\ tou= *a shmei/ou th=| *a*g eu)qei/a| pro\s o)rqa\s h( *a*d kai\ kei/sqw th=| *b*a i)/sh h( *a*d, kai\ e)pezeu/xqw h( *d*g. e)pei\ i)/sh e)sti\n h( *d*a th=| *a*b, i)/son e)sti\ kai\ to\ a)po\ th=s *d*a tetra/gwnon tw=| a)po\ th=s *a*b tetragw/nw|. koino\n proskei/sqw to\ a)po\ th=s *a*g tetra/gwnon: ta\ a)/ra a)po\ tw=n

*d*a, *a*g tetra/gwna i)/sa e)sti\ toi=s a)po\ tw=n *b*a, *a*g tetragw/nois. a)lla\ toi=s me\n a)po\ tw=n *d*a, *a*g i)/son e)sti\ to\ a)po\ th=s *d*g: o)rqh\ ga/r e)stin h( u(po\ *d*a*g gwni/a: toi=s de\ a)po\ tw=n *b*a, *a*g i)/son e)sti\ to\ a)po\ *b*g: u(po/keitai ga/r: to\ a)/ra a)po\ th=s *d*g tetra/gwnon i)/son e)sti\ tw=| a)po\ th=s *b*g tetragw/nw|: w(/ste kai\ pleura\ h( *d*g th=| *b*g e)stin i)/sh: kai\ e)pei\ i)/sh e)sti\n h( *d*a th=| *a*b, koinh\ de\ h( *a*g, du/o dh\ ai( *d*a, *a*g du/o tai=s *b*a, *a*g i)/sai ei)si/n: kai\ ba/sis h( *d*g ba/sei th=| *b*g i)/sh: gwni/a a)/ra h( u(po\ *d*a*g gwni/a| th=| u(po\ *b*a*g ~~e)stin~~ i)/sh. o)rqh\ de\ h( u(po\ *d*a*g: o)rqh\ a)/ra kai\ h( u(po\ *b*a*g.

e)a\n a)/ra trigw/nou to\ a)po\ mia=s tw=n pleurw=n tetra/gwnon i)/son h)=| toi=s a)po\ tw=n loipw=n tou= trigw/nou du/o pleurw=n tetragw/nois, h( periexome/nh gwni/a u(po\ tw=n loipw=n tou= trigw/nou du/o pleurw=n o)rqh/ e)stin: o(/per e)/dei dei=cai.

pa=n parallhlo/grammon o)rqogw/nion perie/xesqai le/getai u(po\ du/o tw=n th\n o)rqh\n gwni/an periexousw=n eu)qeiw=n.

panto\s de\ parallhlogra/mmou xwri/ou tw=n peri\ th\n dia/metron au)tou= parallhlogra/mmwn e(\n o(poionou=n su\n toi=s dusi\ paraplhrw/masi gnw/mwn kalei/sqw.

e)a\n w)=si du/o eu)qei=ai, tmhqh=| de\ h( e(te/ra au)tw=n ei)s o(sadhpotou=n tmh/mata, to\ periexo/menon o)rqogw/nion u(po\ tw=n du/o eu)qeiw=n i)/son e)sti\ toi=s u(po/ te th=s a)tmh/tou kai\ e(ka/stou tw=n tmhma/twn periexome/nois o)rqogwni/ois.

e)/stwsan du/o eu)qei=ai ai( *a, *b*g, kai\ tetmh/sqw h( *b*g, w(s e)/tuxen, kata\ ta\ *d, *e shmei=a: le/gw, o(/ti to\ u(po\ tw=n *a, *b*g periexo/menon o)rqogw/nion i)/son e)sti\ tw=| te u(po\ tw=n *a, *b*d periexome/nw| o)rqogwni/w| kai\ tw=| u(po\ tw=n *a, *d*e kai\ e)/ti tw=| u(po\ tw=n *a, *e*g.

h)/xqw ga\r a)po\ tou= *b th=| *b*g pro\s o)rqa\s h( *b*z, kai\ kei/sqw th=| *a i)/sh h( *b*h, kai\ dia\ me\n tou= *h th=| *b*g para/llhlos

h)/xqw h( *h*q, dia\ de\ tw=n *d, *e, *g th=| *b*h para/llhloi h)/xqwsan ai( *d*k, *e*l, *g*q.

i)/son dh/ e)sti to\ *b*q toi=s *b*k, *d*l, *e*q. kai/ e)sti to\ me\n *b*q to\ u(po\ tw=n *a, *b*g: perie/xetai me\n ga\r u(po\ tw=n *h*b, *b*g, i)/sh de\ h( *b*h th=| *a: to\ de\ *b*k to\ u(po\ tw=n *a, *b*d: perie/xetai me\n ga\r u(po\ tw=n *h*b, *b*d, i)/sh de\ h( *b*h th=| *a. to\ de\ *d*l to\ u(po\ tw=n *a, *d*e: i)/sh ga\r h( *d*k, toute/stin h( *b*h, th=| *a. kai\ e)/ti o(moi/ws to\ *e*q to\ u(po\ tw=n *a, *e*g: to\ a)/ra u(po\ tw=n *a, *b*g i)/son e)sti\ tw=| te u(po\ *a, *b*d kai\ tw=| u(po\ *a, *d*e kai\ e)/ti tw=| u(po\ *a, *e*g.

e)a\n a)/ra w)=si du/o eu)qei=ai, tmhqh=| de\ h( e(te/ra au)tw=n ei)s o(sadhpotou=n tmh/mata, to\ periexo/menon o)rqogw/nion u(po\ tw=n du/o eu)qeiw=n i)/son e)sti\ toi=s u(po/ te th=s a)tmh/tou kai\ e(ka/stou tw=n tmhma/twn periexome/nois o)rqogwni/ois: o(/per e)/dei dei=cai.

e)a\n eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ u(po\ th=s o(/lhs kai\ e(kate/rou tw=n tmhma/twn periexo/menon o)rqogw/nion i)/son e)sti\ tw=| a)po\ th=s o(/lhs tetragw/nw|.

eu)qei=a ga\r h( *a*b tetmh/sqw, w(s e)/tuxen, kata\ to\ *g shmei=on: le/gw, o(/ti to\ u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion meta\ tou= u(po\ *b*a, *a*g periexome/nou o)rqogwni/ou i)/son e)sti\ tw=| a)po\ th=s *a*b tetragw/nw|.

*)anagegra/fqw ga\r a)po\ th=s *a*b tetra/gwnon to\ *a*d*e*b, kai\ h)/xqw dia\ tou= *g o(pote/ra| tw=n *a*d, *b*e para/llhlos h( *g*z.

i)/son dh/ e)sti to\ *a*e toi=s *a*z, *g*e. kai/

e)sti to\ me\n *a*e to\ a)po\ th=s *a*b tetra/gwnon, to\ de\ *a*z to\ u(po\ tw=n *b*a, *a*g periexo/menon o)rqogw/nion: perie/xetai me\n ga\r u(po\ tw=n *d*a, *a*g, i)/sh de\ h( *a*d th=| *a*b: to\ de\ *g*e to\ u(po\ tw=n *a*b, *b*g: i)/sh ga\r h( *b*e th=| *a*b. to\ a)/ra u(po\ tw=n *b*a, *a*g meta\ tou= u(po\ tw=n *a*b, *b*g i)/son e)sti\ tw=| a)po\ th=s *a*b tetragw/nw|.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ u(po\ th=s o(/lhs kai\ e(kate/rou tw=n tmhma/twn periexo/menon o)rqogw/nion i)/son e)sti\ tw=| a)po\ th=s o(/lhs tetragw/nw|: o(/per e)/dei dei=cai.

eu)qei=a ga\r h( *a*b tetmh/sqw, w(s e)/tuxen, kata\ to\ *g: le/gw, o(/ti to\ u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion i)/son e)sti\ tw=| te u(po\ tw=n *a*g, *g*b periexome/nw| o)rqogwni/w| meta\ tou= a)po\ th=s *b*g tetragw/nou.

*)anagegra/fqw ga\r a)po\ th=s *g*b tetra/gwnon to\ *g*d*e*b, kai\ dih/xqw h( *e*d e)pi\ to\ *z, kai\ dia\ tou= *a o(pote/ra| tw=n

*g*d, *b*e para/llhlos h)/xqw h( *a*z. i)/son dh/ e)sti to\ *a*e toi=s *a*d, *g*e: kai/ e)sti to\ me\n *a*e to\ u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion: perie/xetai me\n ga\r u(po\ tw=n *a*b, *b*e, i)/sh de\ h( *b*e th=| *b*g: to\ de\ *a*d to\ u(po\ tw=n *a*g, *g*b: i)/sh ga\r h( *d*g th=| *g*b: to\ de\ *d*b to\ a)po\ th=s *g*b tetra/gwnon: to\ a)/ra u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion i)/son e)sti\ tw=| u(po\ tw=n *a*g, *g*b periexome/nw| o)rqogwni/w| meta\ tou= a)po\ th=s *b*g tetragw/nou.

e)a\n eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ a)po\ th=s o(/lhs tetra/gwnon i)/son e)sti\ toi=s te a)po\ tw=n tmhma/twn tetragw/nois kai\ tw=| di\s u(po\ tw=n tmhma/twn periexome/nw| o)rqogwni/w|.

eu)qei=a ga\r grammh\ h( *a*b tetmh/sqw, w(s e)/tuxen, kata\ to\ *g. le/gw, o(/ti to\ a)po\ th=s *a*b tetra/gwnon i)/son e)sti\ toi=s te a)po\ tw=n *a*g, *g*b tetragw/nois kai\ tw=| di\s u(po\ tw=n *a*g, *g*b periexome/nw| o)rqogwni/w|.

*)anagegra/fqw ga\r a)po\ th=s *a*b tetra/gwnon to\ *a*d*e*b, kai\ e)pezeu/xqw h( *b*d, kai\ dia\ me\n tou= *g o(pote/ra| tw=n *a*d, *e*b para/llhlos h)/xqw h( *g*z, dia\ de\ tou= *h o(pote/ra| tw=n *a*b, *d*e para/llhlos h)/xqw h( *q*k. kai\ e)pei\ para/llhlo/s e)stin h( *g*z th=| *a*d, kai\ ei)s au)ta\s e)mpe/ptwken h( *b*d, h( e)kto\s gwni/a h( u(po\ *g*h*b i)/sh e)sti\ th=| e)nto\s kai\

a)penanti/on th=| u(po\ *a*d*b. a)ll' h( u(po\ *a*d*b th=| u(po\ *a*b*d e)stin i)/sh, e)pei\ kai\ pleura\ h( *b*a th=| *a*d e)stin i)/sh: kai\ h( u(po\ *g*h*b a)/ra gwni/a th=| u(po\ *h*b*g e)stin i)/sh: w(/ste kai\ pleura\ h( *b*g pleura=| th=| *g*h e)stin i)/sh: a)ll' h( me\n *g*b th=| *h*k e)stin i)/sh, h( de\ *g*h th=| *k*b: kai\ h( *h*k a)/ra th=| *k*b e)stin i)/sh: i)so/pleuron a)/ra e)sti\ to\ *g*h*k*b. le/gw dh/, o(/ti kai\ o)rqogw/nion. e)pei\ ga\r para/llhlo/s e)stin h( *g*h th=| *b*k ~~kai\ ei)s au)ta\s e)mpe/ptwken eu)qei=a h( *g*b~~, ai( a)/ra u(po\ *k*b*g, *h*g*b gwni/ai du/o o)rqai=s ei)sin i)/sai. o)rqh\ de\ h( u(po\ *k*b*g: o)rqh\ a)/ra kai\ h( u(po\ *b*g*h: w(/ste kai\ ai( a)penanti/on ai( u(po\ *g*h*k, *h*k*b o)rqai/ ei)sin. o)rqogw/nion a)/ra e)sti\ to\ *g*h*k*b: e)dei/xqh de\ kai\ i)so/pleuron: tetra/gwnon a)/ra e)sti/n: kai/ e)stin a)po\ th=s *g*b. dia\ ta\ au)ta\ dh\ kai\ to\ *q*z tetra/gwno/n e)stin: kai/ e)stin a)po\ th=s *q*h, toute/stin ~~a)po\~~ th=s *a*g: ta\ a)/ra *q*z, *k*g tetra/gwna a)po\ tw=n *a*g, *g*b ei)sin. kai\ e)pei\ i)/son e)sti\ to\ *a*h tw=| *h*e, kai/ e)sti to\ *a*h to\ u(po\ tw=n *a*g, *g*b: i)/sh ga\r h( *h*g th=| *g*b: kai\ to\ *h*e a)/ra i)/son e)sti\ tw=| u(po\ *a*g, *g*b: ta\ a)/ra *a*h, *h*e i)/sa e)sti\ tw=| di\s u(po\ tw=n *a*g, *g*b. e)/sti de\ kai\ ta\ *q*z, *g*k tetra/gwna a)po\ tw=n *a*g, *g*b: ta\ a)/ra te/ssara ta\ *q*z, *g*k, *a*h, *h*e i)/sa e)sti\ toi=s te a)po\ tw=n *a*g, *g*b tetragw/nois kai\ tw=| di\s u(po\ tw=n *a*g, *g*b periexome/nw| o)rqogwni/w|. a)lla\ ta\ *q*z, *g*k, *a*h, *h*e o(/lon e)sti\ to\ *a*d*e*b, o(/ e)stin a)po\ th=s *a*b tetra/gwnon: to\ a)/ra a)po\ th=s *a*b tetra/gwnon i)/son e)sti\ toi=s te a)po\ tw=n *a*g, *g*b tetragw/nois kai\ tw=| di\s u(po\ tw=n *a*g, *g*b periexome/nw| o)rqogwni/w|.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ a)po\ th=s o(/lhs tetra/gwnon i)/son e)sti\ toi=s te a)po\ tw=n tmhma/twn tetragw/nois kai\ tw=| di\s u(po\ tw=n tmhma/twn periexome/nw| o)rqogwni/w|: o(/per e)/dei dei=cai.

~~po/risma~~

~~e)k dh\ tou/tou fanero/n, o(/ti e)n toi=s tetragw/nois xwri/ois ta\ peri\ th\n dia/metron parallhlo/gramma tetra/gwna/ e)stin~~.

e)a\n eu)qei=a grammh\ tmhqh=| ei)s i)/sa kai\ a)/nisa, to\ u(po\ tw=n a)ni/swn th=s o(/lhs tmhma/twn periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s metacu\ tw=n tomw=n tetragw/nou i)/son e)sti\ tw=| a)po\ th=s h(misei/as tetragw/nw|.

eu)qei=a ga/r tis h( *a*b tetmh/sqw ei)s me\n i)/sa kata\ to\ *g, ei)s de\ a)/nisa kata\ to\ *d: le/gw, o(/ti to\ u(po\ tw=n *a*d, *d*b periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *g*d tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *g*b tetragw/nw|.

*)anagegra/fqw ga\r a)po\ th=s *g*b tetra/gwnon to\ *g*e*z*b, kai\ e)pezeu/xqw h( *b*e, kai\ dia\ me\n tou= *d o(pote/ra| tw=n *g*e, *b*z para/llhlos h)/xqw h( *d*h, dia\ de\ tou= *q o(pote/ra| tw=n *a*b, *e*z para/llhlos pa/lin h)/xqw h( *k*m, kai\ pa/lin dia\

tou= *a o(pote/ra| tw=n *g*l, *b*m para/llhlos h)/xqw h( *a*k. kai\ e)pei\ i)/son e)sti\ to\ *g*q paraplh/rwma tw=| *q*z paraplhrw/mati, koino\n proskei/sqw to\ *d*m: o(/lon a)/ra to\ *g*m o(/lw| tw=| *d*z i)/son e)sti/n. a)lla\ to\ *g*m tw=| *a*l i)/son e)sti/n, e)pei\ kai\ h( *a*g th=| *g*b e)stin i)/sh: kai\ to\ *a*l a)/ra tw=| *d*z i)/son e)sti/n. koino\n proskei/sqw to\ *g*q: o(/lon a)/ra to\ *a*q tw=| *m*n*c gnw/moni i)/son e)sti/n. a)lla\ to\ *a*q to\ u(po\ tw=n *a*d, *d*b e)stin: i)/sh ga\r h( *d*q th=| *d*b: kai\ o( *m*n*c a)/ra gnw/mwn i)/sos e)sti\ tw=| u(po\ *a*d, *d*b. koino\n proskei/sqw to\ *l*h, o(/ e)stin i)/son tw=| a)po\ th=s *g*d: o( a)/ra *m*n*c gnw/mwn kai\ to\ *l*h i)/sa e)sti\ tw=| u(po\ tw=n *a*d, *d*b periexome/nw| o)rqogwni/w| kai\ tw=| a)po\ th=s *g*d tetragw/nw|. a)lla\ o( *m*n*c gnw/mwn kai\ to\ *l*h o(/lon e)sti\ to\ *g*e*z*b tetra/gwnon, o(/ e)stin a)po\ th=s *g*b: to\ a)/ra u(po\ tw=n *a*d, *d*b periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *g*d tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *g*b tetragw/nw|.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=| ei)s i)/sa kai\ a)/nisa, to\ u(po\ tw=n a)ni/swn th=s o(/lhs tmhma/twn periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s metacu\ tw=n tomw=n tetragw/nou i)/son e)sti\ tw=| a)po\ th=s h(misei/as tetragw/nw|: o(/per e)/dei dei=cai.

eu)qei=a ga/r tis h( *a*b tetmh/sqw di/xa

kata\ to\ *g shmei=on, proskei/sqw de/ tis au)th=| eu)qei=a e)p' eu)qei/as h( *b*d: le/gw, o(/ti to\ u(po\ tw=n *a*d, *d*b periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *g*b tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *g*d tetragw/nw|.

*)anagegra/fqw ga\r a)po\ th=s *g*d tetra/gwnon to\ *g*e*z*d, kai\ e)pezeu/xqw h( *d*e, kai\ dia\ me\n tou= *b shmei/ou o(pote/ra| tw=n *e*g, *d*z para/llhlos h)/xqw h( *b*h, dia\ de\ tou= *q shmei/ou o(pote/ra| tw=n *a*b, *e*z para/llhlos h)/xqw h( *k*m, kai\ e)/ti dia\ tou= *a o(pote/ra| tw=n *g*l, *d*m para/llhlos h)/xqw h( *a*k.

e)pei\ ou)=n i)/sh e)sti\n h( *a*g th=| *g*b, i)/son e)sti\ kai\ to\ *a*l tw=| *g*q. a)lla\ to\ *g*q tw=| *q*z i)/son e)sti/n. kai\ to\ *a*l a)/ra tw=| *q*z e)stin i)/son. koino\n proskei/sqw to\ *g*m: o(/lon a)/ra to\ *a*m tw=| *n*c*o gnw/moni/ e)stin i)/son. a)lla\ to\ *a*m e)sti to\ u(po\ tw=n *a*d, *d*b: i)/sh ga/r e)stin h( *d*m th=| *d*b: kai\ o( *n*c*o a)/ra gnw/mwn i)/sos e)sti\ tw=| u(po\ tw=n *a*d, *d*b ~~periexome/nw| o)rqogwni/w|~~. koino\n proskei/sqw to\ *l*h, o(/ e)stin i)/son tw=| a)po\ th=s *b*g tetragw/nw|: to\ a)/ra u(po\ tw=n *a*d, *d*b periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *g*b tetragw/nou i)/son e)sti\ tw=| *n*c*o gnw/moni kai\ tw=| *l*h. a)lla\ o( *n*c*o gnw/mwn kai\ to\ *l*h o(/lon e)sti\ to\ *g*e*z*d tetra/gwnon, o(/ e)stin a)po\ th=s *g*d: to\ a)/ra u(po\ tw=n *a*d, *d*b periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *g*b tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *g*d tetragw/nw|.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=| di/xa, prosteqh=| de/ tis au)th=| eu)qei=a e)p' eu)qei/as, to\ u(po\ th=s o(/lhs su\n th=| proskeime/nh| kai\ th=s proskeime/nhs periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s h(misei/as tetragw/nou i)/son e)sti\ tw=| a)po\ th=s sugkeime/nhs e)/k te th=s h(misei/as kai\ th=s proskeime/nhs tetragw/nw|: o(/per e)/dei dei=cai.

*)anagegra/fqw ga\r a)po\ th=s *a*b tetra/gwnon to\ *a*d*e*b: kai\ katagegra/fqw to\ sxh=ma.

e)pei\ ou)=n i)/son e)sti\ to\ *a*h tw=| *h*e, koino\n proskei/sqw to\ *g*z: o(/lon a)/ra to\ *a*z o(/lw| tw=| *g*e i)/son e)sti/n: ta\ a)/ra *a*z, *g*e dipla/sia/ e)sti tou= *a*z. a)lla\ ta\ *a*z, *g*e o( *k*l*m e)sti gnw/mwn kai\ to\ *g*z tetra/gwnon: o( *k*l*m a)/ra gnw/mwn kai\ to\ *g*z dipla/sia/ e)sti tou= *a*z. e)/sti

de\ tou= *a*z dipla/sion kai\ to\ di\s u(po\ tw=n *a*b, *b*g: i)/sh ga\r h( *b*z th=| *b*g: o( a)/ra *k*l*m gnw/mwn kai\ to\ *g*z tetra/gwnon i)/son e)sti\ tw=| di\s u(po\ tw=n *a*b, *b*g. koino\n proskei/sqw to\ *d*h, o(/ e)stin a)po\ th=s *a*g tetra/gwnon: o( a)/ra *k*l*m gnw/mwn kai\ ta\ *b*h, *h*d tetra/gwna i)/sa e)sti\ tw=| te di\s u(po\ tw=n *a*b, *b*g periexome/nw| o)rqogwni/w| kai\ tw=| a)po\ th=s *a*g tetragw/nw|. a)lla\ o( *k*l*m gnw/mwn kai\ ta\ *b*h, *h*d tetra/gwna o(/lon e)sti\ to\ *a*d*e*b kai\ to\ *g*z, a(/ e)stin a)po\ tw=n *a*b, *b*g tetra/gwna: ta\ a)/ra a)po\ tw=n *a*b, *b*g tetra/gwna i)/sa e)sti\ tw=| te di\s u(po\ tw=n *a*b, *b*g periexome/nw| o)rqogwni/w| meta\ tou= a)po\ th=s *a*g tetragw/nou.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ a)po\ th=s o(/lhs kai\ to\ a)f' e(no\s tw=n tmhma/twn ta\ sunamfo/tera tetra/gwna i)/sa e)sti\ tw=| te di\s u(po\ th=s o(/lhs kai\ tou= ei)rhme/nou tmh/matos periexome/nw| o)rqogwni/w| kai\ tw=| a)po\ tou= loipou= tmh/matos tetragw/nw|: o(/per e)/dei dei=cai.

e)a\n eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ tetra/kis u(po\ th=s o(/lhs kai\ e(no\s tw=n tmhma/twn periexo/menon o)rqogw/nion meta\ tou= a)po\ tou= loipou= tmh/matos tetragw/nou i)/son e)sti\ tw=| a)po/ te th=s o(/lhs kai\ tou= ei)rhme/nou tmh/matos w(s a)po\ mia=s a)nagrafe/nti tetragw/nw|.

eu)qei=a ga/r tis h( *a*b tetmh/sqw, w(s e)/tuxen, kata\ to\ *g shmei=on: le/gw, o(/ti to\ tetra/kis u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *a*g tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *a*b, *b*g w(s a)po\ mia=s a)nagrafe/nti tetragw/nw|.

