Multò maiorem.] Quia a d ſubtendit multò maiorem an
gulum, vtpote b obtuſum, & ideò maiorem recto: quam b g, quæ
ſubtendit a angulum acutum, & ideò etiam minorem recto.
gulum, vtpote b obtuſum, & ideò maiorem recto: quam b g, quæ
ſubtendit a angulum acutum, & ideò etiam minorem recto.
Et latus b d. ] Attingit ſecundum problema quod generaliter
verum non eſt. In Rhombo enim cuius, qui acutus eſt angulus, maior
eſt dimidio obtuſi, vt in E
75[Figure 75]
F G H: quia F H an
gulum E maiorem ſubten
dit: quam E H, erit F H
maior E H prop. 18. lib. 1.
Sed verum eſt in certo ca
ſu, eo nimirum (licet hîc
non ſit expreſſus ) in quo
Rhombi acutus eſſet mi
nor: quam dimidius obtu
ſi, vt angulus A Rhombi
A B C D ſit minor: quam dimidius obtuſi B, id eſt quam A B C.
Dico latus A C maius eſſe diametro B C per eandem prop. 18.
ſubtendit enim trianguli A B C maiorem angulum. Poſſe autem
talem Rhombum conſtitui, patet. quia angulus acutus ſeruata late
rum quorumuis aſſumptorum longitudine, infinitè minor fieri poteſt,
prop. 9. lib. 1. Ergo & tandem dabitur minor dimidio obtuſi. Nam
& dimidius recti, qui acutus eſt, eſt eo minor prop. 15. lib. 5. Ergo in
tali Rhombo latus A B per A C vna latione motum, plus ſpatij
confecit: quam B, quod peragrans B C duabus lationibus ferebatur.
verum non eſt. In Rhombo enim cuius, qui acutus eſt angulus, maior
eſt dimidio obtuſi, vt in E
75[Figure 75]F G H: quia F H an
gulum E maiorem ſubten
dit: quam E H, erit F H
maior E H prop. 18. lib. 1.
Sed verum eſt in certo ca
ſu, eo nimirum (licet hîc
non ſit expreſſus ) in quo
Rhombi acutus eſſet mi
nor: quam dimidius obtu
ſi, vt angulus A Rhombi
A B C D ſit minor: quam dimidius obtuſi B, id eſt quam A B C.
Dico latus A C maius eſſe diametro B C per eandem prop. 18.
ſubtendit enim trianguli A B C maiorem angulum. Poſſe autem
talem Rhombum conſtitui, patet. quia angulus acutus ſeruata late
rum quorumuis aſſumptorum longitudine, infinitè minor fieri poteſt,
prop. 9. lib. 1. Ergo & tandem dabitur minor dimidio obtuſi. Nam
& dimidius recti, qui acutus eſt, eſt eo minor prop. 15. lib. 5. Ergo in
tali Rhombo latus A B per A C vna latione motum, plus ſpatij
confecit: quam B, quod peragrans B C duabus lationibus ferebatur.
a)/topon ga/r, w(/sper e)le/xqh, to\
du/o fora\s fero/menon e)ni/ote bradu/teron fe/resqai tou= mi/an,
kai\ a)mfote/rwn i)sotaxw=n shmei/wn doqe/ntwn, mei/zw diecie/nai
qa/teron. ai)/tion de\, o(/ti tou= me\n a)po\ th=s a)mblei/as ferome/nou
sxedo\n e)nanti/ai a)mfo/terai gi/nontai, h(/n te au)th\
fe/retai kai\ h(\n u(po\ th=s pleura=s u(pofe/retai. tou= de\ a)po\
th=s o)cei/as, w/(sper sumbai/nei fe/resqai e)pi\ to\ au)to/. sunepouri/zei
ga\r h( th=s pleura=s, th\n e)pi\ th=s diame/trou: kai\ o(/sw| a)\n
th\n me\n o)cute/ran poih/sh|, th\n de\ a)mblute/ran, h( me\n bradute/ra
e)/stai, h( de\ qa/ttwn. ai( me\n ga\r e)nantiw/terai gi/nontai,
dia\ to\ a)mblute/ran gi/nesqai th\n gwni/an. ai( de\
ma=llon e)pi\ ta\ au)ta\, dia\ to\ suna/gesqai ta\s gramma/s.
to\ me\n ga\r *a sxedo\n e)pi\ to\ au)to\ fe/retai kat' a)mfote/ras
ta\s fora/s: sunepouri/zetai ou)=n h( e(te/ra, kai\ o(/sw| a)\n
o)cute/ra gi/nhtai h( gwni/a, tosou/tw| ma=llon: to\ de\ *a de\ e)pi\
tou)nanti/on: au)to\ me\n ga\r pro\s to\ *a fe/retai, h( de\ pleura\
u(pofe/rei au)to\ pro\s to\ *g. kai\ o(/sw| a)\n a)mblute/ra h( gwni/a
h)=|, e)nantiw/terai ai( forai\ gi/nontai: eu)qute/ra ga\r h(
grammh\ gi/netai. ei) d' o(/lws eu)qei=a ge/noito, pantelw=s a)\n
ei)/hsan e)nanti/ai. h( de\ pleura\ u(p' ou)qeno\s kwlu/etai mi/an
ferome/nh fora/n. eu)lo/gws ou)=n th\n mei/zw die/rxetai.
du/o fora\s fero/menon e)ni/ote bradu/teron fe/resqai tou= mi/an,
kai\ a)mfote/rwn i)sotaxw=n shmei/wn doqe/ntwn, mei/zw diecie/nai
qa/teron. ai)/tion de\, o(/ti tou= me\n a)po\ th=s a)mblei/as ferome/nou
sxedo\n e)nanti/ai a)mfo/terai gi/nontai, h(/n te au)th\
fe/retai kai\ h(\n u(po\ th=s pleura=s u(pofe/retai. tou= de\ a)po\
th=s o)cei/as, w/(sper sumbai/nei fe/resqai e)pi\ to\ au)to/. sunepouri/zei
ga\r h( th=s pleura=s, th\n e)pi\ th=s diame/trou: kai\ o(/sw| a)\n
th\n me\n o)cute/ran poih/sh|, th\n de\ a)mblute/ran, h( me\n bradute/ra
e)/stai, h( de\ qa/ttwn. ai( me\n ga\r e)nantiw/terai gi/nontai,
dia\ to\ a)mblute/ran gi/nesqai th\n gwni/an. ai( de\
ma=llon e)pi\ ta\ au)ta\, dia\ to\ suna/gesqai ta\s gramma/s.
to\ me\n ga\r *a sxedo\n e)pi\ to\ au)to\ fe/retai kat' a)mfote/ras
ta\s fora/s: sunepouri/zetai ou)=n h( e(te/ra, kai\ o(/sw| a)\n
o)cute/ra gi/nhtai h( gwni/a, tosou/tw| ma=llon: to\ de\ *a de\ e)pi\
tou)nanti/on: au)to\ me\n ga\r pro\s to\ *a fe/retai, h( de\ pleura\
u(pofe/rei au)to\ pro\s to\ *g. kai\ o(/sw| a)\n a)mblute/ra h( gwni/a
h)=|, e)nantiw/terai ai( forai\ gi/nontai: eu)qute/ra ga\r h(
grammh\ gi/netai. ei) d' o(/lws eu)qei=a ge/noito, pantelw=s a)\n
ei)/hsan e)nanti/ai. h( de\ pleura\ u(p' ou)qeno\s kwlu/etai mi/an
ferome/nh fora/n. eu)lo/gws ou)=n th\n mei/zw die/rxetai.