*)ekbeblh/sqw ga\r e)p' eu)qei/as ~~th=| *a*b eu)qei=a~~ h( *b*d, kai\ kei/sqw th=| *g*b i)/sh h( *b*d, kai\ a)nagegra/fqw a)po\ th=s *a*d tetra/gwnon to\ *a*e*z*d, kai\ katagegra/fqw

diplou=n to\ sxh=ma.

e)pei\ ou)=n i)/sh e)sti\n h( *g*b th=| *b*d, a)lla\ h( me\n *g*b th=| *h*k e)stin i)/sh, h( de\ *b*d th=| *k*n, kai\ h( *h*k a)/ra th=| *k*n e)stin i)/sh. dia\ ta\ au)ta\ dh\ kai\ h( *p*r th=| *r*o e)stin i)/sh. kai\ e)pei\ i)/sh e)sti\n h( *b*g th=| *b*d, h( de\ *h*k th=| *k*n, i)/son a)/ra e)sti\ kai\ to\ me\n *g*k tw=| *k*d, to\ de\ *h*r tw=| *r*n. a)lla\ to\ *g*k tw=| *r*n e)stin i)/son: paraplhrw/mata ga\r tou= *g*o parallhlogra/mmou: kai\ to\ *k*d a)/ra tw=| *h*r i)/son e)sti/n: ta\ te/ssara a)/ra ta\ *d*k, *g*k, *h*r, *r*n i)/sa a)llh/lois e)sti/n. ta\ te/ssara a)/ra tetrapla/sia/ e)sti tou= *g*k. pa/lin, e)pei\ i)/sh e)sti\n h( *g*b th=| *b*d, a)lla\ h( me\n *b*d th=| *b*k, toute/sti th=| *g*h i)/sh, h( de\ *g*b th=| *h*k, toute/sti th=| *h*p, e)stin i)/sh, kai\ h( *g*h a)/ra th=| *h*p i)/sh e)sti/n. kai\ e)pei\ i)/sh e)sti\n h( me\n *g*h th=| *h*p, h( de\ *p*r th=| *r*o, i)/son e)sti\ kai\ to\ me\n *a*h tw=| *m*p, to\ de\ *p*l tw=| *r*z. a)lla\ to\ *m*p tw=| *p*l e)stin i)/son: paraplhrw/mata ga\r tou= *m*l parallhlogra/mmou: kai\ to\ *a*h a)/ra tw=| *r*z i)/son e)sti/n: ta\ te/ssara a)/ra ta\ *a*h, *m*p, *p*l, *r*z i)/sa a)llh/lois e)sti/n: ta\ te/ssara a)/ra tou= *a*h e)sti tetrapla/sia. e)dei/xqh de\ kai\ ta\ te/ssara ta\ *g*k, *k*d, *h*r, *r*n tou= *g*k tetrapla/sia: ta\ a)/ra o)ktw/, a(\ perie/xei to\n *s*t*u gnw/mona, tetrapla/sia/ e)sti tou= *a*k. kai\ e)pei\ to\ *a*k to\ u(po\ tw=n *a*b, *b*d e)stin: i)/sh ga\r h( *b*k th=| *b*d: to\ a)/ra tetra/kis u(po\ tw=n *a*b, *b*d tetrapla/sio/n e)sti tou= *a*k. e)dei/xqh de\ tou= *a*k tetrapla/sios kai\ o( *s*t*u gnw/mwn: to\ a)/ra tetra/kis u(po\ tw=n *a*b, *b*d i)/son e)sti\ tw=| *s*t*u gnw/moni. koino\n proskei/sqw to\ *c*q, o(/ e)stin i)/son tw=| a)po\ th=s *a*g tetragw/nw|: to\ a)/ra tetra/kis u(po\ tw=n *a*b, *b*d periexo/menon o)rqogw/nion meta\ tou= a)po\ *a*g tetragw/nou i)/son e)sti\ tw=| *s*t*u gnw/moni kai\ tw=| *c*q. a)lla\ o( *s*t*u gnw/mwn kai\ to\ *c*q o(/lon e)sti\ to\ *a*e*z*d tetra/gwnon, o(/ e)stin a)po\ th=s *a*d: to\ a)/ra tetra/kis u(po\ tw=n *a*b, *b*d meta\ tou= a)po\ *a*g i)/son e)sti\ tw=| a)po\ *a*d tetragw/nw|: i)/sh de\ h( *b*d th=| *b*g. to\ a)/ra tetra/kis u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion meta\ tou= a)po\ *a*g tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *a*d, toute/sti tw=| a)po\ th=s *a*b kai\ *b*g w(s a)po\ mia=s a)nagrafe/nti tetragw/nw|.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=|, w(s e)/tuxen, to\ tetra/kis u(po\ th=s o(/lhs kai\ e(no\s tw=n tmhma/twn periexo/menon o)rqogw/nion meta\ tou= a)po\ tou= loipou= tmh/matos tetragw/nou i)/son e)sti\ tw=| a)po/ te th=s o(/lhs kai\ tou= ei)rhme/nou tmh/matos w(s a)po\ mia=s a)nagrafe/nti tetragw/nw|: o(/per e)/dei dei=cai.

e)a\n eu)qei=a grammh\ tmhqh=| ei)s i)/sa kai\ a)/nisa, ta\ a)po\ tw=n a)ni/swn th=s o(/lhs tmhma/twn tetra/gwna dipla/sia/ e)sti tou= te a)po\ th=s h(misei/as kai\ tou= a)po\ th=s metacu\ tw=n tomw=n tetragw/nou.

eu)qei=a ga/r tis h( *a*b tetmh/sqw ei)s me\n i)/sa kata\ to\ *g, ei)s de\ a)/nisa kata\ to\ *d: le/gw, o(/ti ta\ a)po\ tw=n *a*d, *d*b tetra/gwna dipla/sia/ e)sti tw=n a)po\ tw=n

*a*g, *g*d tetragw/nwn.

h)/xqw ga\r a)po\ tou= *g th=| *a*b pro\s o)rqa\s h( *g*e, kai\ kei/sqw i)/sh e(kate/ra| tw=n *a*g, *g*b, kai\ e)pezeu/xqwsan ai( *e*a, *e*b, kai\ dia\ me\n tou= *d th=| *e*g para/llhlos h)/xqw h( *d*z, dia\ de\ tou= *z th=| *a*b h( *z*h, kai\ e)pezeu/xqw h( *a*z. kai\ e)pei\ i)/sh e)sti\n h( *a*g th=| *g*e, i)/sh e)sti\ kai\ h( u(po\ *e*a*g gwni/a th=| u(po\ *a*e*g. kai\ e)pei\ o)rqh/ e)stin h( pro\s tw=| *g, loipai\ a)/ra ai( u(po\ *e*a*g, *a*e*g mia=| o)rqh=| i)/sai ei)si/n: kai/ ei)sin i)/sai: h(mi/seia a)/ra o)rqh=s e)stin e(kate/ra tw=n u(po\ *g*e*a, *g*a*e. dia\ ta\ au)ta\ dh\ kai\ e(kate/ra tw=n u(po\ *g*e*b, *e*b*g h(mi/seia/ e)stin o)rqh=s: o(/lh a)/ra h( u(po\ *a*e*b o)rqh/ e)stin. kai\ e)pei\ h( u(po\ *h*e*z h(mi/seia/ e)stin o)rqh=s, o)rqh\ de\ h( u(po\ *e*h*z: i)/sh ga/r e)sti th=| e)nto\s kai\ a)penanti/on th=| u(po\ *e*g*b: loiph\ a)/ra h( u(po\ *e*z*h h(mi/seia/ e)stin o)rqh=s: i)/sh a)/ra ~~e)sti\n~~ h( u(po\ *h*e*z gwni/a th=| u(po\ *e*z*h: w(/ste kai\ pleura\ h( *e*h th=| *h*z e)stin i)/sh. pa/lin e)pei\ h( pro\s tw=| b gwni/a h(mi/seia/ e)stin o)rqh=s, o)rqh\ de\ h( u(po\ *z*d*b: i)/sh ga\r pa/lin e)sti\ th=| e)nto\s kai\ a)penanti/on th=| u(po\ *e*g*b: loiph\ a)/ra h( u(po\ *b*z*d h(mi/seia/ e)stin o)rqh=s: i)/sh a)/ra h( pro\s tw=| *b gwni/a th=| u(po\ *d*z*b: w(/ste kai\ pleura\ h( *z*d pleura=| th=| *d*b e)stin i)/sh. kai\ e)pei\ i)/sh e)sti\n h( *a*g th=| *g*e, i)/son e)sti\ kai\ to\ a)po\ *a*g tw=| a)po\ *g*e: ta\ a)/ra a)po\ tw=n *a*g, *g*e tetra/gwna dipla/sia/ e)sti tou= a)po\ *a*g. toi=s de\ a)po\ tw=n *a*g, *g*e i)/son e)sti\ to\ a)po\ th=s *e*a tetra/gwnon: o)rqh\ ga\r h( u(po\ *a*g*e gwni/a: to\ a)/ra a)po\ th=s *e*a dipla/sio/n e)sti tou= a)po\ th=s *a*g. pa/lin, e)pei\ i)/sh e)sti\n h( *e*h th=| *h*z, i)/son kai\ to\ a)po\ th=s *e*h tw=| a)po\ th=s *h*z: ta\ a)/ra a)po\ tw=n *e*h, *h*z tetra/gwna dipla/sia/ e)sti tou= a)po\ th=s *h*z tetragw/nou. toi=s de\ a)po\ tw=n *e*h, *h*z tetragw/nois i)/son e)sti\ to\ a)po\ th=s *e*z tetra/gwnon: to\ a)/ra a)po\ th=s *e*z tetra/gwnon dipla/sio/n e)sti tou= a)po\ th=s *h*z. i)/sh de\ h( *h*z th=| *g*d: to\ a)/ra a)po\ th=s *e*z dipla/sio/n e)sti tou= a)po\ th=s *g*d. e)/sti de\ kai\ to\ a)po\ th=s *e*a dipla/sion tou= a)po\ th=s *a*g: ta\ a)/ra a)po\ tw=n *a*e, *e*z tetra/gwna dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn. toi=s de\ a)po\ tw=n *a*e, *e*z i)/son e)sti\ to\ a)po\ th=s *a*z tetra/gwnon: o)rqh\ ga/r e)stin h( u(po\ *a*e*z gwni/a: to\ a)/ra a)po\ th=s *a*z tetra/gwnon dipla/sio/n e)sti tw=n a)po\ tw=n *a*g, *g*d. tw=| de\ a)po\ th=s *a*z i)/sa ta\ a)po\ tw=n *a*d, *d*z: o)rqh\ ga\r h( pro\s tw=| *d gwni/a: ta\ a)/ra a)po\ tw=n *a*d, *d*z dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn. i)/sh de\ h( *d*z th=| *d*b: ta\ a)/ra a)po\ tw=n *a*d, *d*b tetra/gwna dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=| ei)s i)/sa kai\ a)/nisa, ta\ a)po\ tw=n a)ni/swn th=s o(/lhs tmhma/twn tetra/gwna dipla/sia/ e)sti tou= te a)po\ th=s h(misei/as kai\ tou= a)po\ th=s metacu\ tw=n tomw=n tetragw/nou: o(/per e)/dei dei=cai.

e)a\n eu)qei=a grammh\ tmhqh=| di/xa, prosteqh=| de/ tis au)th=| eu)qei=a e)p' eu)qei/as, to\ a)po\ th=s o(/lhs su\n th=| proskeime/nh| kai\ to\ a)po\ th=s proskeime/nhs ta\ sunamfo/tera tetra/gwna dipla/sia/ e)sti tou= te a)po\ th=s h(misei/as kai\ tou= a)po\ th=s sugkeime/nhs e)/k te th=s h(misei/as kai\ th=s proskeime/nhs w(s a)po\ mia=s a)nagrafe/ntos tetragw/nou.

eu)qei=a ga/r tis h( *a*b tetmh/sqw di/xa kata\ to\ *g, proskei/sqw de/ tis au)th=| eu)qei=a e)p' eu)qei/as h( *b*d: le/gw, o(/ti

ta\ a)po\ tw=n *a*d, *d*b tetra/gwna dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn.

h)/xqw ga\r a)po\ tou= *g shmei/ou th=| *a*b pro\s o)rqa\s h( *g*e, kai\ kei/sqw i)/sh e(kate/ra|, tw=n *a*g, *g*b, kai\ e)pezeu/xqwsan ai( *e*a, *e*b: kai\ dia\ me\n tou= *e th=| *a*d para/llhlos h)/xqw h( *e*z, dia\ de\ tou= *d th=| *g*e para/llhlos h)/xqw h( *z*d. kai\ e)pei\ ei)s parallh/lous eu)qei/as ta\s *e*g, *z*d eu)qei=a/ tis e)ne/pesen h( *e*z, ai( u(po\ *g*e*z, *e*z*d a)/ra dusi\n o)rqai=s i)/sai ei)si/n: ai( a)/ra u(po\ *z*e*b, *e*z*d du/o o)rqw=n e)la/ssone/s ei)sin: ai( de\ a)p' e)lasso/nwn h)\ du/o o)rqw=n e)kballo/menai sumpi/ptousin: ai( a)/ra *e*b, *z*d e)kballo/menai e)pi\ ta\ *b, *d me/rh sumpesou=ntai. e)kbeblh/sqwsan kai\ sumpipte/twsan kata\ to\ *h, kai\ e)pezeu/xqw h( *a*h. kai\ e)pei\ i)/sh e)sti\n h( *a*g th=| *g*e, i)/sh e)sti\ kai\ gwni/a h( u(po\ *e*a*g th=| u(po\ *a*e*g: kai\ o)rqh\ h( pro\s tw=| *g: h(mi/seia a)/ra o)rqh=s ~~e)stin~~ e(kate/ra tw=n u(po\ *e*a*g, *a*e*g. dia\ ta\ au)ta\ dh\ kai\ e(kate/ra tw=n u(po\ *g*e*b, *e*b*g h(mi/seia/ e)stin o)rqh=s: o)rqh\ a)/ra e)sti\n h( u(po\ *a*e*b. kai\ e)pei\ h(mi/seia o)rqh=s e)stin h( u(po\ *e*b*g, h(mi/seia a)/ra o)rqh=s kai\ h( u(po\ *d*b*h. e)/sti de\ kai\ h( u(po\ *b*d*h o)rqh/: i)/sh ga/r e)sti th=| u(po\ *d*g*e: e)nalla\c ga/r: loiph\ a)/ra h( u(po\ *d*h*b h(mi/seia/ e)stin o)rqh=s: h( a)/ra u(po\ *d*h*b th=| u(po\ *d*b*h e)stin i)/sh: w(/ste kai\ pleura\ h( *b*d pleura=| th=| *h*d e)stin i)/sh. pa/lin, e)pei\ h( u(po\ *e*h*z h(mi/seia/ e)stin o)rqh=s, o)rqh\ de\ h( pro\s tw=| *z: i)/sh ga/r e)sti th=| a)penanti/on th=| pro\s tw=| *g: loiph\ a)/ra h( u(po\ *z*e*h h(mi/seia/ e)stin o)rqh=s: i)/sh a)/ra h( u(po\ *e*h*z gwni/a th=| u(po\ *z*e*h: w(/ste kai\ pleura\ h( *h*z pleura=| th=| *e*z e)stin i)/sh. kai\ e)pei\ ~~i)/sh e)sti\n h( *e*g th=| *g*a,~~ i)/son e)sti\ ~~kai\~~ to\ a)po\ th=s *e*g tetra/gwnon tw=| a)po\ th=s *g*a tetragw/nw|: ta\ a)/ra a)po\ tw=n *e*g, *g*a tetra/gwna dipla/sia/ e)sti tou= a)po\ th=s *g*a tetragw/nou. toi=s de\ a)po\ tw=n *e*g, *g*a i)/son e)sti\ to\ a)po\ th=s *e*a: to\ a)/ra a)po\ th=s *e*a tetra/gwnon dipla/sio/n e)sti tou= a)po\ th=s *a*g tetragw/nou. pa/lin, e)pei\ i)/sh e)sti\n h( *z*h th=| *e*z, i)/son e)sti\ kai\ to\ a)po\ th=s *z*h tw=| a)po\ th=s *z*e: ta\ a)/ra a)po\ tw=n *h*z, *z*e dipla/sia/ e)sti tou= a)po\ th=s *e*z. toi=s de\ a)po\ tw=n *h*z, *z*e i)/son e)sti\ to\ a)po\ th=s *e*h: to\ a)/ra a)po\ th=s *e*h dipla/sio/n e)sti tou= a)po\ th=s *e*z. i)/sh de\ h( *e*z th=| *g*d: to\ a)/ra a)po\ th=s *e*h tetra/gwnon dipla/sio/n e)sti tou= a)po\ th=s *g*d. e)dei/xqh de\ kai\ to\ a)po\ th=s *e*a dipla/sion tou= a)po\ th=s *a*g: ta\ a)/ra a)po\ tw=n *a*e, *e*h tetra/gwna dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn. toi=s de\ a)po\ tw=n *a*e, *e*h tetragw/nois i)/son e)sti\ to\ a)po\ th=s *a*h tetra/gwnon: to\ a)/ra a)po\ th=s *a*h dipla/sio/n e)sti tw=n a)po\ tw=n *a*g, *g*d. tw=| de\ a)po\ th=s *a*h i)/sa e)sti\ ta\ a)po\ tw=n *a*d, *d*h: ta\ a)/ra a)po\ tw=n *a*d, *d*h ~~tetra/gwna~~ dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d ~~tetragw/nwn~~. i)/sh de\ h( *d*h th=| *d*b: ta\ a)/ra a)po\ tw=n *a*d, *d*b ~~tetra/gwna~~ dipla/sia/ e)sti tw=n a)po\ tw=n *a*g, *g*d tetragw/nwn.

e)a\n a)/ra eu)qei=a grammh\ tmhqh=| di/xa, prosteqh=| de/ tis au)th=| eu)qei=a e)p' eu)qei/as, to\ a)po\ th=s o(/lhs su\n th=| proskeime/nh| kai\ to\ a)po\ th=s proskeime/nhs ta\ sunamfo/tera tetra/gwna dipla/sia/ e)sti tou= te a)po\ th=s h(misei/as kai\ tou= a)po\ th=s sugkeime/nhs e)/k te th=s h(misei/as kai\ th=s proskeime/nhs w(s a)po\ mia=s a)nagrafe/ntos tetragw/nou: o(/per e)/dei dei=cai.

th\n doqei=san eu)qei=an temei=n w(/ste to\ u(po\ th=s o(/lhs kai\ tou= e(te/rou tw=n tmhma/twn periexo/menon o)rqogw/nion i)/son ei)=nai tw=| a)po\ tou= loipou= tmh/matos tetragw/nw|.

e)/stw h( doqei=sa eu)qei=a h( *a*b: dei= dh\ th\n *a*b temei=n w(/ste to\ u(po\ th=s o(/lhs kai\ tou= e(te/rou tw=n tmhma/twn periexo/menon o)rqogw/nion i)/son ei)=nai tw=| a)po\ tou= loipou= tmh/matos tetragw/nw|.

*)anagegra/fqw ga\r a)po\ th=s *a*b tetra/gwnon to\ *a*b*d*g, kai\ tetmh/sqw h( *a*g di/xa kata\ to\ *e shmei=on, kai\ e)pezeu/xqw h( *b*e, kai\ dih/xqw h( *g*a e)pi\ to\ *z, kai\

kei/sqw th=| *b*e i)/sh h( *e*z, kai\ a)nagegra/fqw a)po\ th=s *a*z tetra/gwnon to\ *z*q, kai\ dih/xqw h( *h*q e)pi\ to\ *k: le/gw, o(/ti h( *a*b te/tmhtai kata\ to\ *q, w(/ste to\ u(po\ tw=n *a*b, *b*q periexo/menon o)rqogw/nion i)/son poiei=n tw=| a)po\ th=s *a*q tetragw/nw|.

e)pei\ ga\r eu)qei=a h( *a*g te/tmhtai di/xa kata\ to\ *e, pro/skeitai de\ au)th=| h( *z*a, to\ a)/ra u(po\ tw=n *g*z, *z*a periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *a*e tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *e*z tetragw/nw|. i)/sh de\ h( *e*z th=| *e*b: to\ a)/ra u(po\ tw=n *g*z, *z*a meta\ tou= a)po\ th=s *a*e i)/son e)sti\ tw=| a)po\ *e*b. a)lla\ tw=| a)po\ *e*b i)/sa e)sti\ ta\ a)po\ tw=n *b*a, *a*e: o)rqh\ ga\r h( pro\s tw=| *a gwni/a: to\ a)/ra u(po\ tw=n *g*z, *z*a meta\ tou= a)po\ th=s *a*e i)/son e)sti\ toi=s a)po\ tw=n *b*a, *a*e. koino\n a)fh|rh/sqw to\ a)po\ th=s *a*e: loipo\n a)/ra to\ u(po\ tw=n *g*z, *z*a periexo/menon o)rqogw/nion i)/son e)sti\ tw=| a)po\ th=s *a*b tetragw/nw|. kai/ e)sti to\ me\n u(po\ tw=n *g*z, *z*a to\ *z*k: i)/sh ga\r h( *a*z th=| *z*h: to\ de\ a)po\ th=s *a*b to\ *a*d: to\ a)/ra *z*k i)/son e)sti\ tw=| *a*d. koino\n a)fh|rh/sqw to\ *a*k: loipo\n a)/ra to\ *z*q tw=| *q*d i)/son e)sti/n. kai/ e)sti to\ me\n *q*d to\ u(po\ tw=n *a*b, *b*q: i)/sh ga\r h( *a*b th=| *b*d: to\ de\ *z*q to\ a)po\ th=s *a*q: to\ a)/ra u(po\ tw=n *a*b, *b*q periexo/menon o)rqogw/nion i)/son e)sti\ tw=| a)po\ *q*a tetragw/nw|.

h( a)/ra doqei=sa eu)qei=a h( *a*b te/tmhtai kata\ to\ *q w(/ste to\ u(po\ tw=n *a*b, *b*q periexo/menon o)rqogw/nion i)/son poiei=n tw=| a)po\ th=s *q*a tetragw/nw|: o(/per e)/dei poih=sai.

e)n toi=s a)mblugwni/ois trigw/nois to\ a)po\ th=s th\n a)mblei=an gwni/an u(poteinou/shs pleura=s tetra/gwnon mei=zo/n e)sti tw=n a)po\ tw=n th\n a)mblei=an gwni/an periexousw=n pleurw=n tetragw/nwn tw=| periexome/nw| di\s u(po/ te mia=s tw=n peri\ th\n a)mblei=an gwni/an, e)f' h(\n h( ka/qetos pi/ptei, kai\ th=s a)polambanome/nhs e)kto\s u(po\ th=s kaqe/tou pro\s th=| a)mblei/a| gwni/a|.

e)/stw a)mblugw/nion tri/gwnon to\ *a*b*g a)mblei=an e)/xon th\n u(po\ *b*a*g, kai\ h)/xqw a)po\ tou= *b shmei/ou e)pi\ th\n *g*a e)kblhqei=san ka/qetos h( *b*d. le/gw, o(/ti to\ a)po\ th=s *b*g tetra/gwnon mei=zo/n e)sti tw=n a)po\ tw=n *b*a, *a*g tetragw/nwn tw=| di\s u(po\ tw=n *g*a, *a*d periexome/nw| o)rqogwni/w|.

e)pei\ ga\r eu)qei=a h( *g*a te/tmhtai, w(s e)/tuxen, kata\ to\ *a shmei=on, to\ a)/ra a)po\ th=s *d*g i)/son e)sti\ toi=s a)po\ tw=n *g*a, *a*d tetragw/nois kai\ tw=| di\s u(po\ tw=n *g*a, *a*d periexome/nw| o)rqogwni/w|. koino\n proskei/sqw to\ a)po\ th=s *d*b: ta\ a)/ra a)po\ tw=n *g*d, *d*b i)/sa e)sti\ toi=s te

a)po\ tw=n *g*a, *a*d, *d*b tetragw/nois kai\ tw=| di\s u(po\ tw=n *g*a, *a*d ~~periexome/nw| o)rqogwni/w|~~. a)lla\ toi=s me\n a)po\ tw=n *g*d, *d*b i)/son e)sti\ to\ a)po\ th=s *g*b: o)rqh\ ga\r h( pro\s tw=| *d gwni/a: toi=s de\ a)po\ tw=n *a*d, *d*b i)/son to\ a)po\ th=s *a*b: to\ a)/ra a)po\ th=s *g*b tetra/gwnon i)/son e)sti\ toi=s te a)po\ tw=n *g*a, *a*b tetragw/nois kai\ tw=| di\s u(po\ tw=n *g*a, *a*d periexome/nw| o)rqogwni/w|: w(/ste to\ a)po\ th=s *g*b tetra/gwnon tw=n a)po\ tw=n *g*a, *a*b tetragw/nwn mei=zo/n e)sti tw=| di\s u(po\ tw=n *g*a, *a*d periexome/nw| o)rqogwni/w|.

e)n a)/ra toi=s a)mblugwni/ois trigw/nois to\ a)po\ th=s th\n a)mblei=an gwni/an u(poteinou/shs pleura=s tetra/gwnon mei=zo/n e)sti tw=n a)po\ tw=n th\n a)mblei=an gwni/an periexousw=n pleurw=n tetragw/nwn tw=| periexome/nw| di\s u(po/ te mia=s tw=n peri\ th\n a)mblei=an gwni/an, e)f' h(\n h( ka/qetos pi/ptei, kai\ th=s a)polambanome/nhs e)kto\s u(po\ th=s kaqe/tou pro\s th=| a)mblei/a| gwni/a|: o(/per e)/dei dei=cai.

e)n toi=s o)cugwni/ois trigw/nois to\ a)po\ th=s th\n o)cei=an gwni/an u(poteinou/shs pleura=s tetra/gwnon e)/latto/n e)sti tw=n a)po\ tw=n th\n o)cei=an gwni/an periexousw=n pleurw=n tetragw/nwn tw=| periexome/nw| di\s u(po/ te mia=s tw=n peri\ th\n o)cei=an gwni/an, e)f' h(\n h( ka/qetos pi/ptei, kai\ th=s a)polambanome/nhs e)nto\s u(po\ th=s kaqe/tou pro\s th=| o)cei/a| gwni/a|.

e)/stw o)cugw/nion tri/gwnon to\ *a*b*g o)cei=an e)/xon th\n pro\s tw=| *b gwni/an, kai\ h)/xqw a)po\ tou= *a shmei/ou e)pi\ th\n *b*g ka/qetos h( *a*d: le/gw, o(/ti to\ a)po\ th=s *a*g tetra/gwnon e)/latto/n e)sti tw=n a)po\ tw=n *g*b, *b*a tetragw/nwn tw=| di\s u(po\ tw=n *g*b, *b*d periexome/nw| o)rqogwni/w|.

e)pei\ ga\r eu)qei=a h( *g*b te/tmhtai, w(s e)/tuxen, kata\ to\ *d, ta\ a)/ra a)po\ tw=n *g*b, *b*d tetra/gwna i)/sa e)sti\ tw=| te di\s u(po\ tw=n *g*b, *b*d periexome/nw| o)rqogwni/w| kai\ tw=| a)po\ th=s *d*g tetragw/nw|. koino\n proskei/sqw to\ a)po\ th=s *d*a tetra/gwnon: ta\ a)/ra a)po\ tw=n *g*b, *b*d, *d*a tetra/gwna i)/sa e)sti\ tw=| te di\s u(po\ tw=n *g*b, *b*d periexome/nw| o)rqogwni/w| kai\ toi=s a)po\ tw=n *a*d, *d*g tetragw/nois. a)lla\ toi=s me\n a)po\ tw=n *b*d, *d*a i)/son to\ a)po\ th=s *a*b: o)rqh\ ga\r h( pro\s tw=| *d gwni/a|: toi=s de\ a)po\ tw=n *a*d, *d*g i)/son to\ a)po\ th=s *a*g: ta\ a)/ra a)po\ tw=n *g*b, *b*a i)/sa e)sti\ tw=| te a)po\ th=s *a*g kai\ tw=| di\s u(po\ tw=n *g*b, *b*d: w(/ste mo/non to\ a)po\ th=s *a*g e)/latto/n e)sti tw=n a)po\ tw=n *g*b, *b*a tetragw/nwn tw=| di\s u(po\ tw=n *g*b, *b*d periexome/nw| o)rqogwni/w|.

e)n a)/ra toi=s o)cugwni/ois trigw/nois to\ a)po\ th=s th\n o)cei=an gwni/an u(poteinou/shs pleura=s tetra/gwnon e)/latto/n e)sti tw=n a)po\ tw=n th\n o)cei=an gwni/an periexousw=n pleurw=n tetragw/nwn tw=| periexome/nw| di\s u(po/ te mia=s tw=n peri\ th\n o)cei=an gwni/an, e)f' h(\n h( ka/qetos pi/ptei, kai\ th=s a)polambanome/nhs e)nto\s u(po\ th=s kaqe/tou pro\s th=| o)cei/a| gwni/a|: o(/per e)/dei dei=cai.

tw=| doqe/nti eu)qugra/mmw| i)/son tetra/gwnon susth/sasqai.

e)/stw to\ doqe\n eu)qu/grammon to\ *a: dei= dh\ tw=| *a eu)qugra/mmw| i)/son tetra/gwnon susth/sasqai.

*b*d: ei) de\ ou)/, mi/a tw=n *b*e, *e*d mei/zwn e)sti/n. e)/stw mei/zwn h( *b*e, kai\ e)kbeblh/sqw e)pi\ to\ *z, kai\ kei/sqw th=| *e*d i)/sh h( *e*z, kai\ tetmh/sqw h( *b*z di/xa kata\ to\ *h, kai\ ke/ntrw| tw=| *h, diasth/mati de\ e(ni\ tw=n *h*b, *h*z h(miku/klion gegra/fqw to\ *b*q*z, kai\ e)kbeblh/sqw h( *d*e e)pi\ to\ *q, kai\ e)pezeu/xqw h( *h*q.

e)pei\ ou)=n eu)qei=a h( *b*z te/tmhtai ei)s me\n i)/sa kata\ to\ *h, ei)s de\ a)/nisa kata\ to\ *e, to\ a)/ra u(po\ tw=n *b*e, *e*z periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *e*h tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *h*z tetragw/nw|. i)/sh de\ h( *h*z th=| *h*q: to\ a)/ra u(po\ tw=n *b*e, *e*z meta\ tou= a)po\ th=s *h*e i)/son e)sti\ tw=| a)po\ th=s *h*q. tw=| de\ a)po\ th=s *h*q i)/sa e)sti\ ta\ a)po\ tw=n *q*e, *e*h tetra/gwna: to\ a)/ra u(po\ tw=n *b*e, *e*z meta\ tou= a)po\ *h*e i)/sa e)sti\ toi=s a)po\ tw=n *q*e, *e*h. koino\n a)fh|rh/sqw to\ a)po\ th=s *h*e tetra/gwnon: loipo\n a)/ra to\ u(po\ tw=n *b*e, *e*z periexo/menon o)rqogw/nion i)/son e)sti\ tw=| a)po\ th=s *e*q tetragw/nw|. a)lla\ to\ u(po\ tw=n *b*e, *e*z to\ *b*d e)stin: i)/sh ga\r h( *e*z th=| *e*d: to\ a)/ra *b*d parallhlo/grammon i)/son e)sti\ tw=| a)po\ th=s *q*e tetragw/nw|. i)/son de\ to\ *b*d tw=| *a eu)qugra/mmw|. kai\ to\ *a a)/ra eu)qu/grammon i)/son e)sti\ tw=| a)po\ th=s *e*q a)nagrafhsome/nw| tetragw/nw|.

tw=| a)/ra doqe/nti eu)qugra/mmw| tw=| *a i)/son tetra/gwnon sune/statai to\ a)po\ th=s *e*q a)nagrafhso/menon: o(/per e)/dei poih=sai.

i)/soi ku/kloi ei)si/n, w(=n ai( dia/metroi i)/sai ei)si/n, h)\ w(=n ai( e)k tw=n ke/ntrwn i)/sai ei)si/n.

eu)qei=a ku/klou e)fa/ptesqai le/getai, h(/tis a(ptome/nh tou= ku/klou kai\ e)kballome/nh ou) te/mnei to\n ku/klon.

ku/kloi e)fa/ptesqai a)llh/lwn le/gontai oi(/tines a(pto/menoi a)llh/lwn ou) te/mnousin a)llh/lous.

e)n ku/klw| i)/son a)pe/xein a)po\ tou= ke/ntrou eu)qei=ai le/gontai, o(/tan ai( a)po\ tou= ke/ntrou e)p' au)ta\s ka/qetoi a)go/menai i)/sai w)=sin.

mei=zon de\ a)pe/xein le/getai, e)f' h(\n h( mei/zwn ka/qetos pi/ptei.

tmh=ma ku/klou e)sti\ to\ periexo/menon sxh=ma u(po/ te eu)qei/as kai\ ku/klou periferei/as.

tmh/matos de\ gwni/a e)sti\n h( periexome/nh u(po/ te eu)qei/as kai\ ku/klou periferei/as.

e)n tmh/mati de\ gwni/a e)sti/n, o(/tan e)pi\ th=s periferei/as tou= tmh/matos lhfqh=| ti shmei=on kai\ a)p' au)tou= e)pi\ ta\ pe/rata th=s eu)qei/as, h(/ e)sti ba/sis tou= tmh/matos, e)pizeuxqw=sin eu)qei=ai, h( periexome/nh gwni/a u(po\ tw=n e)pizeuxqeisw=n eu)qeiw=n.

o(/tan de\ ai( perie/xousai th\n gwni/an eu)qei=ai a)polamba/nwsi/ tina perife/reian, e)p' e)kei/nhs le/getai bebhke/nai h( gwni/a.

*tomeu\s de\ ku/klou e)sti/n, o(/tan pro\s tw=| ke/ntrw| tou= ku/klou sustaqh=| gwni/a, to\ periexo/menon sxh=ma u(po/ te tw=n th\n gwni/an periexousw=n eu)qeiw=n kai\ th=s a)polambanome/nhs u(p' au)tw=n periferei/as.

o(/moia tmh/mata ku/klwn e)sti\ ta\ dexo/mena gwni/as i)/sas, h)\ e)n oi(=s ai( gwni/ai i)/sai a)llh/lais ei)si/n.

tou= doqe/ntos ku/klou to\ ke/ntron eu(rei=n.

e)/stw o( doqei\s ku/klos o( *a*b*g: dei= dh\ tou= *a*b*g ku/klou to\ ke/ntron eu(rei=n.

dih/xqw tis ei)s au)to/n, w(s e)/tuxen, eu)qei=a h( *a*b, kai\ tetmh/sqw di/xa kata\ to\ *d shmei=on, kai\ a)po\ tou= *d th=| *a*b

pro\s o)rqa\s h)/xqw h( *d*g kai\ dih/xqw e)pi\ to\ *e, kai\ tetmh/sqw h( *g*e di/xa kata\ to\ *z: le/gw, o(/ti to\ *z ke/ntron e)sti\ tou= *a*b*g ~~ku/klou~~.

mh\ ga/r, a)ll' ei) dunato/n, e)/stw to\ *h, kai\ e)pezeu/xqwsan ai( *h*a, *h*d, *h*b. kai\ e)pei\ i)/sh e)sti\n h( *a*d th=| *d*b, koinh\ de\ h( *d*h, du/o dh\ ai( *a*d, *d*h du/o tai=s *h*d, *d*b i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ ba/sis h( *h*a ba/sei th=| *h*b e)stin i)/sh: e)k ke/ntrou ga/r: gwni/a a)/ra h( u(po\ *a*d*h gwni/a| th=| u(po\ *h*d*b i)/sh e)sti/n. o(/tan de\ eu)qei=a e)p' eu)qei=an staqei=sa ta\s e)fech=s gwni/as i)/sas a)llh/lais poih=|, o)rqh\ e(kate/ra tw=n i)/swn gwniw=n e)stin: o)rqh\ a)/ra e)sti\n h( u(po\ *h*d*b. e)sti\ de\ kai\ h( u(po\ *z*d*b o)rqh/: i)/sh a)/ra h( u(po\ *z*d*b th=| u(po\ *h*d*b, h( mei/zwn th=| e)la/ttoni: o(/per e)sti\n a)du/naton. ou)k a)/ra to\ *h ke/ntron e)sti\ tou= *a*b*g ku/klou. o(moi/ws dh\ dei/comen, o(/ti ou)d' a)/llo ti plh\n tou= *z.

to\ *z a)/ra shmei=on ke/ntron e)sti\ tou= *a*b*g ~~ku/klou~~.

*po/risma

e)k dh\ tou/tou fanero/n, o(/ti e)a\n e)n ku/klw| eu)qei=a/ tis eu)qei=a/n tina di/xa kai\ pro\s o)rqa\s te/mnh|, e)pi\ th=s temnou/shs e)sti\ to\ ke/ntron tou= ku/klou: o(/per e)/dei poih=sai.

e)a\n ku/klou e)pi\ th=s periferei/as lhfqh=| du/o tuxo/nta shmei=a, h( e)pi\ ta\ shmei=a e)pizeugnume/nh eu)qei=a e)nto\s pesei=tai tou= ku/klou.

e)/stw ku/klos o( *a*b*g, kai\ e)pi\ th=s periferei/as au)tou= ei)lh/fqw du/o tuxo/nta shmei=a ta\ *a, *b: le/gw, o(/ti h( a)po\ tou= *a e)pi\ to\ *b e)pizeugnume/nh eu)qei=a e)nto\s pesei=tai tou= ku/klou.

mh\ ga/r, a)ll' ei) dunato/n, pipte/tw e)kto\s w(s h( *a*e*b, kai\ ei)lh/fqw to\ ke/ntron tou= *a*b*g ku/klou, kai\ e)/stw to\ d, kai\ e)pezeu/xqwsan ai( *d*a, *d*b, kai\ dih/xqw h( *d*z*e.

e)pei\ ou)=n i)/sh e)sti\n h( *d*a th=| *d*b, i)/sh a)/ra kai\ gwni/a h( u(po\ *d*a*e th=| u(po\ *d*b*e: kai\ e)pei\ trigw/nou tou= *d*a*e mi/a pleura\ prosekbe/blhtai h( *a*e*b, mei/zwn a)/ra h( u(po\ *d*e*b gwni/a th=s u(po\ *d*a*e. i)/sh de\ h( u(po\ *d*a*e th=| u(po\ *d*b*e: mei/zwn a)/ra h( u(po\ *d*e*b th=s u(po\ *d*b*e. u(po\ de\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei: mei/zwn a)/ra h( *d*b th=s *d*e. i)/sh de\ h( *d*b th=| *d*z. mei/zwn a)/ra h( *d*z th=s *d*e h( e)la/ttwn th=s mei/zonos: o(/per e)sti\n a)du/naton. ou)k a)/ra h( a)po\ tou= *a e)pi\ to\ *b e)pizeugnume/nh eu)qei=a e)kto\s pesei=tai tou= ku/klou. o(moi/ws dh\ dei/comen, o(/ti ou)de\ e)p' au)th=s th=s periferei/as: e)nto\s a)/ra.

e)a\n a)/ra ku/klou e)pi\ th=s periferei/as lhfqh=| du/o tuxo/nta shmei=a, h( e)pi\ ta\ shmei=a e)pizeugnume/nh eu)qei=a e)nto\s pesei=tai tou= ku/klou: o(/per e)/dei dei=cai.

e)a\n e)n ku/klw| eu)qei=a/ tis dia\ tou= ke/ntrou eu)qei=a/n tina mh\ dia\ tou= ke/ntrou di/xa te/mnh|, kai\ pro\s o)rqa\s au)th\n te/mnei: kai\ e)a\n pro\s o)rqa\s au)th\n te/mnh|, kai\ di/xa au)th\n te/mnei.

e)/stw ku/klos o( *a*b*g, kai\ e)n au)tw=| eu)qei=a/ tis dia\ tou= ke/ntrou h( *g*d eu)qei=a/n tina mh\ dia\ tou= ke/ntrou th\n *a*b di/xa temne/tw kata\ to\ *z shmei=on: le/gw, o(/ti kai\ pro\s o)rqa\s au)th\n te/mnei.

ei)lh/fqw ga\r to\ ke/ntron tou= *a*b*g ku/klou, kai\ e)/stw to\ *e, kai\ e)pezeu/xqwsan ai( *e*a, *e*b.

kai\ e)pei\ i)/sh e)sti\n h( *a*z th=| *z*b, koinh\ de\ h( *z*e, du/o dusi\n i)/sai ~~ei)si/n~~. kai\ ba/sis h( *e*a ba/sei th=| *e*b i)/sh: gwni/a a)/ra h( u(po\ *a*z*e gwni/a| th=| u(po\ *b*z*e i)/sh e)sti/n. o(/tan de\ eu)qei=a e)p' eu)qei=an staqei=sa ta\s e)fech=s gwni/as i)/sas a)llh/lais poih=|, o)rqh\ e(kate/ra tw=n i)/swn gwniw=n e)stin: e(kate/ra a)/ra tw=n u(po\ *a*z*e, *b*z*e o)rqh/ e)stin. h( *g*d a)/ra dia\ tou= ke/ntrou ou)=sa th\n *a*b mh\ dia\ tou= ke/ntrou ou)=san di/xa te/mnousa kai\ pro\s o)rqa\s

te/mnei.

a)lla\ dh\ h( *g*d th\n *a*b pro\s o)rqa\s temne/tw: le/gw, o(/ti kai\ di/xa au)th\n te/mnei, toute/stin, o(/ti i)/sh e)sti\n h( *a*z th=| *z*b.

tw=n ga\r au)tw=n kataskeuasqe/ntwn, e)pei\ i)/sh e)sti\n h( *e*a th=| *e*b, i)/sh e)sti\ kai\ gwni/a h( u(po\ *e*a*z th=| u(po\ *e*b*z. e)sti\ de\ kai\ o)rqh\ h( u(po\ *a*z*e o)rqh=| th=| u(po\ *b*z*e i)/sh: du/o a)/ra tri/gwna/ e)sti ta\ *e*a*z, *e*z*b ta\s du/o gwni/as dusi\ gwni/ais i)/sas e)/xonta kai\ mi/an pleura\n mia=| pleura=| i)/shn koinh\n au)tw=n th\n *e*z u(potei/nousan u(po\ mi/an tw=n i)/swn gwniw=n: kai\ ta\s loipa\s a)/ra pleura\s tai=s loipai=s pleurai=s i)/sas e(/cei: i)/sh a)/ra h( *a*z th=| *z*b.

e)a\n a)/ra e)n ku/klw| eu)qei=a/ tis dia\ tou= ke/ntrou eu)qei=a/n tina mh\ dia\ tou= ke/ntrou di/xa te/mnh|, kai\ pro\s o)rqa\s au)th\n te/mnei: kai\ e)a\n pro\s o)rqa\s au)th\n te/mnh|, kai\ di/xa au)th\n te/mnei: o(/per e)/dei dei=cai.

e)a\n e)n ku/klw| du/o eu)qei=ai te/mnwsin a)llh/las mh\ dia\ tou= ke/ntrou ou)=sai, ou) te/mnousin a)llh/las di/xa.

e)/stw ku/klos o( *a*b*g*d, kai\ e)n au)tw=| du/o eu)qei=ai ai( *a*g, *b*d temne/twsan a)llh/las kata\ to\ *e mh\ dia\ tou= ke/ntrou ou)=sai: le/gw, o(/ti ou) te/mnousin a)llh/las di/xa.

ei) ga\r dunato/n, temne/twsan a)llh/las di/xa w(/ste i)/shn ei)=nai th\n me\n *a*e th=| *e*g, th\n de\ *b*e th=| *e*d: kai\ ei)lh/fqw to\ ke/ntron tou= *a*b*g*d ku/klou, kai\ e)/stw to\ *z, kai\ e)pezeu/xqw h( *z*e.

e)pei\ ou)=n eu)qei=a/ tis dia\ tou= ke/ntrou h( *z*e eu)qei=a/n tina mh\ dia\ tou= ke/ntrou th\n *a*g di/xa te/mnei, kai\ pro\s o)rqa\s au)th\n te/mnei: o)rqh\ a)/ra e)sti\n h( u(po\ *z*e*a: pa/lin, e)pei\ eu)qei=a/ tis h( *z*e eu)qei=a/n tina th\n *b*d di/xa te/mnei, kai\ pro\s o)rqa\s au)th\n te/mnei: o)rqh\ a)/ra h( u(po\ *z*e*b. e)dei/xqh de\ kai\ h( u(po\ *z*e*a o)rqh/: i)/sh a)/ra h( u(po\ *z*e*a th=| u(po\ *z*e*b h( e)la/ttwn th=| mei/zoni: o(/per e)sti\n a)du/naton. ou)k a)/ra ai( *a*g, *b*d te/mnousin a)llh/las di/xa.

e)a\n a)/ra e)n ku/klw| du/o eu)qei=ai te/mnwsin a)llh/las mh\ dia\ tou= ke/ntrou ou)=sai, ou) te/mnousin a)llh/las di/xa: o(/per e)/dei dei=cai.

e)a\n du/o ku/kloi te/mnwsin a)llh/lous, ou)k e)/stai au)tw=n to\ au)to\ ke/ntron.

du/o ga\r ku/kloi oi( *a*b*g, *g*d*h temne/twsan a)llh/lous kata\ ta\ *b, *g shmei=a. le/gw, o(/ti ou)k e)/stai au)tw=n to\ au)to\ ke/ntron.

ei) ga\r dunato/n, e)/stw to\ *e, kai\ e)pezeu/xqw h( *e*g, kai\ dih/xqw h( *e*z*h, w(s e)/tuxen. kai\ e)pei\ to\ *e shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou, i)/sh e)sti\n h( *e*g th=| *e*z. pa/lin, e)pei\ to\ *e shmei=on ke/ntron e)sti\ tou= *g*d*h

ku/klou, i)/sh e)sti\n h( *e*g th=| *e*h: e)dei/xqh de\ h( *e*g kai\ th=| *e*z i)/sh: kai\ h( *e*z a)/ra th=| *e*h e)stin i)/sh h( e)la/sswn th=| mei/zoni: o(/per e)sti\n a)du/naton. ou)k a)/ra to\ *e shmei=on ke/ntron e)sti\ tw=n *a*b*g, *g*d*h ku/klwn.

e)a\n a)/ra du/o ku/kloi te/mnwsin a)llh/lous, ou)k e)/stin au)tw=n to\ au)to\ ke/ntron: o(/per e)/dei dei=cai.

e)a\n du/o ku/kloi e)fa/ptwntai a)llh/lwn, ou)k e)/stai au)tw=n to\ au)to\ ke/ntron.

du/o ga\r ku/kloi oi( *a*b*g, *g*d*e e)fapte/sqwsan a)llh/lwn kata\ to\ *g shmei=on: le/gw, o(/ti ou)k e)/stai au)tw=n to\ au)to\ ke/ntron.

ei) ga\r dunato/n, e)/stw to\ *z, kai\ e)pezeu/xqw h( *z*g, kai\ dih/xqw, w(s e)/tuxen, h( *z*e*b.

e)pei\ ou)=n to\ *z shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou, i)/sh e)sti\n h( *z*g th=| *z*b. pa/lin, e)pei\ to\ *z shmei=on ke/ntron e)sti\ tou= *g*d*e ku/klou, i)/sh e)sti\n h( *z*g th=| *z*e. e)dei/xqh de\ h( *z*g th=| *z*b i)/sh: kai\ h( *z*e a)/ra th=| *z*b e)stin i)/sh, h( e)la/ttwn th=| mei/zoni: o(/per e)sti\n a)du/naton. ou)k a)/ra to\ *z shmei=on ke/ntron e)sti\ tw=n *a*b*g, *g*d*e ku/klwn.

e)a\n a)/ra du/o ku/kloi e)fa/ptwntai a)llh/lwn, ou)k e)/stai au)tw=n to\ au)to\ ke/ntron: o(/per e)/dei dei=cai.

e)a\n ku/klou e)pi\ th=s diame/trou lhfqh=| ti shmei=on, o(\ mh/ e)sti ke/ntron tou= ku/klou, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsin eu)qei=ai/ tines, megi/sth me\n e)/stai, e)f' h(=s to\ ke/ntron, e)laxi/sth de\ h( loiph/, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s dia\ tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n, du/o de\ mo/non i)/sai a)po\ tou= shmei/ou prospesou=ntai pro\s to\n ku/klon e)f' e(ka/tera th=s e)laxi/sths.

e)/stw ku/klos o( *a*b*g*d, dia/metros de\ au)tou= e)/stw h( *a*d, kai\ e)pi\ th=s *a*d ei)lh/fqw ti shmei=on to\ *z, o(\ mh/ e)sti ke/ntron tou= ku/klou, ke/ntron de\ tou= ku/klou e)/stw to\ *e, kai\ a)po\ tou= *z pro\s to\n *a*b*g*d ku/klon prospipte/twsan eu)qei=ai/ tines ai( *z*b, *z*g, *z*h: le/gw, o(/ti megi/sth me/n e)stin h( *z*a, e)laxi/sth de\ h( *z*d, tw=n de\

a)/llwn h( me\n *z*b th=s *z*g mei/zwn, h( de\ *z*g th=s *z*h.

e)pezeu/xqwsan ga\r ai( *b*e, *g*e, *h*e. kai\ e)pei\ panto\s trigw/nou ai( du/o pleurai\ th=s loiph=s mei/zone/s ei)sin, ai( a)/ra *e*b, *e*z th=s *b*z mei/zone/s ei)sin. i)/sh de\ h( *a*e th=| *b*e ~~ai( a)/ra *b*e, *e*z i)/sai ei)si\ th=| *a*z~~: mei/zwn a)/ra h( *a*z th=s *b*z. pa/lin, e)pei\ i)/sh e)sti\n h( *b*e th=| *g*e, koinh\ de\ h( *z*e, du/o dh\ ai( *b*e, *e*z dusi\ tai=s *g*e, *e*z i)/sai ei)si/n. a)lla\ kai\ gwni/a h( u(po\ *b*e*z gwni/as th=s u(po\ *g*e*z mei/zwn. ba/sis a)/ra h( *b*z ba/sews th=s *g*z mei/zwn e)sti/n. dia\ ta\ au)ta\ dh\ kai\ h( *g*z th=s *z*h mei/zwn e)sti/n.

pa/lin, e)pei\ ai( *h*z, *z*e th=s *e*h mei/zone/s ei)sin, i)/sh de\ h( *e*h th=| *e*d, ai( a)/ra *h*z, *z*e th=s *e*d mei/zone/s ei)sin. koinh\ a)fh|rh/sqw h( *e*z: loiph\ a)/ra h( *h*z loiph=s th=s *z*d mei/zwn e)sti/n. megi/sth me\n a)/ra h( *z*a, e)laxi/sth de\ h( *z*d, mei/zwn de\ h( me\n *z*b th=s *z*g, h( de\ *z*g th=s *z*h.

le/gw, o(/ti kai\ a)po\ tou= *z shmei/ou du/o mo/non i)/sai prospesou=ntai pro\s to\n *a*b*g*d ku/klon e)f' e(ka/tera th=s *z*d e)laxi/sths. sunesta/tw ga\r pro\s th=| *e*z eu)qei/a| kai\ tw=| pro\s au)th=| shmei/w| tw=| *e th=| u(po\ *h*e*z gwni/a| i)/sh h( u(po\ *z*e*q, kai\ e)pezeu/xqw h( *z*q. e)pei\ ou)=n i)/sh e)sti\n h( *h*e th=| *e*q, koinh\ de\ h( *e*z, du/o dh\ ai( *h*e, *e*z dusi\ tai=s *q*e, *e*z i)/sai ei)si/n: kai\ gwni/a h( u(po\ *h*e*z gwni/a| th=| u(po\ *q*e*z i)/sh: ba/sis a)/ra h( *z*h ba/sei th=| *z*q i)/sh e)sti/n. le/gw dh/, o(/ti th=| *z*h a)/llh i)/sh ou) prospesei=tai pro\s to\n ku/klon a)po\ tou= *z shmei/ou. ei) ga\r dunato/n, prospipte/tw h( *z*k. kai\ e)pei\ h( *z*k th=| *z*h i)/sh e)sti/n, a)lla\ h( *z*q th=| *z*h ~~i)/sh e)sti/n~~, kai\ h( *z*k a)/ra th=| *z*q e)stin i)/sh, h( e)/ggion th=s dia\ tou= ke/ntrou th=| a)pw/teron i)/sh: o(/per a)du/naton. ou)k a)/ra a)po\ tou= *z shmei/ou e(te/ra tis prospesei=tai pro\s to\n ku/klon i)/sh th=| *h*z: mi/a a)/ra mo/nh.

e)a\n a)/ra ku/klou e)pi\ th=s diame/trou lhfqh=| ti shmei=on, o(\ mh/ e)sti ke/ntron tou= ku/klou, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsin eu)qei=ai/ tines, megi/sth me\n e)/stai, e)f' h(=s to\ ke/ntron, e)laxi/sth de\ h( loiph/, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s dia\ tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n, du/o de\ mo/non i)/sai a)po\ tou= au)tou= shmei/ou prospesou=ntai pro\s to\n ku/klon e)f' e(ka/tera th=s e)laxi/sths: o(/per e)/dei dei=cai.

e)a\n ku/klou lhfqh=| ti shmei=on e)kto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon diaxqw=sin eu)qei=ai/ tines, w(=n mi/a me\n dia\ tou= ke/ntrou, ai( de\ loipai/, w(s e)/tuxen, tw=n me\n pro\s th\n koi/lhn perife/reian prospiptousw=n eu)qeiw=n megi/sth me/n e)stin h( dia\ tou= ke/ntrou, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s dia\ tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n, tw=n de\ pro\s th\n kurth\n perife/reian prospiptousw=n eu)qeiw=n e)laxi/sth me/n e)stin h( metacu\ tou= te shmei/ou kai\ th=s diame/trou, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s e)laxi/sths

th=s a)pw/tero/n e)stin e)la/ttwn, du/o de\ mo/non i)/sai a)po\ tou= shmei/ou prospesou=ntai pro\s to\n ku/klon e)f' e(ka/tera th=s e)laxi/sths.

e)/stw ku/klos o( *a*b*g, kai\ tou= *a*b*g ei)lh/fqw ti shmei=on e)kto\s to\ *d, kai\ a)p' au)tou= dih/xqwsan eu)qei=ai/ tines ai( *d*a, *d*e, *d*z, *d*g, e)/stw de\ h( *d*a dia\ tou= ke/ntrou. le/gw, o(/ti tw=n me\n pro\s th\n *a*e*z*g koi/lhn perife/reian prospiptousw=n eu)qeiw=n megi/sth me/n e)stin h( dia\ tou= ke/ntrou h( *d*a, mei/zwn de\ h( me\n *d*e th=s *d*z h( de\ *d*z th=s *d*g, tw=n de\ pro\s th\n *q*l*k*h kurth\n perife/reian prospiptousw=n eu)qeiw=n e)laxi/sth me/n e)stin h( *d*h h( metacu\ tou= shmei/ou kai\ th=s diame/trou th=s *a*h, a)ei\ de\ h( e)/ggion th=s *d*h e)laxi/sths e)la/ttwn e)sti\ th=s a)pw/teron, h( me\n *d*k th=s *d*l, h( de\ *d*l th=s *d*q.

ei)lh/fqw ga\r to\ ke/ntron tou= *a*b*g ku/klou kai\ e)/stw to\ *m: kai\ e)pezeu/xqwsan ai( *m*e, *m*z, *m*g, *m*k, *m*l, *m*q.

kai\ e)pei\ i)/sh e)sti\n h( *a*m th=| *e*m, koinh\ proskei/sqw h( *m*d: h( a)/ra *a*d i)/sh e)sti\ tai=s *e*m, *m*d. a)ll' ai( *e*m, *m*d th=s *e*d mei/zone/s ei)sin: kai\ h( *a*d a)/ra th=s *e*d mei/zwn e)sti/n. pa/lin, e)pei\ i)/sh e)sti\n h( *m*e th=| *m*z, koinh\ de\ h( *m*d, ai( *e*m, *m*d a)/ra tai=s *z*m, *m*d i)/sai ei)si/n: kai\ gwni/a h( u(po\ *e*m*d gwni/as th=s u(po\ *z*m*d mei/zwn e)sti/n. ba/sis a)/ra h( *e*d ba/sews th=s *z*d mei/zwn e)sti/n. o(moi/ws dh\ dei/comen, o(/ti kai\ h( *z*d th=s *g*d mei/zwn e)sti/n: megi/sth me\n a)/ra h( *d*a, mei/zwn de\ h( me\n *d*e th=s *d*z, h( de\ *d*z th=s *d*g.

kai\ e)pei\ ai( *m*k, *k*d th=s *m*d mei/zone/s ei)sin, i)/sh de\ h( *m*h th=| *m*k, loiph\ a)/ra h( *k*d loiph=s th=s *h*d mei/zwn e)sti/n: w(/ste h( *h*d th=s *k*d e)la/ttwn e)sti/n: kai\ e)pei\ trigw/nou tou= *m*l*d e)pi\ mia=s tw=n pleurw=n th=s *m*d du/o eu)qei=ai e)nto\s sunesta/qhsan ai( *m*k, *k*d, ai( a)/ra *m*k, *k*d tw=n *m*l, *l*d e)la/ttone/s ei)sin: i)/sh de\ h( *m*k th=| *m*l: loiph\ a)/ra h( *d*k loiph=s th=s *d*l e)la/ttwn e)sti/n. o(moi/ws dh\ dei/comen, o(/ti kai\ h( *d*l th=s *d*q e)la/ttwn e)sti/n: e)laxi/sth me\n a)/ra h( *d*h, e)la/ttwn de\ h( me\n *d*k th=s *d*l h( de\ *d*l th=s *d*q.

le/gw, o(/ti kai\ du/o mo/non i)/sai a)po\ tou= *d shmei/ou prospesou=ntai pro\s to\n ku/klon e)f' e(ka/tera th=s *d*h e)laxi/sths: sunesta/tw pro\s th=| *m*d eu)qei/a| kai\ tw=| pro\s au)th=| shmei/w| tw=| *m th=| u(po\ *k*m*d gwni/a| i)/sh gwni/a h( u(po\ *d*m*b kai\ e)pezeu/xqw h( *d*b. kai\ e)pei\ i)/sh e)sti\n h( *m*k th=| *m*b, koinh\ de\ h( *m*d, du/o dh\ ai( *k*m, *m*d du/o tai=s *b*m, *m*d i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *k*m*d gwni/a| th=| u(po\ *b*m*d i)/sh: ba/sis a)/ra h( *d*k ba/sei th=| *d*b i)/sh e)sti/n. le/gw ~~dh/~~, o(/ti th=| *d*k eu)qei/a| a)/llh i)/sh ou) prospesei=tai pro\s to\n ku/klon a)po\ tou= *d shmei/ou. ei) ga\r dunato/n, prospipte/tw kai\ e)/stw h( *d*n. e)pei\ ou)=n h( *d*k th=| *d*n e)stin i)/sh, a)ll' h( *d*k th=| *d*b e)stin i)/sh, kai\ h( *d*b a)/ra th=| *d*n e)stin i)/sh, h( e)/ggion th=s *d*h e)laxi/sths th=| a)pw/teron ~~e)stin~~ i)/sh: o(/per a)du/naton e)dei/xqh. ou)k a)/ra plei/ous h)\ du/o i)/sai pro\s to\n *a*b*g ku/klon a)po\ tou= *d shmei/ou e)f' e(ka/tera th=s *d*h e)laxi/sths prospesou=ntai.

e)a\n a)/ra ku/klou lhfqh=| ti shmei=on e)kto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon diaxqw=sin eu)qei=ai/ tines, w(=n mi/a me\n dia\ tou= ke/ntrou ai( de\ loipai/, w(s e)/tuxen, tw=n me\n pro\s th\n koi/lhn perife/reian prospiptousw=n eu)qeiw=n megi/sth me/n e)stin h( dia\ tou= ke/ntrou, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s dia\ tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n, tw=n de\ pro\s th\n kurth\n perife/reian prospiptousw=n eu)qeiw=n e)laxi/sth me/n e)stin h( metacu\ tou= te shmei/ou kai\ th=s diame/trou, tw=n de\ a)/llwn a)ei\ h( e)/ggion th=s e)laxi/sths th=s a)pw/tero/n e)stin e)la/ttwn, du/o de\ mo/non i)/sai a)po\ tou= shmei/ou prospesou=ntai pro\s to\n ku/klon e)f' e(ka/tera th=s e)laxi/sths: o(/per e)/dei dei=cai.

e)a\n ku/klou lhfqh=| ti shmei=on e)nto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsi plei/ous h)\ du/o i)/sai eu)qei=ai, to\ lhfqe\n shmei=on ke/ntron e)sti\ tou= ku/klou.

e)/stw ku/klos o( *a*b*g, e)nto\s de\ au)tou= shmei=on to\ *d, kai\ a)po\ tou= *d pro\s to\n *a*b*g ku/klon prospipte/twsan plei/ous h)\ du/o i)/sai eu)qei=ai ai( *d*a,

*d*b, *d*g: le/gw, o(/ti to\ *d shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou.

e)pezeu/xqwsan ga\r ai( *a*b, *b*g kai\ tetmh/sqwsan di/xa kata\ ta\ *e, *z shmei=a, kai\ e)pizeuxqei=sai ai( *e*d, *z*d dih/xqwsan e)pi\ ta\ *h, *k, *q, *l shmei=a.

e)pei\ ou)=n i)/sh e)sti\n h( *a*e th=| *e*b, koinh\ de\ h( *e*d, du/o dh\ ai( *a*e, *e*d du/o tai=s *b*e, *e*d i)/sai ei)si/n: kai\ ba/sis h( *d*a ba/sei th=| *d*b i)/sh: gwni/a a)/ra h( u(po\ *a*e*d gwni/a| th=| u(po\ *b*e*d i)/sh e)sti/n: o)rqh\ a)/ra e(kate/ra tw=n u(po\ *a*e*d, *b*e*d gwniw=n: h( *h*k a)/ra th\n *a*b te/mnei di/xa kai\ pro\s o)rqa/s. kai\ e)pei/, e)a\n e)n ku/klw| eu)qei=a/ tis eu)qei=a/n tina di/xa te kai\ pro\s o)rqa\s te/mnh|, e)pi\ th=s temnou/shs e)sti\ to\ ke/ntron tou= ku/klou, e)pi\ th=s *h*k a)/ra e)sti\ to\ ke/ntron tou= ku/klou. dia\ ta\ au)ta\ dh\ kai\ e)pi\ th=s *q*l e)sti to\ ke/ntron tou= *a*b*g ku/klou. kai\ ou)de\n e(/teron koino\n e)/xousin ai( *h*k, *q*l eu)qei=ai h)\ to\ *d shmei=on: to\ *d a)/ra shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou.

e)a\n a)/ra ku/klou lhfqh=| ti shmei=on e)nto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsi plei/ous h)\ du/o i)/sai eu)qei=ai, to\ lhfqe\n shmei=on ke/ntron e)sti\ tou= ku/klou: o(/per e)/dei dei=cai.

ku/klos ku/klon ou) te/mnei kata\ plei/ona shmei=a h)\ du/o.

ei) ga\r dunato/n, ku/klos o( *a*b*g ku/klon to\n *d*e*z temne/tw kata\ plei/ona shmei=a h)\ du/o ta\ *b, *h, *z, *q, kai\ e)pizeuxqei=sai ai( *b*q, *b*h di/xa temne/sqwsan kata\ ta\ k, *l shmei=a: kai\ a)po\ tw=n *k, *l tai=s *b*q, *b*h pro\s o)rqa\s a)xqei=sai ai( *k*g, *l*m dih/xqwsan e)pi\ ta\ *a, *e shmei=a.

e)pei\ ou)=n e)n ku/klw| tw=|

*a*b*g eu)qei=a/ tis h( *a*g eu)qei=a/n tina th\n *b*q di/xa kai\ pro\s o)rqa\s te/mnei, e)pi\ th=s *a*g a)/ra e)sti\ to\ ke/ntron tou= *a*b*g ku/klou. pa/lin, e)pei\ e)n ku/klw| tw=| au)tw=| tw=| *a*b*g eu)qei=a/ tis h( *n*c eu)qei=a/n tina th\n *b*h di/xa kai\ pro\s o)rqa\s te/mnei, e)pi\ th=s *n*c a)/ra e)sti\ to\ ke/ntron tou= *a*b*g ku/klou. e)dei/xqh de\ kai\ e)pi\ th=s *a*g, kai\ kat' ou)de\n sumba/llousin ai( *a*g, *n*c eu)qei=ai h)\ kata\ to\ *o: to\ *o a)/ra shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou. o(moi/ws dh\ dei/comen, o(/ti kai\ tou= *d*e*z ku/klou ke/ntron e)sti\ to\ *o: du/o a)/ra ku/klwn temno/ntwn a)llh/lous tw=n *a*b*g, *d*e*z to\ au)to/ e)sti ke/ntron to\ *o: o(/per e)sti\n a)du/naton.

ou)k a)/ra ku/klos ku/klon te/mnei kata\ plei/ona shmei=a h)\ du/o: o(/per e)/dei dei=cai.

e)a\n du/o ku/kloi e)fa/ptwntai a)llh/lwn e)nto/s, kai\ lhfqh=| au)tw=n ta\ ke/ntra, h( e)pi\ ta\ ke/ntra au)tw=n e)pizeugnume/nh eu)qei=a kai\ e)kballome/nh e)pi\ th\n sunafh\n pesei=tai tw=n ku/klwn.

du/o ga\r ku/kloi oi( *a*b*g, *a*d*e e)fapte/sqwsan a)llh/lwn e)nto\s kata\ to\ *a shmei=on, kai\ ei)lh/fqw tou= me\n *a*b*g ku/klou ke/ntron to\ *z, tou= de\ *a*d*e to\ *h: le/gw, o(/ti h( a)po\ tou= *h e)pi\ to\ *z e)pizeugnume/nh eu)qei=a e)kballome/nh e)pi\ to\ *a pesei=tai.

mh\ ga/r, a)ll' ei) dunato/n, pipte/tw w(s h( *z*h*q, kai\ e)pezeu/xqwsan ai( *a*z, *a*h.

e)pei\ ou)=n ai( *a*h, *h*z th=s *z*a, toute/sti th=s *z*q, mei/zone/s ei)sin, koinh\ a)fh|rh/sqw h( *z*h: loiph\ a)/ra h( *a*h loiph=s th=s *h*q mei/zwn e)sti/n. i)/sh de\ h( *a*h th=| *h*d: kai\

h( *h*d a)/ra th=s *h*q mei/zwn e)sti\n h( e)la/ttwn th=s mei/zonos: o(/per e)sti\n a)du/naton: ou)k a)/ra h( a)po\ tou= *z e)pi\ to\ *h e)pizeugnume/nh eu)qei=a e)kto\s pesei=tai: kata\ to\ *a a)/ra e)pi\ th=s sunafh=s pesei=tai.

e)a\n a)/ra du/o ku/kloi e)fa/ptwntai a)llh/lwn e)nto/s, ~~kai\ lhfqh=| au)tw=n ta\ ke/ntra~~, h( e)pi\ ta\ ke/ntra au)tw=n e)pizeugnume/nh eu)qei=a ~~kai\ e)kballome/nh~~ e)pi\ th\n sunafh\n pesei=tai tw=n ku/klwn: o(/per e)/dei dei=cai.

e)a\n du/o ku/kloi e)fa/ptwntai a)llh/lwn e)kto/s, h( e)pi\ ta\ ke/ntra au)tw=n e)pizeugnume/nh dia\ th=s e)pafh=s e)leu/setai.

du/o ga\r ku/kloi oi( *a*b*g, *a*d*e e)fapte/sqwsan a)llh/lwn e)kto\s kata\ to\ *a shmei=on, kai\ ei)lh/fqw tou= me\n *a*b*g ke/ntron to\ *z, tou= de\ *a*d*e to\ *h: le/gw, o(/ti h( a)po\ tou= *z e)pi\ to\ *h e)pizeugnume/nh eu)qei=a dia\ th=s kata\ to\ *a e)pafh=s e)leu/setai.

mh\ ga/r, a)ll' ei) dunato/n, e)rxe/sqw w(s h( *z*g*d*h, kai\ e)pezeu/xqwsan ai( *a*z, *a*h.

e)pei\ ou)=n to\ *z shmei=on ke/ntron e)sti\ tou= *a*b*g ku/klou, i)/sh e)sti\n h( *z*a th=| *z*g. pa/lin, e)pei\ to\ *h shmei=on ke/ntron e)sti\ tou= *a*d*e ku/klou, i)/sh e)sti\n h( *h*a

th=| *h*d. e)dei/xqh de\ kai\ h( *z*a th=| *z*g i)/sh: ai( a)/ra *z*a, *a*h tai=s *z*g, *h*d i)/sai ei)si/n: w(/ste o(/lh h( *z*h tw=n *z*a, *a*h mei/zwn e)sti/n: a)lla\ kai\ e)la/ttwn: o(/per e)sti\n a)du/naton. ou)k a)/ra h( a)po\ tou= *z e)pi\ to\ *h e)pizeugnume/nh eu)qei=a dia\ th=s kata\ to\ *a e)pafh=s ou)k e)leu/setai: di' au)th=s a)/ra.

e)a\n a)/ra du/o ku/kloi e)fa/ptwntai a)llh/lwn e)kto/s, h( e)pi\ ta\ ke/ntra au)tw=n e)pizeugnume/nh ~~eu)qei=a~~ dia\ th=s e)pafh=s e)leu/setai: o(/per e)/dei dei=cai.

ku/klos ku/klou ou)k e)fa/ptetai kata\ plei/ona shmei=a h)\ kaq' e(/n, e)a/n te e)nto\s e)a/n te e)kto\s e)fa/pthtai.

ei) ga\r dunato/n, ku/klos o( *a*b*g*d ku/klou tou= *e*b*z*d e)fapte/sqw pro/teron e)nto\s kata\ plei/ona shmei=a h)\ e(\n ta\ d, *b.

kai\ ei)lh/fqw tou= me\n *a*b*g*d ku/klou ke/ntron to\ *h, tou= de\ *e*b*z*d to\ *q.

h( a)/ra a)po\ tou= *h e)pi\ to\ *q e)pizeugnume/nh e)pi\ ta\ *b, *d pesei=tai. pipte/tw w(s h( *b*h*q*d. kai\ e)pei\ to\ *h shmei=on ke/ntron e)sti\ tou= *a*b*g*d ku/klou, i)/sh e)sti\n h( *b*h th=| *h*d:

mei/zwn a)/ra h( *b*h th=s *q*d: pollw=| a)/ra mei/zwn h( *b*q th=s *q*d. pa/lin, e)pei\ to\ *q shmei=on ke/ntron e)sti\ tou= *e*b*z*d ku/klou, i)/sh e)sti\n h( *b*q th=| *q*d: e)dei/xqh de\ au)th=s kai\ pollw=| mei/zwn: o(/per a)du/naton: ou)k a)/ra ku/klos ku/klou e)fa/ptetai e)nto\s kata\ plei/ona shmei=a h)\ e(/n.

le/gw dh/, o(/ti ou)de\ e)kto/s.

ei) ga\r dunato/n, ku/klos o( *a*g*k ku/klou tou= *a*b*g*d e)fapte/sqw e)kto\s kata\ plei/ona shmei=a h)\ e(\n ta\ *a, *g, kai\ e)pezeu/xqw h( *a*g.

e)pei\ ou)=n ku/klwn tw=n *a*b*g*d, *a*g*k ei)/lhptai e)pi\ th=s periferei/as e(kate/rou du/o tuxo/nta shmei=a ta\ *a, *g, h( e)pi\ ta\ shmei=a e)pizeugnume/nh eu)qei=a e)nto\s e(kate/rou pesei=tai: a)lla\ tou= me\n *a*b*g*d e)nto\s e)/pesen, tou= de\ *a*g*k e)kto/s: o(/per a)/topon: ou)k a)/ra ku/klos ku/klou e)fa/ptetai e)kto\s kata\ plei/ona shmei=a h)\ e(/n. e)dei/xqh de/, o(/ti ou)de\ e)nto/s.

ku/klos a)/ra ku/klou ou)k e)fa/ptetai kata\ plei/ona shmei=a h)\ ~~kaq'~~ e(/n, e)a/n te e)nto\s e)a/n te e)kto\s e)fa/pthtai: o(/per e)/dei dei=cai.

e)n ku/klw| ai( i)/sai eu)qei=ai i)/son a)pe/xousin a)po\ tou= ke/ntrou, kai\ ai( i)/son a)pe/xousai a)po\ tou= ke/ntrou i)/sai a)llh/lais ei)si/n.

e)/stw ku/klos o( *a*b*g*d, kai\ e)n au)tw=| i)/sai eu)qei=ai e)/stwsan ai( *a*b, *g*d: le/gw, o(/ti ai( *a*b, *g*d i)/son a)pe/xousin a)po\ tou= ke/ntrou.

ei)lh/fqw ga\r to\ ke/ntron tou= *a*b*g*d ku/klou kai\ e)/stw to\ *e, kai\ a)po\ tou= *e e)pi\ ta\s *a*b, *g*d ka/qetoi h)/xqwsan ai( *e*z, *e*h, kai\ e)pezeu/xqwsan ai( *a*e, *e*g.

e)pei\ ou)=n eu)qei=a/ tis dia\ tou= ke/ntrou h( *e*z eu)qei=a/n tina mh\ dia\ tou= ke/ntrou th\n *a*b pro\s o)rqa\s te/mnei, kai\ di/xa

au)th\n te/mnei. i)/sh a)/ra h( *a*z th=| *z*b: diplh= a)/ra h( *a*b th=s *a*z. dia\ ta\ au)ta\ dh\ kai\ h( *g*d th=s *g*h e)sti diplh=: kai/ e)stin i)/sh h( *a*b th=| *g*d: i)/sh a)/ra kai\ h( *a*z th=| *g*h. kai\ e)pei\ i)/sh e)sti\n h( *a*e th=| *e*g, i)/son kai\ to\ a)po\ th=s *a*e tw=| a)po\ th=s *e*g. a)lla\ tw=| me\n a)po\ th=s *a*e i)/sa ta\ a)po\ tw=n *a*z, *e*z: o)rqh\ ga\r h( pro\s tw=| *z gwni/a: tw=| de\ a)po\ th=s *e*g i)/sa ta\ a)po\ tw=n *e*h, *h*g: o)rqh\ ga\r h( pro\s tw=| *h gwni/a: ta\ a)/ra a)po\ tw=n *a*z, *z*e i)/sa e)sti\ toi=s a)po\ tw=n *g*h, *h*e, w(=n to\ a)po\ th=s *a*z i)/son e)sti\ tw=| a)po\ th=s *g*h: i)/sh ga/r e)stin h( *a*z th=| *g*h: loipo\n a)/ra to\ a)po\ th=s *z*e tw=| a)po\ th=s *e*h i)/son e)sti/n: i)/sh a)/ra h( *e*z th=| *e*h. e)n de\ ku/klw| i)/son a)pe/xein a)po\ tou= ke/ntrou eu)qei=ai le/gontai, o(/tan ai( a)po\ tou= ke/ntrou e)p' au)ta\s ka/qetoi a)go/menai i)/sai w)=sin: ai( a)/ra *a*b, *g*d i)/son a)pe/xousin a)po\ tou= ke/ntrou.

a)lla\ dh\ ai( *a*b, *g*d eu)qei=ai i)/son a)pexe/twsan a)po\ tou= ke/ntrou, toute/stin i)/sh e)/stw h( *e*z th=| *e*h. le/gw, o(/ti i)/sh e)sti\ kai\ h( *a*b th=| *g*d.

tw=n ga\r au)tw=n kataskeuasqe/ntwn o(moi/ws dei/comen, o(/ti diplh= e)stin h( me\n *a*b th=s *a*z, h( de\ *g*d th=s *g*h: kai\ e)pei\ i)/sh e)sti\n h( *a*e th=| *g*e, i)/son e)sti\ to\ a)po\ th=s *a*e tw=| a)po\ th=s *g*e: a)lla\ tw=| me\n a)po\ th=s *a*e i)/sa e)sti\ ta\ a)po\ tw=n *e*z, *z*a, tw=| de\ a)po\ th=s *g*e i)/sa ta\ a)po\ tw=n *e*h, *h*g. ta\ a)/ra a)po\ tw=n *e*z, *z*a i)/sa e)sti\ toi=s a)po\ tw=n *e*h, *h*g: w(=n to\ a)po\ th=s *e*z tw=| a)po\ th=s *e*h e)stin i)/son: i)/sh ga\r h( *e*z th=| *e*h: loipo\n a)/ra to\ a)po\ th=s *a*z i)/son e)sti\ tw=| a)po\ th=s *g*h: i)/sh a)/ra h( *a*z th=| *g*h: kai/ e)sti th=s me\n *a*z diplh= h( *a*b, th=s de\ *g*h diplh= h( *g*d: i)/sh a)/ra h( *a*b th=| *g*d.

e)n ku/klw| a)/ra ai( i)/sai eu)qei=ai i)/son a)pe/xousin a)po\ tou= ke/ntrou, kai\ ai( i)/son a)pe/xousai a)po\ tou= ke/ntrou i)/sai a)llh/lais ei)si/n: o(/per e)/dei dei=cai.

e)n ku/klw| megi/sth me\n h( dia/metros tw=n de\ a)/llwn a)ei\ h( e)/ggion tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n.

e)/stw ku/klos o( *a*b*g*d, dia/metros de\ au)tou= e)/stw h( *a*d, ke/ntron de\ to\ *e, kai\ e)/ggion me\n th=s *a*d diame/trou e)/stw h( *b*g, a)pw/teron de\ h( *z*h: le/gw, o(/ti megi/sth me/n e)stin h( *a*d, mei/zwn de\ h( *b*g th=s *z*h.

h)/xqwsan ga\r a)po\ tou= *e ke/ntrou e)pi\ ta\s *b*g, *z*h ka/qetoi ai( *e*q, *e*k. kai\ e)pei\ e)/ggion me\n tou= ke/ntrou e)sti\n h( *b*g, a)pw/teron de\ h( *z*h, mei/zwn a)/ra h( *e*k th=s *e*q. kei/sqw th=| *e*q i)/sh h( *e*l, kai\ dia\ tou= *l th=| *e*k pro\s o)rqa\s a)xqei=sa h( *l*m dih/xqw e)pi\ to\ *n, kai\ e)pezeu/xqwsan ai( *m*e, *e*n, *z*e, *e*h.

kai\ e)pei\ i)/sh e)sti\n h( *e*q th=| *e*l, i)/sh e)sti\ kai\ h( *b*g th=| *m*n. pa/lin, e)pei\ i)/sh e)sti\n h( me\n *a*e th=| *e*m, h( de\ *e*d

th=| *e*n, h( a)/ra *a*d tai=s *m*e, *e*n i)/sh e)sti/n. a)ll' ai( me\n *m*e, *e*n th=s *m*n mei/zone/s ei)sin [kai\ h( *a*d th=s *m*n mei/zwn e)sti/n, i)/sh de\ h( *m*n th=| *b*g: h( *a*d a)/ra th=s *b*g mei/zwn e)sti/n. kai\ e)pei\ du/o ai( *m*e, *e*n du/o tai=s *z*e, *e*h i)/sai ei)si/n, kai\ gwni/a h( u(po\ *m*e*n gwni/as th=s u(po\ *z*e*h mei/zwn ~~e)sti/n~~, ba/sis a)/ra h( *m*n ba/sews th=s *z*h mei/zwn e)sti/n. a)lla\ h( *m*n th=| *b*g e)dei/xqh i)/sh ~~kai\ h( *b*g th=s *z*h mei/zwn e)sti/n~~. megi/sth me\n a)/ra h( *a*d dia/metros, mei/zwn de\ h( *b*g th=s *z*h.

e)n ku/klw| a)/ra megi/sth me/n e)stin h( dia/metros, tw=n de\ a)/llwn a)ei\ h( e)/ggion tou= ke/ntrou th=s a)pw/teron mei/zwn e)sti/n: o(/per e)/dei dei=cai.

h( th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)kto\s pesei=tai tou= ku/klou, kai\ ei)s to\n metacu\ to/pon th=s te eu)qei/as kai\ th=s periferei/as e(te/ra eu)qei=a ou) parempesei=tai, kai\ h( me\n tou= h(mikukli/ou gwni/a a(pa/shs gwni/as o)cei/as eu)qugra/mmou mei/zwn e)sti/n, h( de\ loiph\ e)la/ttwn.

e)/stw ku/klos o( *a*b*g peri\ ke/ntron to\ *d kai\ dia/metron th\n *a*b: le/gw, o(/ti h( a)po\ tou= *a th=| *a*b pro\s o)rqa\s a)p' a)/kras a)gome/nh e)kto\s pesei=tai tou=

ku/klou.

mh\ ga/r, a)ll' ei) dunato/n, pipte/tw e)nto\s w(s h( *g*a, kai\ e)pezeu/xqw h( *d*g.

e)pei\ i)/sh e)sti\n h( *d*a th=| *d*g, i)/sh e)sti\ kai\ gwni/a h( u(po\ *d*a*g gwni/a| th=| u(po\ *a*g*d. o)rqh\ de\ h( u(po\ *d*a*g: o)rqh\ a)/ra kai\ h( u(po\ *a*g*d: trigw/nou dh\ tou= *a*g*d ai( du/o gwni/ai ai( u(po\ *d*a*g, *a*g*d du/o o)rqai=s i)/sai ei)si/n: o(/per e)sti\n a)du/naton. ou)k a)/ra h( a)po\ tou= *a shmei/ou th=| *b*a pro\s o)rqa\s a)gome/nh e)nto\s pesei=tai tou= ku/klou. o(moi/ws dh\ dei/comen, o(/ti ou)d' e)pi\ th=s periferei/as: e)kto\s a)/ra.

pipte/tw w(s h( *a*e: le/gw dh/, o(/ti ei)s to\n metacu\ to/pon th=s te *a*e eu)qei/as kai\ th=s *g*q*a periferei/as e(te/ra eu)qei=a ou) parempesei=tai.

ei) ga\r dunato/n, parempipte/tw w(s h( *z*a, kai\ h)/xqw a)po\ tou= *d shmei/ou e)pi\ th\n *z*a ka/qetos h( *d*h. kai\ e)pei\ o)rqh/ e)stin h( u(po\ *a*h*d, e)la/ttwn de\ o)rqh=s h( u(po\ *d*a*h, mei/zwn a)/ra h( *a*d th=s *d*h. i)/sh de\ h( *d*a th=| *d*q: mei/zwn a)/ra h( *d*q th=s *d*h, h( e)la/ttwn th=s mei/zonos: o(/per e)sti\n a)du/naton. ou)k a)/ra ei)s to\n metacu\ to/pon th=s te eu)qei/as kai\ th=s periferei/as e(te/ra eu)qei=a parempesei=tai.

le/gw, o(/ti kai\ h( me\n tou= h(mikukli/ou gwni/a h( periexome/nh u(po/ te th=s *b*a eu)qei/as kai\ th=s *g*q*a periferei/as a(pa/shs gwni/as o)cei/as eu)qugra/mmou mei/zwn e)sti/n, h( de\ loiph\ h( periexome/nh u(po/ te th=s *g*q*a periferei/as kai\ th=s *a*e eu)qei/as a(pa/shs gwni/as o)cei/as eu)qugra/mmou e)la/ttwn e)sti/n.

ei) ga\r e)sti/ tis gwni/a eu)qu/grammos mei/zwn me\n th=s periexome/nhs u(po/ te th=s *b*a eu)qei/as kai\ th=s *g*q*a periferei/as, e)la/ttwn de\ th=s periexome/nhs u(po/ te th=s *g*q*a periferei/as kai\ th=s *a*e eu)qei/as, ei)s to\n metacu\ to/pon th=s te *g*q*a periferei/as kai\ th=s *a*e eu)qei/as eu)qei=a perempesei=tai, h(/tis poih/sei mei/zona me\n th=s periexome/nhs u(po/ te th=s *b*a eu)qei/as kai\ th=s *g*q*a periferei/as u(po\ eu)qeiw=n periexome/nhn, e)la/ttona de\ th=s periexome/nhs u(po/ te th=s *g*q*a periferei/as kai\ th=s *a*e eu)qei/as. ou) parempi/ptei de/: ou)k a)/ra th=s periexome/nhs gwni/as u(po/ te th=s *b*a eu)qei/as kai\ th=s *g*q*a periferei/as e)/stai mei/zwn o)cei=a u(po\ eu)qeiw=n periexome/nh, ou)de\ mh\n e)la/ttwn th=s periexome/nhs u(po/ te th=s *g*q*a periferei/as kai\ th=s *a*e eu)qei/as.

*po/risma

e)k dh\ tou/tou fanero/n, o(/ti h( th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)fa/ptetai tou= ku/klou ~~kai\ o(/ti eu)qei=a ku/klou kaq' e(\n mo/non e)fa/ptetai shmei=on, e)peidh/per kai\ h( kata\ du/o au)tw=| sumba/llousa e)nto\s au)tou= pi/ptousa e)dei/xqh~~. o(/per e)/dei dei=cai.

a)po\ tou= doqe/ntos shmei/ou tou= doqe/ntos ku/klou e)faptome/nhn eu)qei=an grammh\n a)gagei=n.

e)/stw to\ me\n doqe\n shmei=on to\ *a, o( de\ doqei\s ku/klos o( *b*g*d: dei= dh\ a)po\ tou= *a shmei/ou tou= *b*g*d ku/klou e)faptome/nhn eu)qei=an grammh\n a)gagei=n.

ei)lh/fqw ga\r to\ ke/ntron tou= ku/klou to\ *e, kai\ e)pezeu/xqw h( *a*e, kai\ ke/ntrw| me\n tw=| *e diasth/mati de\ tw=| *e*a ku/klos gegra/fqw o( *a*z*h, kai\ a)po\ tou= *d th=| *e*a pro\s o)rqa\s h)/xqw h( *d*z, kai\ e)pezeu/xqwsan ai( *e*z, *a*b: le/gw, o(/ti a)po\ tou= *a shmei/ou tou= *b*g*d ku/klou e)faptome/nh h)=ktai h( *a*b.

e)pei\ ga\r to\ *e ke/ntron e)sti\ tw=n *b*g*d, *a*z*h ku/klwn, i)/sh a)/ra e)sti\n h( me\n *e*a th=| *e*z, h( de\ *e*d th=| *e*b: du/o

dh\ ai( *a*e, *e*b du/o tai=s *z*e, *e*d i)/sai ei)si/n: kai\ gwni/an koinh\n perie/xousi th\n pro\s tw=| *e: ba/sis a)/ra h( *d*z ba/sei th=| *a*b i)/sh e)sti/n, kai\ to\ *d*e*z tri/gwnon tw=| *e*b*a trigw/nw| i)/son e)sti/n, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais: i)/sh a)/ra h( u(po\ *e*d*z th=| u(po\ *e*b*a. o)rqh\ de\ h( u(po\ *e*d*z: o)rqh\ a)/ra kai\ h( u(po\ *e*b*a. kai/ e)stin h( *e*b e)k tou= ke/ntrou: h( de\ th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)fa/ptetai tou= ku/klou: h( *a*b a)/ra e)fa/ptetai tou= *b*g*d ku/klou.

a)po\ tou= a)/ra doqe/ntos shmei/ou tou= *a tou= doqe/ntos ku/klou tou= *b*g*d e)faptome/nh eu)qei=a grammh\ h)=ktai h( *a*b: o(/per e)/dei poih=sai.

e)a\n ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ tou= ke/ntrou e)pi\ th\n a(fh\n e)pizeuxqh=| tis eu)qei=a, h( e)pizeuxqei=sa ka/qetos e)/stai e)pi\ th\n e)faptome/nhn.

ku/klou ga\r tou= *a*b*g e)fapte/sqw tis eu)qei=a h( *d*e kata\ to\ *g shmei=on, kai\ ei)lh/fqw to\ ke/ntron tou= *a*b*g ku/klou to\ *z, kai\ a)po\ tou= *z e)pi\ to\ *g e)pezeu/xqw h( *z*g: le/gw, o(/ti h( *z*g ka/qeto/s e)stin e)pi\ th\n *d*e.

ei) ga\r mh/, h)/xqw a)po\ tou= *z e)pi\ th\n *d*e ka/qetos h( *z*h.

e)pei\ ou)=n h( u(po\ *z*h*g gwni/a o)rqh/ e)stin, o)cei=a a)/ra e)sti\n h( u(po\ *z*g*h: u(po\ de\ th\n mei/zona gwni/an h( mei/zwn pleura\ u(potei/nei: mei/zwn a)/ra h(

*z*g th=s *z*h: i)/sh de\ h( *z*g th=| *z*b: mei/zwn a)/ra kai\ h( *z*b th=s *z*h h( e)la/ttwn th=s mei/zonos: o(/per e)sti\n a)du/naton. ou)k a)/ra h( *z*h ka/qeto/s e)stin e)pi\ th\n *d*e. o(moi/ws dh\ dei/comen, o(/ti ou)d' a)/llh tis plh\n th=s *z*g: h( *z*g a)/ra ka/qeto/s e)stin e)pi\ th\n *d*e.

e)a\n a)/ra ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ tou= ke/ntrou e)pi\ th\n a(fh\n e)pizeuxqh=| tis eu)qei=a, h( e)pizeuxqei=sa ka/qetos e)/stai e)pi\ th\n e)faptome/nhn: o(/per e)/dei dei=cai.

e)a\n ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ th=s a(fh=s th=| e)faptome/nh| pro\s o)rqa\s ~~gwni/as~~ eu)qei=a grammh\ a)xqh=|, e)pi\ th=s a)xqei/shs e)/stai to\ ke/ntron tou= ku/klou.

ku/klou ga\r tou= *a*b*g e)fapte/sqw tis eu)qei=a h( *d*e kata\ to\ *g shmei=on, kai\ a)po\ tou= *g th=| *d*e pro\s o)rqa\s h)/xqw h( *g*a: le/gw, o(/ti e)pi\ th=s *a*g e)sti to\ ke/ntron tou= ku/klou.

mh\ ga/r, a)ll' ei) dunato/n, e)/stw to\ *z, kai\ e)pezeu/xqw h( *g*z.

e)pei\ ~~ou)=n~~ ku/klou tou= *a*b*g e)fa/ptetai/ tis eu)qei=a h( *d*e, a)po\ de\ tou= ke/ntrou e)pi\ th\n a(fh\n e)pe/zeuktai h( *z*g,

h( *z*g a)/ra ka/qeto/s e)stin e)pi\ th\n *d*e: o)rqh\ a)/ra e)sti\n h( u(po\ *z*g*e. e)sti\ de\ kai\ h( u(po\ *a*g*e o)rqh/: i)/sh a)/ra e)sti\n h( u(po\ *z*g*e th=| u(po\ *a*g*e h( e)la/ttwn th=| mei/zoni: o(/per e)sti\n a)du/naton. ou)k a)/ra to\ *z ke/ntron e)sti\ tou= *a*b*g ku/klou. o(moi/ws dh\ dei/comen, o(/ti ou)d' a)/llo ti plh\n e)pi\ th=s *a*g.

e)a\n a)/ra ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ th=s a(fh=s th=| e)faptome/nh| pro\s o)rqa\s eu)qei=a grammh\ a)xqh=|, e)pi\ th=s a)xqei/shs e)/stai to\ ke/ntron tou= ku/klou: o(/per e)/dei dei=cai.

e)/stw ku/klos o( *a*b*g, kai\ pro\s me\n tw=| ke/ntrw| au)tou= gwni/a e)/stw h( u(po\ *b*e*g, pro\s de\ th=| periferei/a| h( u(po\ *b*a*g, e)xe/twsan de\ th\n au)th\n perife/reian ba/sin th\n *b*g: le/gw, o(/ti diplasi/wn e)sti\n h( u(po\ *b*e*g gwni/a th=s u(po\ *b*a*g.

e)pizeuxqei=sa ga\r h( *a*e dih/xqw e)pi\ to\ *z.

e)pei\ ou)=n i)/sh e)sti\n h( *e*a th=| *e*b, i)/sh kai\ gwni/a h( u(po\ *e*a*b th=| u(po\ *e*b*a: ai( a)/ra u(po\ *e*a*b, *e*b*a gwni/ai th=s u(po\ *e*a*b diplasi/ous ei)si/n. i)/sh de\ h( u(po\ *b*e*z tai=s u(po\ *e*a*b, *e*b*a: kai\ h( u(po\ *b*e*z a)/ra th=s u(po\ *e*a*b e)sti diplh=. dia\ ta\ au)ta\ dh\ kai\ h( u(po\ *z*e*g th=s u(po\ *e*a*g e)sti diplh=. o(/lh a)/ra h( u(po\ *b*e*g o(/lhs

th=s u(po\ *b*a*g e)sti diplh=.

*kekla/sqw dh\ pa/lin, kai\ e)/stw e(te/ra gwni/a h( u(po\ *b*d*g, kai\ e)pizeuxqei=sa h( *d*e e)kbeblh/sqw e)pi\ to\ *h. o(moi/ws dh\ dei/comen, o(/ti diplh= e)stin h( u(po\ *h*e*g gwni/a th=s u(po\ *e*d*g, w(=n h( u(po\ *h*e*b diplh= e)sti th=s u(po\ *e*d*b: loiph\ a)/ra h( u(po\ *b*e*g diplh= e)sti th=s u(po\ *b*d*g.

e)n ku/klw| ai( e)n tw=| au)tw=| tmh/mati gwni/ai i)/sai a)llh/lais ei)si/n.

e)/stw ku/klos o( *a*b*g*d, kai\ e)n tw=| au)tw=| tmh/mati tw=| *b*a*e*d gwni/ai e)/stwsan ai( u(po\ *b*a*d, *b*e*d: le/gw, o(/ti ai( u(po\ *b*a*d, *b*e*d gwni/ai i)/sai a)llh/lais ei)si/n.

ei)lh/fqw ga\r tou= *a*b*g*d ku/klou to\ ke/ntron, kai\ e)/stw to\ *z, kai\ e)pezeu/xqwsan ai( *b*z, *z*d.

kai\ e)pei\ h( me\n u(po\ *b*z*d gwni/a pro\s tw=| ke/ntrw| e)sti/n, h( de\ u(po\ *b*a*d pro\s th=| periferei/a|, kai\ e)/xousi th\n au)th\n perife/reian ba/sin th\n *b*g*d, h( a)/ra u(po\ *b*z*d gwni/a diplasi/wn e)sti\ th=s u(po\ *b*a*d. dia\ ta\ au)ta\ dh\ h( u(po\ *b*z*d kai\ th=s u(po\ *b*e*d e)sti diplasi/wn: i)/sh a)/ra h( u(po\ *b*a*d th=| u(po\ *b*e*d.

e)n ku/klw| a)/ra ai( e)n tw=| au)tw=| tmh/mati gwni/ai i)/sai a)llh/lais ei)si/n: o(/per e)/dei dei=cai.

tw=n e)n toi=s ku/klois tetrapleu/rwn ai( a)penanti/on gwni/ai dusi\n o)rqai=s i)/sai ei)si/n.

e)/stw ku/klos o( *a*b*g*d, kai\ e)n au)tw=| tetra/pleuron e)/stw to\ *a*b*g*d: le/gw, o(/ti ai( a)penanti/on gwni/ai dusi\n o)rqai=s i)/sai ei)si/n.

e)pezeu/xqwsan ai( *a*g, *b*d.

e)pei\ ou)=n panto\s trigw/nou ai( trei=s gwni/ai dusi\n o)rqai=s i)/sai ei)si/n, tou= *a*b*g a)/ra trigw/nou ai( trei=s gwni/ai ai( u(po\ *g*a*b, *a*b*g, *b*g*a dusi\n o)rqai=s i)/sai ei)si/n. i)/sh de\ h( me\n u(po\ *g*a*b th=| u(po\ *b*d*g: e)n ga\r tw=| au)tw=| tmh/mati/ ei)si tw=| *b*a*d*g: h( de\ u(po\ *a*g*b th=| u(po\ *a*d*b:

e)n ga\r tw=| au)tw=| tmh/mati/ ei)si tw=| *a*d*g*b: o(/lh a)/ra h( u(po\ *a*d*g tai=s u(po\ *b*a*g, *a*g*b i)/sh e)sti/n. koinh\ proskei/sqw h( u(po\ *a*b*g: ai( a)/ra u(po\ *a*b*g, *b*a*g, *a*g*b tai=s u(po\ *a*b*g, *a*d*g i)/sai ei)si/n. a)ll' ai( u(po\ *a*b*g, *b*a*g, *a*g*b dusi\n o)rqai=s i)/sai ei)si/n. kai\ ai( u(po\ *a*b*g, *a*d*g a)/ra dusi\n o)rqai=s i)/sai ei)si/n. o(moi/ws dh\ dei/comen, o(/ti kai\ ai( u(po\ *b*a*d, *d*g*b gwni/ai dusi\n o)rqai=s i)/sai ei)si/n.

tw=n a)/ra e)n toi=s ku/klois tetrapleu/rwn ai( a)penanti/on gwni/ai dusi\n o)rqai=s i)/sai ei)si/n: o(/per e)/dei dei=cai.

e)pi\ th=s au)th=s eu)qei/as du/o tmh/mata ku/klwn o(/moia kai\ a)/nisa ou) sustaqh/setai e)pi\ ta\ au)ta\

me/rh.

ei) ga\r dunato/n, e)pi\ th=s au)th=s eu)qei/as th=s *a*b du/o tmh/mata ku/klwn o(/moia kai\ a)/nisa sunesta/tw e)pi\ ta\ au)ta\ me/rh ta\ *a*g*b, *a*d*b, kai\ dih/xqw h( *a*g*d, kai\ e)pezeu/xqwsan ai( *g*b, *d*b.

e)pei\ ou)=n o(/moio/n e)sti to\ *a*g*b tmh=ma tw=| *a*d*b tmh/mati, o(/moia de\ tmh/mata ku/klwn e)sti\ ta\ dexo/mena gwni/as i)/sas, i)/sh a)/ra e)sti\n h( u(po\ *a*g*b gwni/a th=| u(po\ *a*d*b h( e)kto\s th=| e)nto/s: o(/per e)sti\n a)du/naton.

ou)k a)/ra e)pi\ th=s au)th=s eu)qei/as du/o tmh/mata ku/klwn o(/moia kai\ a)/nisa sustaqh/setai e)pi\ ta\ au)ta\ me/rh: o(/per e)/dei dei=cai.

ta\ e)pi\ i)/swn eu)qeiw=n o(/moia tmh/mata ku/klwn i)/sa a)llh/lois e)sti/n.

e)/stwsan ga\r e)pi\ i)/swn eu)qeiw=n tw=n *a*b, *g*d o(/moia tmh/mata ku/klwn ta\ *a*e*b, *g*z*d: le/gw, o(/ti i)/son e)sti\ to\ *a*e*b tmh=ma tw=| *g*z*d tmh/mati.

*)efarmozome/nou ga\r tou= *a*e*b tmh/matos e)pi\ to\ *g*z*d kai\ tiqeme/nou tou= me\n *a shmei/ou e)pi\ to\ *g th=s de\ *a*b

eu)qei/as e)pi\ th\n *g*d, e)farmo/sei kai\ to\ *b shmei=on e)pi\ to\ *d shmei=on dia\ to\ i)/shn ei)=nai th\n *a*b th=| *g*d: th=s de\ *a*b e)pi\ th\n *g*d e)farmosa/shs e)farmo/sei kai\ to\ *a*e*b tmh=ma e)pi\ to\ *g*z*d. ei) ga\r h( *a*b eu)qei=a e)pi\ th\n *g*d e)farmo/sei, to\ de\ *a*e*b tmh=ma e)pi\ to\ *g*z*d mh\ e)farmo/sei, h)/toi e)nto\s au)tou= pesei=tai h)\ e)kto\s h)\ paralla/cei w(s to\ *g*h*d, kai\ ku/klos ku/klon te/mnei kata\ plei/ona shmei=a h)\ du/o: o(/per e)sti\n a)du/naton. ou)k a)/ra e)farmozome/nhs th=s *a*b eu)qei/as e)pi\ th\n *g*d ou)k e)farmo/sei kai\ to\ *a*e*b tmh=ma e)pi\ to\ *g*z*d: e)farmo/sei a)/ra, kai\ i)/son au)tw=| e)/stai.

ta\ a)/ra e)pi\ i)/swn eu)qeiw=n o(/moia tmh/mata ku/klwn i)/sa a)llh/lois e)sti/n: o(/per e)/dei dei=cai.

ku/klou tmh/matos doqe/ntos prosanagra/yai to\n ku/klon, ou(=pe/r e)sti tmh=ma.

e)/stw to\ doqe\n tmh=ma ku/klou to\ *a*b*g: dei= dh\ tou= *a*b*g tmh/matos prosanagra/yai to\n ku/klon, ou(=pe/r e)sti tmh=ma.

tetmh/sqw ga\r h( *a*g di/xa kata\ to\ *d, kai\ h)/xqw a)po\ tou= *d shmei/ou th=| *a*g pro\s o)rqa\s h( *d*b, kai\ e)pezeu/xqw h( *a*b: h( u(po\ *a*b*d gwni/a a)/ra th=s u(po\ *b*a*d h)/toi mei/zwn e)sti\n h)\ i)/sh h)\ e)la/ttwn.

e)pei\ i)/sh e)sti\n h( *a*d th=| *d*g, koinh\ de\ h( *d*e, du/o dh\ ai( *a*d, *d*e du/o tai=s *g*d, *d*e i)/sai ei)si\n e(kate/ra e(kate/ra|: kai\ gwni/a h( u(po\ *a*d*e gwni/a| th=| u(po\ *g*d*e e)stin i)/sh: o)rqh\ ga\r e(kate/ra: ba/sis a)/ra h( *a*e ba/sei th=| *g*e e)stin i)/sh. a)lla\ h( *a*e th=| *b*e e)dei/xqh i)/sh: kai\ h( *b*e a)/ra th=| *g*e e)stin i)/sh: ai( trei=s a)/ra ai( *a*e, *e*b, *e*g i)/sai a)llh/lais ei)si/n: o( a)/ra ke/ntrw| tw=| *e diasth/mati de\ e(ni\ tw=n *a*e, *e*b, *e*g ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn kai\ e)/stai prosanagegramme/nos. ku/klou a)/ra tmh/matos doqe/ntos prosanage/graptai o( ku/klos. kai\ dh=lon, w(s to\ *a*b*g tmh=ma e)/latto/n e)stin h(mikukli/ou dia\ to\ to\ *e ke/ntron e)kto\s au)tou= tugxa/nein.

o(moi/ws ~~de\~~ ka)\n h)=| h( u(po\ *a*b*d gwni/a i)/sh th=| u(po\ *b*a*d, th=s *a*d i)/shs genome/nhs e(kate/ra| tw=n *b*d, *d*g ai( trei=s ai( *d*a, *d*b, *d*g i)/sai a)llh/lais e)/sontai, kai\ e)/stai to\ *d ke/ntron tou= prosanapeplhrwme/nou ku/klou, kai\ dhladh\ e)/stai to\ *a*b*g h(miku/klion.

e)a\n de\ h( u(po\ *a*b*d e)la/ttwn h)=|

ku/klou a)/ra tmh/matos doqe/ntos prosanage/graptai o( ku/klos: o(/per e)/dei poih=sai.

e)n toi=s i)/sois ku/klois ai( i)/sai gwni/ai e)pi\ i)/swn perifereiw=n bebh/kasin, e)a/n te pro\s toi=s ke/ntrois e)a/n te pro\s tai=s periferei/ais w)=si bebhkui=ai.

e)/stwsan i)/soi ku/kloi oi( *a*b*g, *d*e*z kai\ e)n au)toi=s i)/sai gwni/ai e)/stwsan pro\s me\n toi=s ke/ntrois ai( u(po\ *b*h*g, *e*q*z, pro\s de\ tai=s periferei/ais ai( u(po\ *b*a*g, *e*d*z: le/gw, o(/ti i)/sh e)sti\n h( *b*k*g

perife/reia th=| *e*l*z periferei/a|.

e)pezeu/xqwsan ga\r ai( *b*g, *e*z.

kai\ e)pei\ i)/soi ei)si\n oi( *a*b*g, *d*e*z ku/kloi, i)/sai ei)si\n ai( e)k tw=n ke/ntrwn: du/o dh\ ai( *b*h, *h*g du/o tai=s *e*q, *q*z i)/sai: kai\ gwni/a h( pro\s tw=| h gwni/a| th=| pro\s tw=| *q i)/sh: ba/sis a)/ra h( *b*g ba/sei th=| *e*z e)stin i)/sh. kai\ e)pei\ i)/sh e)sti\n h( pro\s tw=| *a gwni/a th=| pro\s tw=| *d, o(/moion a)/ra e)sti\ to\ *b*a*g tmh=ma tw=| *e*d*z tmh/mati: kai/ ei)sin e)pi\ i)/swn eu)qeiw=n ~~tw=n *b*g, *e*z~~: ta\ de\ e)pi\ i)/swn eu)qeiw=n o(/moia tmh/mata ku/klwn i)/sa a)llh/lois e)sti/n: i)/son a)/ra to\ *b*a*g tmh=ma tw=| *e*d*z. e)/sti de\ kai\ o(/los o( *a*b*g ku/klos o(/lw| tw=| *d*e*z ku/klw| i)/sos: loiph\ a)/ra h( *b*k*g perife/reia th=| *e*l*z periferei/a| e)sti\n i)/sh.

e)n a)/ra toi=s i)/sois ku/klois ai( i)/sai gwni/ai e)pi\ i)/swn perifereiw=n bebh/kasin, e)a/n te pro\s toi=s ke/ntrois e)a/n te pro\s tai=s periferei/ais w)=si bebhkui=ai: o(/per e)/dei dei=cai.

e)n toi=s i)/sois ku/klois ai( e)pi\ i)/swn perifereiw=n bebhkui=ai gwni/ai i)/sai a)llh/lais ei)si/n, e)a/n te pro\s toi=s ke/ntrois e)a/n

te pro\s tai=s periferei/ais w)=si bebhkui=ai.

e)n ga\r i)/sois ku/klois toi=s *a*b*g, *d*e*z e)pi\ i)/swn perifereiw=n tw=n *b*g, *e*z pro\s me\n toi=s *h, *q ke/ntrois gwni/ai bebhke/twsan ai( u(po\ *b*h*g, *e*q*z, pro\s de\ tai=s periferei/ais ai( u(po\ *b*a*g, *e*d*z: le/gw, o(/ti h( me\n u(po\ *b*h*g gwni/a th=| u(po\ *e*q*z e)stin i)/sh, h( de\ u(po\ *b*a*g th=| u(po\ *e*d*z e)stin i)/sh.

e)n a)/ra toi=s i)/sois ku/klois ai( e)pi\ i)/swn perifereiw=n bebhkui=ai gwni/ai i)/sai a)llh/lais ei)si/n, e)a/n te pro\s toi=s ke/ntrois e)a/n te pro\s tai=s periferei/ais w)=si bebhkui=ai: o(/per e)/dei dei=cai.

e)n toi=s i)/sois ku/klois ai( i)/sai eu)qei=ai i)/sas periferei/as a)fairou=si th\n me\n mei/zona th=| mei/zoni th\n de\ e)la/ttona th=| e)la/ttoni.

e)/stwsan i)/soi ku/kloi oi( *a*b*g, *d*e*z, kai\ e)n toi=s ku/klois i)/sai eu)qei=ai e)/stwsan ai( *a*b, *d*e ta\s me\n *a*g*b, *d*z*e periferei/as mei/zonas a)fairou=sai ta\s de\ *a*h*b, *d*q*e e)la/ttonas: le/gw, o(/ti h( me\n *a*g*b mei/zwn perife/reia i)/sh e)sti\ th=| *d*z*e mei/zoni periferei/a|, h( de\ *a*h*b e)la/ttwn perife/reia th=| *d*q*e.

ei)lh/fqw ga\r ta\ ke/ntra tw=n ku/klwn ta\ *k, *l, kai\ e)pezeu/xqwsan ai( *a*k, *k*b, *d*l, *l*e.

kai\ e)pei\ i)/soi ku/kloi ei)si/n, i)/sai ei)si\ kai\ ai( e)k tw=n ke/ntrwn: du/o dh\ ai( *a*k, *k*b dusi\ tai=s *d*l, *l*e i)/sai ei)si/n: kai\ ba/sis h( *a*b ba/sei th=| *d*e i)/sh: gwni/a a)/ra h( u(po\ *a*k*b gwni/a| th=| u(po\ *d*l*e i)/sh e)sti/n. ai( de\ i)/sai gwni/ai e)pi\ i)/swn perifereiw=n bebh/kasin, o(/tan pro\s toi=s ke/ntrois w)=sin: i)/sh a)/ra h( *a*h*b perife/reia th=| *d*q*e. e)sti\ de\ kai\ o(/los o( *a*b*g ku/klos o(/lw| tw=| *d*e*z ku/klw| i)/sos: kai\ loiph\ a)/ra h( *a*g*b perife/reia loiph=| th=| *d*z*e periferei/a| i)/sh e)sti/n.

e)n a)/ra toi=s i)/sois ku/klois ai( i)/sai eu)qei=ai i)/sas periferei/as a)fairou=si th\n me\n mei/zona th=| mei/zoni th\n de\ e)la/ttona th=| e)la/ttoni: o(/per e)/dei dei=cai.

e)n toi=s i)/sois ku/klois ta\s i)/sas periferei/as i)/sai eu)qei=ai u(potei/nousin.

e)/stwsan i)/soi ku/kloi oi( *a*b*g, *d*e*z, kai\ e)n au)toi=s i)/sai perife/reiai a)peilh/fqwsan ai( *b*h*g, *e*q*z, kai\ e)pezeu/xqwsan ai( *b*g, *e*z eu)qei=ai: le/gw, o(/ti i)/sh e)sti\n h( *b*g th=| *e*z.

ei)lh/fqw ga\r ta\ ke/ntra tw=n ku/klwn, kai\ e)/stw ta\ *k, *l, kai\ e)pezeu/xqwsan ai( *b*k, *k*g, *e*l, *l*z.

kai\ e)pei\ i)/sh e)sti\n h( *b*h*g perife/reia th=| *e*q*z periferei/a|, i)/sh e)sti\ kai\ gwni/a h( u(po\ *b*k*g th=| u(po\ *e*l*z. kai\ e)pei\ i)/soi ei)si\n oi( *a*b*g, *d*e*z ku/kloi, i)/sai ei)si\ kai\ ai( e)k tw=n ke/ntrwn: du/o dh\ ai( *b*k, *k*g dusi\ tai=s *e*l, *l*z i)/sai ei)si/n: kai\ gwni/as i)/sas perie/xousin: ba/sis a)/ra h( *b*g ba/sei th=| *e*z i)/sh e)sti/n.

e)n a)/ra toi=s i)/sois ku/klois ta\s i)/sas periferei/as i)/sai eu)qei=ai u(potei/nousin: o(/per e)/dei dei=cai.

th\n doqei=san perife/reian di/xa temei=n.

e)/stw h( doqei=sa perife/reia h( *a*d*b: dei= dh\ th\n *a*d*b perife/reian di/xa temei=n.

e)pezeu/xqw h( *a*b, kai\ tetmh/sqw di/xa kata\ to\ *g, kai\ a)po\ tou= *g shmei/ou th=| *a*b eu)qei/a| pro\s o)rqa\s h)/xqw h( *g*d, kai\ e)pezeu/xqwsan ai( *a*d, *d*b.

kai\ e)pei\ i)/sh e)sti\n h( *a*g th=| *g*b, koinh\ de\ h( *g*d, du/o dh\ ai( *a*g, *g*d dusi\ tai=s *b*g, *g*d i)/sai ei)si/n: kai\ gwni/a h( u(po\ *a*g*d gwni/a| th=| u(po\ *b*g*d i)/sh: o)rqh\ ga\r e(kate/ra: ba/sis a)/ra h( *a*d ba/sei th=| *d*b i)/sh e)sti/n. ai( de\ i)/sai eu)qei=ai i)/sas periferei/as a)fairou=si th\n me\n mei/zona th=| mei/zoni th\n de\ e)la/ttona th=| e)la/ttoni: kai/ e)stin e(kate/ra tw=n *a*d, *d*b perifereiw=n e)la/ttwn h(mikukli/ou: i)/sh a)/ra h( *a*d perife/reia th=| *d*b periferei/a|.

h( a)/ra doqei=sa perife/reia di/xa te/tmhtai kata\ to\ *d shmei=on: o(/per e)/dei poih=sai.

e)n ku/klw| h( me\n e)n tw=| h(mikukli/w| gwni/a o)rqh/ e)stin, h( de\ e)n tw=| mei/zoni tmh/mati e)la/ttwn o)rqh=s, h( de\ e)n tw=| e)la/ttoni tmh/mati mei/zwn o)rqh=s: kai\ e)/ti h( me\n tou= mei/zonos tmh/matos gwni/a mei/zwn e)sti\n o)rqh=s, h( de\ tou= e)la/ttonos tmh/matos gwni/a e)la/ttwn o)rqh=s.

e)/stw ku/klos o( *a*b*g*d, dia/metros de\ au)tou= e)/stw h( *b*g, ke/ntron de\ to\ *e, kai\ e)pezeu/xqwsan ai( *b*a, *a*g, *a*d, *d*g: le/gw, o(/ti h( me\n e)n tw=| *b*a*g h(mikukli/w| gwni/a

h( u(po\ *b*a*g o)rqh/ e)stin, h( de\ e)n tw=| *a*b*g mei/zoni tou= h(mikukli/ou tmh/mati gwni/a h( u(po\ *a*b*g e)la/ttwn e)sti\n o)rqh=s, h( de\ e)n tw=| *a*d*g e)la/ttoni tou= h(mikukli/ou tmh/mati gwni/a h( u(po\ *a*d*g mei/zwn e)sti\n o)rqh=s.

e)pezeu/xqw h( *a*e, kai\ dih/xqw h( *b*a e)pi\ to\ *z.

kai\ e)pei\ i)/sh e)sti\n h( *b*e th=| *e*a, i)/sh e)sti\ kai\ gwni/a h( u(po\ *a*b*e th=| u(po\ *b*a*e. pa/lin, e)pei\ i)/sh e)sti\n h( *g*e th=| *e*a, i)/sh e)sti\ kai\ h( u(po\ *a*g*e th=| u(po\ *g*a*e: o(/lh a)/ra h( u(po\ *b*a*g dusi\ tai=s u(po\ *a*b*g, *a*g*b i)/sh e)sti/n. e)sti\ de\ kai\ h( u(po\ *z*a*g e)kto\s tou= *a*b*g trigw/nou dusi\ tai=s u(po\ *a*b*g, *a*g*b gwni/ais i)/sh: i)/sh a)/ra kai\ h( u(po\ *b*a*g gwni/a th=| u(po\ *z*a*g: o)rqh\ a)/ra e(kate/ra: h( a)/ra e)n tw=| *b*a*g h(mikukli/w| gwni/a h( u(po\ *b*a*g o)rqh/ e)stin.

kai\ e)pei\ tou= *a*b*g trigw/nou du/o gwni/ai ai( u(po\ *a*b*g, *b*a*g du/o o)rqw=n e)la/ttone/s ei)sin, o)rqh\ de\ h( u(po\ *b*a*g, e)la/ttwn a)/ra o)rqh=s e)stin h( u(po\ *a*b*g gwni/a: kai/ e)stin e)n tw=| *a*b*g mei/zoni tou= h(mikukli/ou tmh/mati.

kai\ e)pei\ e)n ku/klw| tetra/pleuro/n e)sti to\ *a*b*g*d, tw=n de\ e)n toi=s ku/klois tetrapleu/rwn ai( a)penanti/on gwni/ai dusi\n o)rqai=s i)/sai ei)si/n ~~ai( a)/ra u(po\ *a*b*g, *a*d*g gwni/ai dusi\n o)rqai=s i)/sai ei)si/n~~, kai/ e)stin h( u(po\ *a*b*g e)la/ttwn o)rqh=s: loiph\ a)/ra h( u(po\ *a*d*g gwni/a mei/zwn o)rqh=s e)stin: kai/ e)stin e)n tw=| *a*d*g e)la/ttoni tou= h(mikukli/ou tmh/mati.

le/gw, o(/ti kai\ h( me\n tou= mei/zonos tmh/matos gwni/a h( periexome/nh u(po/ te th=s *a*b*g periferei/as kai\ th=s *a*g eu)qei/as mei/zwn e)sti\n o)rqh=s, h( de\ tou= e)la/ttonos tmh/matos gwni/a h( periexome/nh u(po/ te th=s *a*d*g periferei/as kai\ th=s *a*g eu)qei/as e)la/ttwn e)sti\n o)rqh=s. kai/ e)stin au)to/qen fanero/n. e)pei\ ga\r h( u(po\ tw=n *b*a, *a*g eu)qeiw=n o)rqh/ e)stin, h( a)/ra u(po\ th=s *a*b*g periferei/as kai\ th=s *a*g eu)qei/as periexome/nh mei/zwn e)sti\n o)rqh=s. pa/lin, e)pei\ h( u(po\ tw=n *a*g, *a*z eu)qeiw=n o)rqh/ e)stin, h( a)/ra u(po\ th=s *g*a eu)qei/as kai\ th=s *a*d*g periferei/as periexome/nh e)la/ttwn e)sti\n o)rqh=s.

e)n ku/klw| a)/ra h( me\n e)n tw=| h(mikukli/w| gwni/a o)rqh/ e)stin, h( de\ e)n tw=| mei/zoni tmh/mati e)la/ttwn o)rqh=s, h( de\ e)n tw=| e)la/ttoni ~~tmh/mati~~ mei/zwn o)rqh=s, kai\ e)/ti h( me\n tou= mei/zonos tmh/matos ~~gwni/a~~ mei/zwn ~~e)sti\n~~ o)rqh=s, h( de\ tou= e)la/ttonos tmh/matos ~~gwni/a~~ e)la/ttwn o)rqh=s: o(/per e)/dei dei=cai.

~~po/risma~~

e)k dh\ tou/tou fanero/n, o(/ti e)a\n h( mi/a gwni/a trigw/nou tai=s dusi\n i)/sh h)=|, o)rqh/ e)stin h( gwni/a dia\ to\ kai\ th\n e)kei/nhs e)kto\s tai=s au)tai=s i)/shn ei)=nai: e)a\n de\ ai( e)fech=s i)/sai w)=sin, o)rqai/ ei)sin.

e)a\n ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ th=s a(fh=s ei)s to\n ku/klon diaxqh=| tis eu)qei=a te/mnousa to\n ku/klon, a(\s

poiei= gwni/as pro\s th=| e)faptome/nh|, i)/sai e)/sontai tai=s e)n toi=s e)nalla\c tou= ku/klou tmh/masi gwni/ais.

ku/klou ga\r tou= *a*b*g*d e)fapte/sqw tis eu)qei=a h( *e*z kata\ to\ *b shmei=on, kai\ a)po\ tou= *b shmei/ou dih/xqw tis eu)qei=a ei)s to\n *a*b*g*d ku/klon te/mnousa au)to\n h( *b*d. le/gw, o(/ti a(\s poiei= gwni/as h( *b*d meta\ th=s *e*z e)faptome/nhs, i)/sai e)/sontai tai=s e)n toi=s e)nalla\c tmh/masi tou= ku/klou gwni/ais, toute/stin, o(/ti h( me\n u(po\ *z*b*d gwni/a i)/sh e)sti\ th=| e)n tw=| *b*a*d tmh/mati sunistame/nh| gwni/a|, h( de\ u(po\ *e*b*d gwni/a i)/sh e)sti\ th=| e)n tw=| *d*g*b tmh/mati sunistame/nh| gwni/a|.

h)/xqw ga\r a)po\ tou= *b th=| *e*z pro\s o)rqa\s h( *b*a, kai\ ei)lh/fqw e)pi\ th=s *b*d periferei/as tuxo\n shmei=on to\ *g, kai\ e)pezeu/xqwsan ai( *a*d, *d*g, *g*b.

kai\ e)pei\ ku/klou tou= *a*b*g*d e)fa/ptetai/ tis eu)qei=a h( *e*z kata\ to\ *b, kai\ a)po\ th=s a(fh=s h)=ktai th=| e)faptome/nh| pro\s o)rqa\s h( *b*a, e)pi\ th=s *b*a a)/ra to\ ke/ntron e)sti\ tou= *a*b*g*d ku/klou. h( *b*a a)/ra dia/metro/s e)sti tou= *a*b*g*d ku/klou: h( a)/ra u(po\ *a*d*b gwni/a e)n h(mikukli/w| ou)=sa o)rqh/ e)stin. loipai\ a)/ra ai( u(po\ *b*a*d, *a*b*d mia=| o)rqh=| i)/sai ei)si/n. e)sti\ de\ kai\ h( u(po\ *a*b*z o)rqh/: h( a)/ra u(po\ *a*b*z i)/sh e)sti\ tai=s u(po\ *b*a*d, *a*b*d. koinh\ a)fh|rh/sqw h( u(po\ *a*b*d: loiph\ a)/ra h( u(po\ *d*b*z gwni/a i)/sh e)sti\ th=| e)n tw=| e)nalla\c tmh/mati tou= ku/klou gwni/a| th=| u(po\ *b*a*d. kai\ e)pei\ e)n ku/klw| tetra/pleuro/n e)sti to\ *a*b*g*d, ai( a)penanti/on au)tou= gwni/ai dusi\n o)rqai=s i)/sai ei)si/n. ei)si\ de\ kai\ ai( u(po\ *d*b*z, *d*b*e dusi\n o)rqai=s i)/sai: ai( a)/ra u(po\ *d*b*z, *d*b*e tai=s u(po\ *b*a*d, *b*g*d i)/sai ei)si/n, w(=n h( u(po\ *b*a*d th=| u(po\ *d*b*z e)dei/xqh i)/sh: loiph\ a)/ra h( u(po\ *d*b*e th=| e)n tw=| e)nalla\c tou= ku/klou tmh/mati tw=| *d*g*b th=| u(po\ *d*g*b gwni/a| e)sti\n i)/sh.

e)a\n a)/ra ku/klou e)fa/pthtai/ tis eu)qei=a, a)po\ de\ th=s a(fh=s ei)s to\n ku/klon diaxqh=| tis eu)qei=a te/mnousa to\n ku/klon, a(\s poiei= gwni/as pro\s th=| e)faptome/nh|, i)/sai e)/sontai tai=s e)n toi=s e)nalla\c tou= ku/klou tmh/masi gwni/ais: o(/per e)/dei dei=cai.

e)pi\ th=s doqei/shs eu)qei/as gra/yai tmh=ma ku/klou dexo/menon gwni/an i)/shn th=| doqei/sh| gwni/a| eu)qugra/mmw|.

e)/stw h( doqei=sa eu)qei=a h( *a*b, h( de\ doqei=sa gwni/a eu)qu/grammos h( pro\s tw=| *g: dei= dh\ e)pi\ th=s doqei/shs eu)qei/as th=s *a*b gra/yai tmh=ma ku/klou dexo/menon gwni/an i)/shn th=| pro\s tw=| *g.

to\ *z, kai\ h)/xqw a)po\ tou= *z shmei/ou th=| *a*b pro\s o)rqa\s h( *z*h, kai\ e)pezeu/xqw h( *h*b.

kai\ e)pei\ i)/sh e)sti\n h( *a*z th=| *z*b, koinh\ de\ h( *z*h, du/o dh\ ai( *a*z, *z*h du/o tai=s *b*z, *z*h i)/sai ei)si/n: kai\ gwni/a h( u(po\ *a*z*h ~~gwni/a|~~ th=| u(po\ *b*z*h i)/sh: ba/sis a)/ra h( *a*h ba/sei th=| *b*h i)/sh e)sti/n. o( a)/ra ke/ntrw| me\n tw=| *h diasth/mati de\ tw=| *h*a ku/klos grafo/menos h(/cei kai\ dia\ tou= *b. gegra/fqw kai\ e)/stw o( *a*b*e, kai\ e)pezeu/xqw h( *e*b. e)pei\ ou)=n a)p' a)/kras th=s *a*e diame/trou a)po\ tou= *a th=| *a*e pro\s o)rqa/s e)stin h( *a*d, h( *a*d a)/ra e)fa/ptetai tou= *a*b*e ku/klou: e)pei\ ou)=n ku/klou tou= *a*b*e e)fa/ptetai/ tis eu)qei=a h( *a*d, kai\ a)po\ th=s kata\ to\ *a a(fh=s ei)s to\n *a*b*e ku/klon dih=ktai/ tis eu)qei=a h( *a*b, h( a)/ra u(po\ *d*a*b gwni/a i)/sh e)sti\ th=| e)n tw=| e)nalla\c tou= ku/klou tmh/mati gwni/a| th=| u(po\ *a*e*b. a)ll' h( u(po\ *d*a*b th=| pro\s tw=| *g e)stin i)/sh: kai\ h( pro\s tw=| *g a)/ra gwni/a i)/sh e)sti\ th=| u(po\ *a*e*b.

e)pi\ th=s doqei/shs a)/ra eu)qei/as th=s *a*b tmh=ma ku/klou ge/graptai to\ *a*e*b dexo/menon gwni/an th\n u(po\ *a*e*b i)/shn th=| doqei/sh| th=| pro\s tw=| *g.

ge/graptai a)/ra pa/lin e)pi\ th=s *a*b tmh=ma ku/klou to\ *a*e*b dexo/menon gwni/an i)/shn th=| pro\s tw=| *g.

e)pi\ th=s a)/ra doqei/shs eu)qei/as th=s *a*b ge/graptai tmh=ma ku/klou to\ *a*q*b dexo/menon gwni/an i)/shn th=| pro\s tw=| *g: o(/per e)/dei poih=sai.

a)po\ tou= doqe/ntos ku/klou tmh=ma a)felei=n dexo/menon gwni/an i)/shn th=| doqei/sh| gwni/a| eu)qugra/mmw|.

h)/xqw tou= *a*b*g e)faptome/nh h( *e*z kata\ to\ *b shmei=on, kai\ sunesta/tw pro\s th=| *z*b eu)qei/a| kai\ tw=| pro\s

e)a\n e)n ku/klw| du/o eu)qei=ai te/mnwsin a)llh/las, to\ u(po\ tw=n th=s mia=s tmhma/twn periexo/menon o)rqogw/nion i)/son e)sti\ tw=| u(po\ tw=n th=s e(te/ras tmhma/twn periexome/nw| o)rqogwni/w|.

e)n ga\r ku/klw| tw=| *a*b*g*d du/o eu)qei=ai ai( *a*g, *b*d temne/twsan a)llh/las kata\ to\ *e shmei=on: le/gw, o(/ti to\ u(po\ tw=n *a*e, *e*g periexo/menon o)rqogw/nion

i)/son e)sti\ tw=| u(po\ tw=n *d*e, *e*b periexome/nw| o)rqogwni/w|.

ei) me\n ou)=n ai( *a*g, *b*d dia\ tou= ke/ntrou ei)si\n w(/ste to\ *e ke/ntron ei)=nai tou= *a*b*g*d ku/klou, fanero/n, o(/ti i)/swn ou)sw=n tw=n *a*e, *e*g, *d*e, *e*b kai\ to\ u(po\ tw=n *a*e, *e*g periexo/menon o)rqogw/nion i)/son e)sti\ tw=| u(po\ tw=n *d*e, *e*b periexome/nw| o)rqogwni/w|.

mh\ e)/stwsan dh\ ai( *a*g, *d*b dia\ tou= ke/ntrou, kai\ ei)lh/fqw to\ ke/ntron tou= *a*b*g*d, kai\ e)/stw to\ *z, kai\ a)po\ tou= *z e)pi\ ta\s *a*g, *d*b eu)qei/as ka/qetoi h)/xqwsan ai( *z*h, *z*q, kai\ e)pezeu/xqwsan ai( *z*b, *z*g,

*z*e.

kai\ e)pei\ eu)qei=a/ tis dia\ tou= ke/ntrou h( *h*z eu)qei=a/n tina mh\ dia\ tou= ke/ntrou th\n *a*g pro\s o)rqa\s te/mnei, kai\ di/xa au)th\n te/mnei: i)/sh a)/ra h( *a*h th=| *h*g. e)pei\ ou)=n eu)qei=a h( *a*g te/tmhtai ei)s me\n i)/sa kata\ to\ *h, ei)s de\ a)/nisa kata\ to\ *e, to\ a)/ra u(po\ tw=n *a*e, *e*g periexo/menon o)rqogw/nion meta\ tou= a)po\ th=s *e*h tetragw/nou i)/son e)sti\ tw=| a)po\ th=s *h*g: ~~koino\n~~ proskei/sqw to\ a)po\ th=s *h*z: to\ a)/ra u(po\ tw=n *a*e, *e*g meta\ tw=n a)po\ tw=n *h*e, *h*z i)/son e)sti\ toi=s a)po\ tw=n *g*h, *h*z. a)lla\ toi=s me\n a)po\ tw=n *e*h, *h*z i)/son e)sti\ to\ a)po\ th=s *z*e, toi=s de\ a)po\ tw=n *g*h, *h*z i)/son e)sti\ to\ a)po\ th=s *z*g: to\ a)/ra u(po\ tw=n *a*e, *e*g meta\ tou= a)po\ th=s *z*e i)/son e)sti\ tw=| a)po\ th=s *z*g. i)/sh de\ h( *z*g th=| *z*b: to\ a)/ra u(po\ tw=n *a*e, *e*g meta\ tou= a)po\ th=s *e*z i)/son e)sti\ tw=| a)po\ th=s *z*b. dia\ ta\ au)ta\ dh\ kai\ to\ u(po\ tw=n *d*e, *e*b meta\ tou= a)po\ th=s *z*e i)/son e)sti\ tw=| a)po\ th=s *z*b. e)dei/xqh de\ kai\ to\ u(po\ tw=n *a*e, *e*g meta\ tou= a)po\ th=s *z*e i)/son tw=| a)po\ th=s *z*b: to\ a)/ra u(po\ tw=n *a*e, *e*g meta\ tou= a)po\ th=s *z*e i)/son e)sti\ tw=| u(po\ tw=n *d*e, *e*b meta\ tou= a)po\ th=s *z*e. koino\n a)fh|rh/sqw to\ a)po\ th=s *z*e: loipo\n a)/ra to\ u(po\ tw=n *a*e, *e*g periexo/menon o)rqogw/nion i)/son e)sti\ tw=| u(po\ tw=n *d*e, *e*b periexome/nw| o)rqogwni/w|.

e)a\n a)/ra e)n ku/klw| eu)qei=ai du/o te/mnwsin a)llh/las, to\ u(po\ tw=n th=s mia=s tmhma/twn periexo/menon o)rqogw/nion i)/son e)sti\ tw=| u(po\ tw=n th=s e(te/ras tmhma/twn periexome/nw| o)rqogwni/w|: o(/per e)/dei dei=cai.

e)a\n ku/klou lhfqh=| ti shmei=on e)kto/s, kai\ a)p' au)tou= pro\s to\n ku/klon prospi/ptwsi du/o eu)qei=ai, kai\ h( me\n au)tw=n te/mnh| to\n ku/klon, h( de\ e)fa/pthtai, e)/stai to\ u(po\ o(/lhs th=s temnou/shs kai\ th=s e)kto\s a)polambanome/nhs metacu\ tou= te shmei/ou kai\ th=s kurth=s periferei/as i)/son tw=| a)po\ th=s e)faptome/nhs tetragw/nw|.

ku/klou ga\r tou= *a*b*g ei)lh/fqw ti shmei=on e)kto\s to\ *d, kai\ a)po\ tou= *d pro\s to\n *a*b*g ku/klon prospipte/twsan du/o eu)qei=ai ai( *d*g*a, *d*b: kai\ h( me\n *d*g*a temne/tw to\n *a*b*g ku/klon, h( de\ *b*d e)fapte/sqw: le/gw, o(/ti to\ u(po\ tw=n *a*d, *d*g periexo/menon o)rqogw/nion

i)/son e)sti\ tw=| a)po\ th=s *d*b tetragw/nw|.

h( a)/ra *d*g*a h)/toi dia\ tou= ke/ntrou e)sti\n h)\ ou)/. e)/stw pro/teron dia\ tou= ke/ntrou, kai\ e)/stw to\ *z ke/ntron tou= *a*b*g ku/klou, kai\ e)pezeu/xqw h( *z*b: o)rqh\ a)/ra e)sti\n h( u(po\ *z*b*d. kai\ e)pei\ eu)qei=a h( *a*g di/xa te/tmhtai kata\ to\ *z, pro/skeitai de\ au)th=| h( *g*d, to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *z*g i)/son e)sti\ tw=| a)po\ th=s *z*d. i)/sh de\ h( *z*g th=| *z*b: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *z*b i)/son e)sti\ tw=| a)po\ th=s *z*d. tw=| de\ a)po\ th=s *z*d i)/sa e)sti\ ta\ a)po\ tw=n *z*b, *b*d: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *z*b i)/son e)sti\ toi=s a)po\ tw=n *z*b, *b*d. koino\n a)fh|rh/sqw to\ a)po\ th=s *z*b: loipo\n a)/ra to\ u(po\ tw=n *a*d, *d*g i)/son e)sti\ tw=| a)po\ th=s *d*b e)faptome/nhs.

a)lla\ dh\ h( *d*g*a mh\ e)/stw dia\ tou= ke/ntrou tou= *a*b*g ku/klou, kai\ ei)lh/fqw to\ ke/ntron to\ *e, kai\ a)po\ tou= *e e)pi\ th\n *a*g ka/qetos h)/xqw h( *e*z, kai\ e)pezeu/xqwsan ai( *e*b, *e*g, *e*d: o)rqh\ a)/ra e)sti\n h( u(po\ *e*b*d. kai\ e)pei\ eu)qei=a/ tis dia\ tou= ke/ntrou h( *e*z eu)qei=a/n tina mh\ dia\ tou= ke/ntrou th\n *a*g pro\s o)rqa\s te/mnei, kai\ di/xa au)th\n te/mnei: h( *a*z a)/ra th=| *z*g e)stin i)/sh. kai\ e)pei\ eu)qei=a h( *a*g te/tmhtai di/xa kata\ to\ *z shmei=on, pro/skeitai de\ au)th=| h( *g*d, to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *z*g i)/son e)sti\ tw=| a)po\ th=s *z*d. koino\n proskei/sqw to\ a)po\ th=s *z*e: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tw=n a)po\ tw=n *g*z, *z*e i)/son e)sti\ toi=s a)po\ tw=n *z*d, *z*e. toi=s de\ a)po\ tw=n *g*z, *z*e i)/son e)sti\ to\ a)po\ th=s *e*g: o)rqh\ ga\r ~~e)stin~~ h( u(po\ *e*z*g ~~gwni/a~~: toi=s de\ a)po\ tw=n *d*z, *z*e i)/son e)sti\ to\ a)po\ th=s *e*d: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *e*g i)/son e)sti\ tw=| a)po\ th=s *e*d. i)/sh de\ h( *e*g th=| *e*b: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *e*b i)/son e)sti\ tw=| a)po\ th=s *e*d. tw=| de\ a)po\ th=s *e*d i)/sa e)sti\ ta\ a)po\ tw=n *e*b, *b*d: o)rqh\ ga\r h( u(po\ *e*b*d gwni/a: to\ a)/ra u(po\ tw=n *a*d, *d*g meta\ tou= a)po\ th=s *e*b i)/son e)sti\ toi=s a)po\ tw=n *e*b, *b*d. koino\n a)fh|rh/sqw to\ a)po\ th=s *e*b: loipo\n a)/ra to\ u(po\ tw=n *a*d, *d*g i)/son e)sti\ tw=| a)po\ th=s *d*b.

e)a\n a)/ra ku/klou lhfqh=| ti shmei=on e)kto/s, kai\ a)p' au)tou= pro\s to\n ku/klon prospi/ptwsi du/o eu)qei=ai, kai\ h( me\n au)tw=n te/mnh| to\n ku/klon, h( de\ e)fa/pthtai, e)/stai to\ u(po\ o(/lhs th=s temnou/shs kai\ th=s e)kto\s a)polambanome/nhs metacu\ tou= te shmei/ou kai\ th=s kurth=s periferei/as i)/son tw=| a)po\ th=s e)faptome/nhs tetragw/nw|: o(/per e)/dei dei=cai.

e)a\n ku/klou lhfqh=| ti shmei=on e)kto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsi du/o eu)qei=ai, kai\ h( me\n au)tw=n te/mnh| to\n ku/klon, h( de\ prospi/pth|, h)=| de\ to\ u(po\ ~~th=s~~ o(/lhs th=s temnou/shs kai\ th=s e)kto\s a)polambanome/nhs metacu\ tou= te shmei/ou kai\ th=s kurth=s periferei/as i)/son tw=| a)po\ th=s prospiptou/shs, h( prospi/ptousa e)fa/yetai tou= ku/klou.

ku/klou ga\r tou= *a*b*g ei)lh/fqw ti shmei=on e)kto\s to\ *d, kai\ a)po\ tou= *d pro\s to\n *a*b*g ku/klon prospipte/twsan du/o eu)qei=ai ai( *d*g*a, *d*b, kai\ h( me\n *d*g*a temne/tw to\n ku/klon, h( de\ *d*b prospipte/tw, e)/stw

de\ to\ u(po\ tw=n *a*d, *d*g i)/son tw=| a)po\ th=s *d*b. le/gw, o(/ti h( *d*b e)fa/ptetai tou= *a*b*g ku/klou.

h)/xqw ga\r tou= *a*b*g e)faptome/nh h( *d*e, kai\ ei)lh/fqw to\ ke/ntron tou= *a*b*g ku/klou, kai\ e)/stw to\ *z, kai\ e)pezeu/xqwsan ai( *z*e, *z*b, *z*d. h( a)/ra u(po\ *z*e*d o)rqh/ e)stin. kai\ e)pei\ h( *d*e e)fa/ptetai tou= *a*b*g ku/klou, te/mnei de\ h( *d*g*a, to\ a)/ra u(po\ tw=n *a*d, *d*g i)/son e)sti\ tw=| a)po\ th=s *d*e. h)=n de\ kai\ to\ u(po\ tw=n *a*d, *d*g i)/son tw=| a)po\ th=s *d*b: to\ a)/ra a)po\ th=s *d*e i)/son e)sti\ tw=| a)po\ th=s *d*b: i)/sh a)/ra h( *d*e th=| *d*b. e)sti\ de\ kai\ h( *z*e th=| *z*b i)/sh: du/o dh\ ai( *d*e, *e*z du/o tai=s *d*b, *b*z i)/sai ei)si/n: kai\ ba/sis au)tw=n koinh\ h( *z*d: gwni/a a)/ra h( u(po\ *d*e*z gwni/a| th=| u(po\ *d*b*z e)stin i)/sh. o)rqh\ de\ h( u(po\ *d*e*z: o)rqh\ a)/ra kai\ h( u(po\ *d*b*z. kai/ e)stin h( *z*b e)kballome/nh dia/metros: h( de\ th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)fa/ptetai tou= ku/klou: h( *d*b a)/ra e)fa/ptetai tou= *a*b*g ku/klou. o(moi/ws dh\ deixqh/setai, ka)\n to\ ke/ntron e)pi\ th=s *a*g tugxa/nh|.

e)a\n a)/ra ku/klou lhfqh=| ti shmei=on e)kto/s, a)po\ de\ tou= shmei/ou pro\s to\n ku/klon prospi/ptwsi du/o eu)qei=ai, kai\ h( me\n au)tw=n te/mnh| to\n ku/klon, h( de\ prospi/pth|, h)=| de\ to\ u(po\ o(/lhs th=s temnou/shs kai\ th=s e)kto\s a)polambanome/nhs metacu\ tou= te shmei/ou kai\ th=s kurth=s periferei/as i)/son tw=| a)po\ th=s prospiptou/shs, h( prospi/ptousa e)fa/yetai tou= ku/klou: o(/per e)/dei dei=cai.

sxh=ma eu)qu/grammon ei)s sxh=ma eu)qu/grammon e)ggra/fesqai le/getai, o(/tan e(ka/sth tw=n tou= e)ggrafome/nou sxh/matos gwniw=n e(ka/sths pleura=s tou=, ei)s o(\ e)ggra/fetai, a(/pthtai.

sxh=ma de\ o(moi/ws peri\ sxh=ma perigra/fesqai le/getai, o(/tan e(ka/sth pleura\ tou= perigrafome/nou e(ka/sths gwni/as tou=, peri\ o(\ perigra/fetai, a(/pthtai.

sxh=ma eu)qu/grammon ei)s ku/klon e)ggra/fesqai le/getai, o(/tan e(ka/sth gwni/a tou= e)ggrafome/nou a(/pthtai th=s tou= ku/klou periferei/as.

sxh=ma de\ eu)qu/grammon peri\ ku/klon perigra/fesqai le/getai, o(/tan e(ka/sth pleura\ tou= perigrafome/nou e)fa/pthtai th=s tou= ku/klou periferei/as.

ku/klos de\ ei)s sxh=ma o(moi/ws e)ggra/fesqai le/getai, o(/tan h( tou= ku/klou perife/reia e(ka/sths pleura=s tou=, ei)s o(\ e)ggra/fetai, a(/pthtai.

ku/klos de\ peri\ sxh=ma perigra/fesqai le/getai, o(/tan h( tou= ku/klou perife/reia e(ka/sths gwni/as tou=, peri\ o(\ perigra/fetai, a(/pthtai.

eu)qei=a ei)s ku/klon e)narmo/zesqai le/getai, o(/tan ta\ pe/rata au)th=s e)pi\ th=s periferei/as h)=| tou= ku/klou.

ei)s to\n doqe/nta ku/klon th=| doqei/sh| eu)qei/a| mh\ mei/zoni ou)/sh| th=s tou= ku/klou diame/trou i)/shn eu)qei=an e)narmo/sai.

e)/stw o( doqei\s ku/klos o( *a*b*g, h( de\ doqei=sa eu)qei=a mh\ mei/zwn th=s tou= ku/klou diame/trou h( *d. dei= dh\ ei)s to\n *a*b*g ku/klon th=| *d eu)qei/a| i)/shn eu)qei=an e)narmo/sai.

h)/xqw tou= *a*b*g ku/klou dia/metros h( *b*g. ei) me\n ou)=n i)/sh e)sti\n h( *b*g th=| *d, gegono\s a)\n ei)/h to\ e)pitaxqe/n: e)nh/rmostai ga\r ei)s to\n *a*b*g ku/klon th=| *d eu)qei/a| i)/sh h( *b*g. ei) de\ mei/zwn e)sti\n h( *b*g th=s *d, kei/sqw th=| *d i)/sh h( *g*e, kai\ ke/ntrw| tw=| *g diasth/mati de\ tw=| *g*e ku/klos gegra/fqw o( *e*a*z, kai\ e)pezeu/xqw h( *g*a.

e)pei\ ou)=n to\ *g shmei=on ke/ntron e)sti\ tou= *e*a*z ku/klou, i)/sh e)sti\n h( *g*a th=| *g*e. a)lla\ th=| *d h( *g*e e)stin i)/sh: kai\ h( *d a)/ra th=| *g*a e)stin i)/sh.

ei)s a)/ra to\n doqe/nta ku/klon to\n *a*b*g th=| doqei/sh| eu)qei/a| th=| *d i)/sh e)nh/rmostai h( *g*a: o(/per e)/dei poih=sai.

ei)s to\n doqe/nta ku/klon tw=| doqe/nti trigw/nw| i)sogw/nion tri/gwnon e)ggra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g, to\ de\ doqe\n tri/gwnon to\ *d*e*z: dei= dh\ ei)s to\n *a*b*g ku/klon tw=| *d*e*z trigw/nw| i)sogw/nion tri/gwnon e)ggra/yai.

e)pei\ ou)=n ku/klou tou= *a*b*g e)fa/ptetai/ tis eu)qei=a h( *a*q, kai\ a)po\ th=s kata\ to\ *a e)pafh=s ei)s to\n ku/klon dih=ktai eu)qei=a h( *a*g, h( a)/ra u(po\ *q*a*g i)/sh e)sti\ th=| e)n tw=| e)nalla\c tou= ku/klou tmh/mati gwni/a| th=| u(po\ *a*b*g. a)ll' h( u(po\ *q*a*g th=| u(po\ *d*e*z e)stin i)/sh: kai\ h( u(po\ *a*b*g a)/ra gwni/a th=| u(po\ *d*e*z e)stin i)/sh. dia\ ta\ au)ta\ dh\ kai\ h( u(po\ *a*g*b th=| u(po\ *d*z*e e)stin i)/sh: kai\ loiph\ a)/ra h( u(po\ *b*a*g loiph=| th=| u(po\ *e*d*z e)stin i)/sh: ~~i)sogw/nion a)/ra e)sti\ to\ *a*b*g tri/gwnon tw=| *d*e*z trigw/nw|, kai\ e)gge/graptai ei)s to\n *a*b*g ku/klon~~.

ei)s to\n doqe/nta a)/ra ku/klon tw=| doqe/nti trigw/nw| i)sogw/nion tri/gwnon e)gge/graptai: o(/per e)/dei poih=sai.

peri\ to\n doqe/nta ku/klon tw=| doqe/nti trigw/nw| i)sogw/nion tri/gwnon perigra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g, to\ de\ doqe\n tri/gwnon to\ *d*e*z: dei= dh\ peri\ to\n *a*b*g ku/klon tw=| *d*e*z trigw/nw| i)sogw/nion tri/gwnon perigra/yai.

*)ekbeblh/sqw h( *e*z e)f' e(ka/tera ta\ me/rh kata\ ta\ *h, *q shmei=a, kai\ ei)lh/fqw tou= *a*b*g ku/klou ke/ntron to\ *k, kai\ dih/xqw, w(s e)/tuxen, eu)qei=a h( *k*b, kai\ sunesta/tw

kai\ e)pei\ e)fa/ptontai tou= *a*b*g ku/klou ai( *l*m, *m*n, *n*l kata\ ta\ *a, *b, *g shmei=a, a)po\ de\ tou= *k ke/ntrou e)pi\ ta\ *a, *b, *g shmei=a e)pezeugme/nai ei)si\n ai( *k*a, *k*b, *k*g, o)rqai\ a)/ra ei)si\n ai( pro\s toi=s *a, *b, *g shmei/ois gwni/ai. kai\ e)pei\ tou= *a*m*b*k tetrapleu/rou ai( te/ssares gwni/ai te/trasin o)rqai=s i)/sai ei)si/n, e)peidh/per kai\ ei)s du/o tri/gwna diairei=tai to\ *a*m*b*k, kai/ ei)sin o)rqai\ ai( u(po\ *k*a*m, *k*b*m gwni/ai, loipai\ a)/ra ai( u(po\ *a*k*b, *a*m*b dusi\n o)rqai=s i)/sai ei)si/n. ei)si\ de\ kai\ ai( u(po\ *d*e*h, *d*e*z dusi\n o)rqai=s i)/sai: ai( a)/ra u(po\ *a*k*b, *a*m*b tai=s u(po\ *d*e*h, *d*e*z i)/sai ei)si/n, w(=n h( u(po\ *a*k*b th=| u(po\ *d*e*h e)stin i)/sh: loiph\ a)/ra h( u(po\ *a*m*b loiph=| th=| u(po\ *d*e*z e)stin i)/sh. o(moi/ws dh\ deixqh/setai, o(/ti kai\ h( u(po\ *l*n*b th=| u(po\ *d*z*e e)stin i)/sh: kai\ loiph\ a)/ra h( u(po\ *m*l*n ~~loiph=|~~ th=| u(po\ *e*d*z e)stin i)/sh. i)sogw/nion a)/ra e)sti\ to\ *l*m*n tri/gwnon tw=| *d*e*z trigw/nw|: kai\ perige/graptai peri\ to\n *a*b*g ku/klon.

peri\ to\n doqe/nta a)/ra ku/klon tw=| doqe/nti trigw/nw| i)sogw/nion tri/gwnon perige/graptai: o(/per e)/dei poih=sai.

ei)s to\ doqe\n tri/gwnon ku/klon e)ggra/yai.

e)/stw to\ doqe\n tri/gwnon to\ *a*b*g: dei= dh\ ei)s to\ *a*b*g tri/gwnon ku/klon e)ggra/yai.

tetmh/sqwsan ai( u(po\ *a*b*g, *a*g*b gwni/ai di/xa tai=s *b*d, *g*d eu)qei/ais, kai\ sumballe/twsan a)llh/lais kata\ to\ *d shmei=on, kai\ h)/xqwsan a)po\ tou= *d e)pi\ ta\s *a*b, *b*g, *g*a eu)qei/as ka/qetoi ai( *d*e, *d*z, *d*h.

kai\ e)pei\ i)/sh e)sti\n h( u(po\ *a*b*d gwni/a th=| u(po\ *g*b*d, e)sti\ de\ kai\ o)rqh\ h( u(po\ *b*e*d o)rqh=| th=| u(po\ *b*z*d i)/sh, du/o

dh\ tri/gwna/ e)sti ta\ *e*b*d, *z*b*d ta\s du/o gwni/as tai=s dusi\ gwni/ais i)/sas e)/xonta kai\ mi/an pleura\n mia=| pleura=| i)/shn th\n u(potei/nousan u(po\ mi/an tw=n i)/swn gwniw=n koinh\n au)tw=n th\n *b*d: kai\ ta\s loipa\s a)/ra pleura\s tai=s loipai=s pleurai=s i)/sas e(/cousin: i)/sh a)/ra h( *d*e th=| *d*z. dia\ ta\ au)ta\ dh\ kai\ h( *d*h th=| *d*z e)stin i)/sh. ai( trei=s a)/ra eu)qei=ai ai( *d*e, *d*z, *d*h i)/sai a)llh/lais ei)si/n: o( a)/ra ke/ntrw| tw=| *d kai\ diasth/mati e(ni\ tw=n *e, *z, *h ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn kai\ e)fa/yetai tw=n *a*b, *b*g, *g*a eu)qeiw=n dia\ to\ o)rqa\s ei)=nai ta\s pro\s toi=s *e, *z, *h shmei/ois gwni/as. ei) ga\r temei= au)ta/s, e)/stai h( th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)nto\s pi/ptousa tou= ku/klou: o(/per a)/topon e)dei/xqh: ou)k a)/ra o( ke/ntrw| tw=| *d diasth/mati de\ e(ni\ tw=n *e, *z, *h grafo/menos ku/klos temei= ta\s *a*b, *b*g, *g*a eu)qei/as: e)fa/yetai a)/ra au)tw=n, kai\ e)/stai o( ku/klos e)ggegramme/nos ei)s to\ *a*b*g tri/gwnon. e)ggegra/fqw w(s o( *z*h*e.

ei)s a)/ra to\ doqe\n tri/gwnon to\ *a*b*g ku/klos e)gge/graptai o( *e*z*h: o(/per e)/dei poih=sai.

peri\ to\ doqe\n tri/gwnon ku/klon perigra/yai.

e)/stw to\ doqe\n tri/gwnon to\ *a*b*g: dei= ~~2dh\~~2 peri\ to\ doqe\n tri/gwnon to\ *a*b*g ku/klon perigra/yai.

tetmh/sqwsan ai( *a*b, *a*g eu)qei=ai di/xa kata\ ta\ *d, *e shmei=a, kai\ a)po\ tw=n *d, *e shmei/wn tai=s *a*b, *a*g pro\s o(rqa\s h)/xqwsan ai( *d*z, *e*z: sumpesou=ntai dh\ h)/toi e)nto\s tou= *a*b*g trigw/nou h)\ e)pi\ th=s *b*g eu)qei/as h)\ e)kto\s th=s *b*g.

sumpipte/twsan pro/teron e)nto\s kata\ to\ *z, kai\ e)pezeu/xqwsan ai( *z*b, *z*g, *z*a. kai\ e)pei\ i)/sh e)sti\n h( *a*d th=| *d*b, koinh\ de\ kai\ pro\s o)rqa\s h( *d*z, ba/sis a)/ra h( *a*z ba/sei th=| *z*b e)stin i)/sh. o(moi/ws dh\ dei/comen, o(/ti kai\ h( *g*z th=| *a*z e)stin i)/sh: w(/ste kai\ h( *z*b th=| *z*g e)stin i)/sh: ai( trei=s a)/ra ai( *z*a, *z*b, *z*g i)/sai a)llh/lais ei)si/n. o( a)/ra ke/ntrw| tw=| *z diasth/mati de\ e(ni\ tw=n *a, *b, *g ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn, kai\ e)/stai perigegramme/nos o( ku/klos peri\ to\ *a*b*g tri/gwnon. perigegra/fqw w(s o( *a*b*g.

a)lla\ dh\ ai( *d*z, *e*z sumpipte/twsan e)pi\ th=s *b*g eu)qei/as kata\ to\ *z, w(s e)/xei e)pi\ th=s deute/ras katagrafh=s, kai\ e)pezeu/xqw h( *a*z. o(moi/ws dh\ dei/comen, o(/ti to\ *z shmei=on ke/ntron e)sti\ tou= peri\ to\ *a*b*g tri/gwnon perigrafome/nou ku/klou.

a)lla\ dh\ ai( *d*z, *e*z sumpipte/twsan e)kto\s tou= *a*b*g trigw/nou kata\ to\ *z pa/lin, w(s e)/xei e)pi\ th=s tri/ths katagrafh=s, kai\ e)pezeu/xqwsan ai( *a*z, *b*z, *g*z. kai\ e)pei\ pa/lin i)/sh e)sti\n h( *a*d th=| *d*b, koinh\ de\ kai\ pro\s o)rqa\s h( *d*z, ba/sis a)/ra h( *a*z ba/sei th=| *b*z e)stin i)/sh. o(moi/ws dh\ dei/comen, o(/ti kai\ h( *g*z th=| *a*z e)stin i)/sh: w(/ste kai\ h( *b*z th=| *z*g e)stin i)/sh: o( a)/ra ~~pa/lin~~ ke/ntrw| tw=| *z diasth/mati de\ e(ni\ tw=n *z*a, *z*b, *z*g ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn, kai\ e)/stai perigegramme/nos peri\ to\ *a*b*g tri/gwnon.

peri\ to\ doqe\n a)/ra tri/gwnon ku/klos perige/graptai: o(/per e)/dei poih=sai.

*po/risma

kai\ fanero/n, o(/ti, o(/te me\n e)nto\s tou= trigw/nou pi/ptei to\ ke/ntron tou= ku/klou, h( u(po\ *b*a*g gwni/a e)n mei/zoni tmh/mati tou= h(mikukli/ou tugxa/nousa e)la/ttwn e)sti\n o)rqh=s: o(/te de\ e)pi\ th=s *b*g eu)qei/as to\ ke/ntron pi/ptei, h( u(po\ *b*a*g gwni/a e)n h(mikukli/w| tugxa/nousa o)rqh/ e)stin: o(/te de\ to\ ke/ntron tou= ku/klou e)kto\s tou= trigw/nou pi/ptei, h( u(po\ *b*a*g e)n e)la/ttoni tmh/mati tou= h(mikukli/ou tugxa/nousa mei/zwn e)sti\n o)rqh=s. w(/ste kai\ o(/tan e)la/ttwn o)rqh=s tugxa/nh| h( didome/nh gwni/a, e)nto\s tou= trigw/nou pesou=ntai ai( *d*z, *e*z, o(/tan de\ o)rqh/, e)pi\ th=s *b*g, o(/tan de\ mei/zwn o)rqh=s, e)kto\s th=s *b*g: o(/per e)/dei poih=sai.

ei)s to\n doqe/nta ku/klon tetra/gwnon e)ggra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g*d: dei= dh\ ei)s to\n *a*b*g*d ku/klon tetra/gwnon e)ggra/yai.

h)/xqwsan tou= *a*b*g*d ku/klou du/o dia/metroi pro\s o)rqa\s a)llh/lais ai( *a*g, *b*d, kai\ e)pezeu/xqwsan ai( *a*b, *b*g, *g*d, *d*a.

kai\ e)pei\ i)/sh e)sti\n h( *b*e th=| *e*d: ke/ntron ga\r to\ *e: koinh\ de\ kai\ pro\s o)rqa\s h( *e*a, ba/sis a)/ra h( *a*b ba/sei

th=| *a*d i)/sh e)sti/n. dia\ ta\ au)ta\ dh\ kai\ e(kate/ra tw=n *b*g, *g*d e(kate/ra| tw=n *a*b, *a*d i)/sh e)sti/n: i)so/pleuron a)/ra e)sti\ to\ *a*b*g*d tetra/pleuron. le/gw dh/, o(/ti kai\ o)rqogw/nion. e)pei\ ga\r h( *b*d eu)qei=a dia/metro/s e)sti tou= *a*b*g*d ku/klou, h(miku/klion a)/ra e)sti\ to\ *b*a*d: o)rqh\ a)/ra h( u(po\ *b*a*d gwni/a. dia\ ta\ au)ta\ dh\ kai\ e(ka/sth tw=n u(po\ *a*b*g, *b*g*d, *g*d*a o)rqh/ e)stin: o)rqogw/nion a)/ra e)sti\ to\ *a*b*g*d tetra/pleuron. e)dei/xqh de\ kai\ i)so/pleuron: tetra/gwnon a)/ra e)sti/n. kai\ e)gge/graptai ei)s to\n *a*b*g*d ku/klon.

ei)s a)/ra to\n doqe/nta ku/klon tetra/gwnon e)gge/graptai to\ *a*b*g*d: o(/per e)/dei poih=sai.

peri\ to\n doqe/nta ku/klon tetra/gwnon perigra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g*d: dei= dh\ peri\ to\n *a*b*g*d ku/klon tetra/gwnon perigra/yai.

h)/xqwsan tou= *a*b*g*d ku/klou du/o dia/metroi pro\s o)rqa\s a)llh/lais ai( *a*g, *b*d, kai\ dia\ tw=n *a, *b, *g, *d shmei/wn h)/xqwsan e)fapto/menai tou= *a*b*g*d ku/klou ai( *z*h, *h*q, *q*k, *k*z.

e)pei\ ou)=n e)fa/ptetai h( *z*h tou= *a*b*g*d ku/klou, a)po\ de\ tou= *e ke/ntrou e)pi\ th\n kata\ to\ *a e)pafh\n e)pe/zeuktai h( *e*a, ai( a)/ra pro\s tw=| *a gwni/ai o)rqai/ ei)sin. dia\ ta\ au)ta\ dh\ kai\ ai( pro\s toi=s *b, *g, *d shmei/ois gwni/ai o)rqai/ ei)sin. kai\ e)pei\ o)rqh/ e)stin h( u(po\ *a*e*b gwni/a,

e)sti\ de\ o)rqh\ kai\ h( u(po\ *e*b*h, para/llhlos a)/ra e)sti\n h( *h*q th=| *a*g. dia\ ta\ au)ta\ dh\ kai\ h( *a*g th=| *z*k e)sti para/llhlos. w(/ste kai\ h( *h*q th=| *z*k e)sti para/llhlos. o(moi/ws dh\ dei/comen, o(/ti kai\ e(kate/ra tw=n *h*z, *q*k th=| *b*e*d e)sti para/llhlos. parallhlo/gramma a)/ra e)sti\ ta\ *h*k, *h*g, *a*k, *z*b, *b*k: i)/sh a)/ra e)sti\n h( me\n *h*z th=| *q*k, h( de\ *h*q th=| *z*k. kai\ e)pei\ i)/sh e)sti\n h( *a*g th=| *b*d, a)lla\ kai\ h( me\n *a*g e(kate/ra| tw=n *h*q, *z*k, h( de\ *b*d e(kate/ra| tw=n *h*z, *q*k e)stin i)/sh ~~kai\ e(kate/ra a)/ra tw=n *h*q, *z*k e(kate/ra| tw=n *h*z, *q*k e)stin i)/sh~~, i)so/pleuron a)/ra e)sti\ to\ *z*h*q*k tetra/pleuron. le/gw dh/, o(/ti kai\ o)rqogw/nion. e)pei\ ga\r parallhlo/grammo/n e)sti to\ *h*b*e*a, kai/ e)stin o)rqh\ h( u(po\ *a*e*b, o)rqh\ a)/ra kai\ h( u(po\ *a*h*b. o(moi/ws dh\ dei/comen, o(/ti kai\ ai( pro\s toi=s *q, *k, *z gwni/ai o)rqai/ ei)sin. o)rqogw/nion a)/ra e)sti\ to\ *z*h*q*k. e)dei/xqh de\ kai\ i)so/pleuron: tetra/gwnon a)/ra e)sti/n. kai\ perige/graptai peri\ to\n *a*b*g*d ku/klon.

peri\ to\n doqe/nta a)/ra ku/klon tetra/gwnon perige/graptai: o(/per e)/dei poih=sai.

ei)s to\ doqe\n tetra/gwnon ku/klon e)ggra/yai.

e)/stw to\ doqe\n tetra/gwnon to\ *a*b*g*d: dei= dh\ ei)s to\ *a*b*g*d tetra/gwnon ku/klon e)ggra/yai.

tetmh/sqw e(kate/ra tw=n *a*d, *a*b di/xa kata\ ta\ *e, *z shmei=a, kai\ dia\ me\n tou= *e o(pote/ra| tw=n *a*b, *g*d para/llhlos h)/xqw h( *e*q, dia\ de\ tou= *z o(pote/ra| tw=n *a*d, *b*g para/llhlos h)/xqw h( *z*k: parallhlo/grammon a)/ra e)sti\n

e(/kaston tw=n *a*k, *k*b, *a*q, *q*d, *a*h, *h*g, *b*h, *h*d, kai\ ai( a)penanti/on au)tw=n pleurai\ dhlono/ti i)/sai ~~ei)si/n~~. kai\ e)pei\ i)/sh e)sti\n h( *a*d th=| *a*b, kai/ e)sti th=s me\n *a*d h(mi/seia h( *a*e, th=s de\ *a*b h(mi/seia h( *a*z, i)/sh a)/ra kai\ h( *a*e th=| *a*z: w(/ste kai\ ai( a)penanti/on: i)/sh a)/ra kai\ h( *z*h th=| *h*e. o(moi/ws dh\ dei/comen, o(/ti kai\ e(kate/ra tw=n *h*q, *h*k e(kate/ra| tw=n *z*h, *h*e e)stin i)/sh: ai( te/ssares a)/ra ai( *h*e, *h*z, *h*q, *h*k i)/sai a)llh/lais ~~ei)si/n~~. o( a)/ra ke/ntrw| me\n tw=| *h diasth/mati de\ e(ni\ tw=n *e, *z, *q, *k ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn: kai\ e)fa/yetai tw=n *a*b, *b*g, *g*d, *d*a eu)qeiw=n dia\ to\ o)rqa\s ei)=nai ta\s pro\s toi=s *e, *z, *q, *k gwni/as: ei) ga\r temei= o( ku/klos ta\s *a*b, *b*g, *g*d, *d*a, h( th=| diame/trw| tou= ku/klou pro\s o)rqa\s a)p' a)/kras a)gome/nh e)nto\s pesei=tai tou= ku/klou: o(/per a)/topon e)dei/xqh. ou)k a)/ra o( ke/ntrw| tw=| *h diasth/mati de\ e(ni\ tw=n *e, *z, *q, *k ku/klos grafo/menos temei= ta\s *a*b, *b*g, *g*d, *d*a eu)qei/as. e)fa/yetai a)/ra au)tw=n kai\ e)/stai e)ggegramme/nos ei)s to\ *a*b*g*d tetra/gwnon.

ei)s a)/ra to\ doqe\n tetra/gwnon ku/klos e)gge/graptai: o(/per e)/dei poih=sai.

peri\ to\ doqe\n tetra/gwnon ku/klon perigra/yai.

e)/stw to\ doqe\n tetra/gwnon to\ *a*b*g*d: dei= dh\ peri\ to\ *a*b*g*d tetra/gwnon ku/klon perigra/yai.

e)pizeuxqei=sai ga\r ai( *a*g, *b*d temne/twsan a)llh/las kata\ to\ *e.

kai\ e)pei\ i)/sh e)sti\n h( *d*a th=| *a*b, koinh\ de\ h( *a*g, du/o dh\ ai( *d*a, *a*g dusi\ tai=s *b*a, *a*g i)/sai ei)si/n: kai\ ba/sis h( *d*g ba/sei th=| *b*g i)/sh: gwni/a a)/ra h( u(po\ *d*a*g gwni/a| th=| u(po\ *b*a*g i)/sh e)sti/n: h( a)/ra u(po\ *d*a*b gwni/a di/xa te/tmhtai u(po\ th=s *a*g. o(moi/ws dh\ dei/comen, o(/ti kai\ e(ka/sth

tw=n u(po\ *a*b*g, *b*g*d, *g*d*a di/xa te/tmhtai u(po\ tw=n *a*g, *d*b eu)qeiw=n. kai\ e)pei\ i)/sh e)sti\n h( u(po\ *d*a*b gwni/a th=| u(po\ *a*b*g, kai/ e)sti th=s me\n u(po\ *d*a*b h(mi/seia h( u(po\ *e*a*b, th=s de\ u(po\ *a*b*g h(mi/seia h( u(po\ *e*b*a, kai\ h( u(po\ *e*a*b a)/ra th=| u(po\ *e*b*a e)stin i)/sh: w(/ste kai\ pleura\ h( *e*a th=| *e*b e)stin i)/sh. o(moi/ws dh\ dei/comen, o(/ti kai\ e(kate/ra tw=n *e*a, *e*b ~~eu)qeiw=n~~ e(kate/ra| tw=n *e*g, *e*d i)/sh e)sti/n. ai( te/ssares a)/ra ai( *e*a, *e*b, *e*g, *e*d i)/sai a)llh/lais ei)si/n. o( a)/ra ke/ntrw| tw=| *e kai\ diasth/mati e(ni\ tw=n *a, *b, *g, *d ku/klos grafo/menos h(/cei kai\ dia\ tw=n loipw=n shmei/wn kai\ e)/stai perigegramme/nos peri\ to\ *a*b*g*d tetra/gwnon. perigegra/fqw w(s o( *a*b*g*d.

peri\ to\ doqe\n a)/ra tetra/gwnon ku/klos perige/graptai: o(/per e)/dei poih=sai.

i)soskele\s tri/gwnon susth/sasqai e)/xon e(kate/ran tw=n pro\s th=| ba/sei gwniw=n diplasi/ona th=s loiph=s.

*)ekkei/sqw tis eu)qei=a h( *a*b, kai\ tetmh/sqw kata\ to\ *g shmei=on, w(/ste to\ u(po\ tw=n *a*b, *b*g periexo/menon o)rqogw/nion i)/son ei)=nai tw=| a)po\ th=s *g*a

kai\ e)pei\ to\ u(po\ tw=n *a*b, *b*g i)/son e)sti\ tw=| a)po\ th=s *a*g, i)/sh de\ h( *a*g th=| *b*d, to\ a)/ra u(po\ tw=n *a*b, *b*g i)/son e)sti\ tw=| a)po\ th=s *b*d. kai\ e)pei\ ku/klou tou= *a*g*d ei)/lhptai/ ti shmei=on e)kto\s to\ *b, kai\ a)po\ tou= *b pro\s to\n *a*g*d ku/klon prospeptw/kasi du/o eu)qei=ai ai( *b*a, *b*d, kai\ h( me\n au)tw=n te/mnei, h( de\ prospi/ptei, kai/ e)sti to\ u(po\ tw=n *a*b, *b*g i)/son tw=| a)po\ th=s *b*d, h( *b*d a)/ra e)fa/ptetai tou= *a*g*d ku/klou. e)pei\ ou)=n e)fa/ptetai me\n h( *b*d, a)po\ de\ th=s kata\ to\ *d e)pafh=s dih=ktai h( *d*g, h( a)/ra u(po\ *b*d*g gwni/a i)/sh e)sti\ th=| e)n tw=| e)nalla\c tou= ku/klou tmh/mati gwni/a| th=| u(po\ *d*a*g. e)pei\ ou)=n i)/sh e)sti\n h( u(po\ *b*d*g th=| u(po\ *d*a*g, koinh\ proskei/sqw h( u(po\ *g*d*a: o(/lh a)/ra h( u(po\ *b*d*a i)/sh e)sti\ dusi\ tai=s u(po\ *g*d*a, *d*a*g. a)lla\ tai=s u(po\ *g*d*a, *d*a*g i)/sh e)sti\n h( e)kto\s h( u(po\ *b*g*d: kai\ h( u(po\ *b*d*a a)/ra i)/sh e)sti\ th=| u(po\ *b*g*d. a)lla\ h( u(po\ *b*d*a th=| u(po\ *g*b*d e)stin i)/sh, e)pei\ kai\ pleura\ h( *a*d th=| *a*b e)stin i)/sh: w(/ste kai\ h( u(po\ *d*b*a th=| u(po\ *b*g*d e)stin i)/sh. ai( trei=s a)/ra ai( u(po\ *b*d*a, *d*b*a, *b*g*d i)/sai a)llh/lais ei)si/n. kai\ e)pei\ i)/sh e)sti\n h( u(po\ *d*b*g gwni/a th=| u(po\ *b*g*d, i)/sh e)sti\ kai\ pleura\ h( *b*d pleura=| th=| *d*g. a)lla\ h( *b*d th=| *g*a u(po/keitai i)/sh: kai\ h( *g*a a)/ra th=| *g*d e)stin i)/sh: w(/ste kai\ gwni/a h( u(po\ *g*d*a gwni/a| th=| u(po\ *d*a*g e)stin i)/sh: ai( a)/ra u(po\ *g*d*a, *d*a*g th=s u(po\ *d*a*g ei)si diplasi/ous. i)/sh de\ h( u(po\ *b*g*d tai=s u(po\ *g*d*a, *d*a*g: kai\ h( u(po\ *b*g*d a)/ra th=s u(po\ *g*a*d e)sti diplh=. i)/sh de\ h( u(po\ *b*g*d e(kate/ra| tw=n u(po\ *b*d*a, *d*b*a: kai\ e(kate/ra a)/ra tw=n u(po\ *b*d*a, *d*b*a th=s u(po\ *d*a*b e)sti diplh=.

i)soskele\s a)/ra tri/gwnon sune/statai to\ *a*b*d e)/xon e(kate/ran tw=n pro\s th=| *d*b ba/sei gwniw=n diplasi/ona th=s loiph=s: o(/per e)/dei poih=sai.

ei)s to\n doqe/nta ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion e)ggra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g*d*e: dei= dh\ ei)s to\n *a*b*g*d*e ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion e)ggra/yai.

*g*a*d, e(kate/ran de\ tw=n pro\s toi=s *h, *q i)/shn e(kate/ra| tw=n u(po\ *a*g*d, *g*d*a: kai\ e(kate/ra a)/ra tw=n u(po\ *a*g*d, *g*d*a th=s u(po\ *g*a*d e)sti diplh=. tetmh/sqw dh\ e(kate/ra tw=n u(po\ *a*g*d, *g*d*a di/xa u(po\ e(kate/ras tw=n *g*e, *d*b eu)qeiw=n, kai\ e)pezeu/xqwsan ai( *a*b, *b*g, *g*d, *d*e, *e*a.

e)pei\ ou)=n e(kate/ra tw=n u(po\ *a*g*d, *g*d*a gwniw=n diplasi/wn e)sti\ th=s u(po\ *g*a*d, kai\ tetmhme/nai ei)si\ di/xa u(po\ tw=n *g*e, *d*b eu)qeiw=n, ai( pe/nte a)/ra gwni/ai ai( u(po\ *d*a*g, *a*g*e, *e*g*d, *g*d*b, *b*d*a i)/sai a)llh/lais ei)si/n. ai( de\ i)/sai gwni/ai e)pi\ i)/swn perifereiw=n bebh/kasin: ai( pe/nte a)/ra perife/reiai ai( *a*b, *b*g, *g*d, *d*e, *e*a i)/sai a)llh/lais ei)si/n. u(po\ de\ ta\s i)/sas periferei/as i)/sai eu)qei=ai u(potei/nousin: ai( pe/nte a)/ra eu)qei=ai ai( *a*b, *b*g, *g*d, *d*e, *e*a i)/sai a)llh/lais ei)si/n: i)so/pleuron a)/ra e)sti\ to\ *a*b*g*d*e penta/gwnon. le/gw dh/, o(/ti kai\ i)sogw/nion. e)pei\ ga\r h( *a*b perife/reia th=| *d*e periferei/a| e)sti\n i)/sh, koinh\ proskei/sqw h( *b*g*d: o(/lh a)/ra h( *a*b*g*d perife/reia o(/lh| th=| *e*d*g*b periferei/a| e)sti\n i)/sh. kai\ be/bhken e)pi\ me\n th=s *a*b*g*d periferei/as gwni/a h( u(po\ *a*e*d, e)pi\ de\ th=s *e*d*g*b periferei/as gwni/a h( u(po\ *b*a*e: kai\ h( u(po\ *b*a*e a)/ra gwni/a th=| u(po\ *a*e*d e)stin i)/sh. dia\ ta\ au)ta\ dh\ kai\ e(ka/sth tw=n u(po\ *a*b*g, *b*g*d, *g*d*e gwniw=n e(kate/ra| tw=n u(po\ *b*a*e, *a*e*d e)stin i)/sh: i)sogw/nion a)/ra e)sti\ to\ *a*b*g*d*e penta/gwnon. e)dei/xqh de\ kai\ i)so/pleuron.

ei)s a)/ra to\n doqe/nta ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion e)gge/graptai: o(/per e)/dei poih=sai.

peri\ to\n doqe/nta ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion perigra/yai.

e)/stw o( doqei\s ku/klos o( *a*b*g*d*e: dei= ~~2dh\~~2 peri\ to\n *a*b*g*d*e ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion perigra/yai.

nenoh/sqw tou= e)ggegramme/nou pentagw/nou tw=n gwniw=n shmei=a ta\ *a, *b, *g, *d, *e, w(/ste i)/sas ei)=nai ta\s *a*b, *b*g, *g*d, *d*e, *e*a periferei/as: kai\ dia\ tw=n *a, *b, *g, *d, *e h)/xqwsan tou= ku/klou e)fapto/menai ai( *h*q, *q*k, *k*l, *l*m, *m*h, kai\ ei)lh/fqw tou= *a*b*g*d*e ku/klou ke/ntron to\ *z, kai\ e)pezeu/xqwsan ai( *z*b, *z*k, *z*g, *z*l, *z*d.

kai\ e)pei\ h( me\n *k*l eu)qei=a e)fa/ptetai tou=

*a*b*g*d*e kata\ to\ *g, a)po\ de\ tou= *z ke/ntrou e)pi\ th\n kata\ to\ *g e)pafh\n e)pe/zeuktai h( *z*g, h( *z*g a)/ra ka/qeto/s e)stin e)pi\ th\n *k*l: o)rqh\ a)/ra e)sti\n e(kate/ra tw=n pro\s tw=| *g gwniw=n. dia\ ta\ au)ta\ dh\ kai\ ai( pro\s toi=s *b, *d shmei/ois gwni/ai o)rqai/ ei)sin. kai\ e)pei\ o)rqh/ e)stin h( u(po\ *z*g*k gwni/a, to\ a)/ra a)po\ th=s *z*k i)/son e)sti\ toi=s a)po\ tw=n *z*g, *g*k. dia\ ta\ au)ta\ dh\ kai\ toi=s a)po\ tw=n *z*b, *b*k i)/son e)sti\ to\ a)po\ th=s *z*k: w(/ste ta\ a)po\ tw=n *z*g, *g*k toi=s a)po\ tw=n *z*b, *b*k e)stin i)/sa, w(=n to\ a)po\ th=s *z*g tw=| a)po\ th=s *z*b e)stin i)/son: loipo\n a)/ra to\ a)po\ th=s *g*k tw=| a)po\ th=s *b*k e)stin i)/son. i)/sh a)/ra h( *b*k th=| *g*k. kai\ e)pei\ i)/sh e)sti\n h( *z*b th=| *z*g, kai\ koinh\ h( *z*k, du/o dh\ ai( *b*z, *z*k dusi\ tai=s *g*z, *z*k i)/sai ei)si/n: kai\ ba/sis h( *b*k ba/sei th=| *g*k ~~e)stin~~ i)/sh: gwni/a a)/ra h( me\n u(po\ *b*z*k ~~gwni/a|~~ th=| u(po\ *k*z*g e)stin i)/sh: h( de\ u(po\ *b*k*z th=| u(po\ *z*k*g: diplh= a)/ra h( me\n u(po\ *b*z*g th=s u(po\ *k*z*g, h( de\ u(po\ *b*k*g th=s u(po\ *z*k*g. dia\ ta\ au)ta\ dh\ kai\ h( me\n u(po\ *g*z*d th=s u(po\ *g*z*l e)sti diplh=, h( de\ u(po\ *d*l*g th=s u(po\ *z*l*g. kai\ e)pei\ i)/sh e)sti\n h( *b*g perife/reia th=| *g*d, i)/sh e)sti\ kai\ gwni/a h( u(po\ *b*z*g th=| u(po\ *g*z*d. kai/ e)stin h( me\n u(po\ *b*z*g th=s u(po\ *k*z*g diplh=, h( de\ u(po\ *d*z*g th=s u(po\ *l*z*g: i)/sh a)/ra kai\ h( u(po\ *k*z*g th=| u(po\ *l*z*g: e)sti\ de\ kai\ h( u(po\ *z*g*k gwni/a th=| u(po\ *z*g*l i)/sh. du/o dh\ tri/gwna/ e)sti ta\ *z*k*g, *z*l*g ta\s du/o gwni/as tai=s dusi\ gwni/ais i)/sas e)/xonta kai\ mi/an pleura\n mia=| pleura=| i)/shn koinh\n au)tw=n th\n *z*g: kai\ ta\s loipa\s a)/ra pleura\s tai=s loipai=s pleurai=s i)/sas e(/cei kai\ th\n loiph\n gwni/an th=| loiph=| gwni/a|: i)/sh a)/ra h( me\n *k*g eu)qei=a th=| *g*l, h( de\ u(po\ *z*k*g gwni/a th=| u(po\ *z*l*g. kai\ e)pei\ i)/sh e)sti\n h( *k*g th=| *g*l, diplh= a)/ra h( *k*l th=s *k*g. dia\ ta\ au)ta\ dh\ deixqh/setai kai\ h( *q*k th=s *b*k diplh=. kai/ e)stin h( *b*k th=| *k*g i)/sh: kai\ h( *q*k a)/ra th=| *k*l e)stin i)/sh. o(moi/ws dh\ deixqh/setai kai\ e(ka/sth tw=n *q*h, *h*m, *m*l e(kate/ra| tw=n *q*k, *k*l i)/sh: i)so/pleuron a)/ra e)sti\ to\ *h*q*k*l*m penta/gwnon. le/gw dh/, o(/ti kai\ i)sogw/nion. e)pei\ ga\r i)/sh e)sti\n h( u(po\ *z*k*g gwni/a th=| u(po\ *z*l*g, kai\ e)dei/xqh th=s me\n u(po\ *z*k*g diplh= h( u(po\ *q*k*l, th=s de\ u(po\ *z*l*g diplh= h( u(po\ *k*l*m, kai\ h( u(po\ *q*k*l a)/ra th=| u(po\ *k*l*m e)stin i)/sh. o(moi/ws dh\ deixqh/setai kai\ e(ka/sth tw=n u(po\ *k*q*h, *q*h*m, *h*m*l e(kate/ra| tw=n u(po\ *q*k*l, *k*l*m i)/sh: ai( pe/nte a)/ra gwni/ai ai( u(po\ *h*q*k, *q*k*l, *k*l*m, *l*m*h, *m*h*q i)/sai a)llh/lais ei)si/n. i)sogw/nion a)/ra e)sti\ to\ *h*q*k*l*m penta/gwnon. e)dei/xqh de\ kai\ i)so/pleuron, kai\ perige/graptai peri\ to\n *a*b*g*d*e ku/klon.

*peri\ to\n doqe/nta a)/ra ku/klon penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion perige/graptai: o(/per e)/dei poih=sai.

ei)s to\ doqe\n penta/gwnon, o(/ e)stin i)so/pleuro/n te kai\ i)sogw/nion, ku/klon e)ggra/yai.

e)/stw to\ doqe\n penta/gwnon i)so/pleuro/n te kai\ i)sogw/nion to\ *a*b*g*d*e: dei= dh\ ei)s to\ *a*b*g*d*e penta/gwnon ku/klon e)ggra/yai.

tetmh/sqw ga\r e(kate/ra tw=n u(po\ *b*g*d, *g*d*e gwniw=n di/xa u(po\ e(kate/ras tw=n *g*z, *d*z eu)qeiw=n: kai\ a)po\ tou= *z shmei/ou, kaq' o(\ sumba/llousin a)llh/lais ai( *g*z, *d*z eu)qei=ai, e)pezeu/xqwsan ai( *z*b, *z*a, *z*e eu)qei=ai. kai\ e)pei\ i)/sh e)sti\n h( *b*g th=| *g*d, koinh\ de\ h( *g*z, du/o dh\ ai( *b*g, *g*z

dusi\ tai=s *d*g, *g*z i)/sai ei)si/n: kai\ gwni/a h( u(po\ *b*g*z gwni/a| th=| u(po\ *d*g*z ~~e)stin~~ i)/sh: ba/sis a)/ra h( *b*z ba/sei th=| *d*z e)stin i)/sh, kai\ to\ *b*g*z tri/gwnon tw=| *d*g*z trigw/nw| e)stin i)/son, kai\ ai( loipai\ gwni/ai tai=s loipai=s gwni/ais i)/sai e)/sontai, u(f' a(\s ai( i)/sai pleurai\ u(potei/nousin: i)/sh a)/ra h( u(po\ gwni/a th=| u(po\ . kai\ e)pei\ diplh= e)stin h( u(po\ th=s u(po\ , i)/sh de\ h( me\n u(po\ th=| u(po\ ,