Præterea duro.] Alterum eſt quaſi problema quod nuci
frangibulum durum & graue facilius frangat: quam ligneum &
leue. Cum tamen contra euenire deberet. Siquidem graue quod eſt,
difficilius emoueatur.
frangibulum durum & graue facilius frangat: quam ligneum &
leue. Cum tamen contra euenire deberet. Siquidem graue quod eſt,
difficilius emoueatur.
An quia ſic vtrinque.] Demonſtratio eſt problematis ſic.
Valide comprimentia compreſſum frangunt.
Nucifrangibulum validè nucem comprehenſam comprimit.
quia duplicatus eſt vectis, vnum hypomochlium, vt in A
commiſſura habentibus. Diductis enim B C extremis
vectium E A B & F A C à viribus in E & F.
alteris vectium extremis exiſtentibus, ſi ipſa compriman
tur etiam B & C comprimentur. Quare & nux D in
terpoſita, & valide compreſſa frangitur, tantò celerius:
quantò extrema B & C minus diſtabunt ab hypomoch
lio A. Sic enim aliæ partes vectium ab ipſo diſtantes
maiorem rationem habebunt. Et proinde facilius moue
bunt pondus mouendum, vt ante ſæpius eſt declaratum,
Quare quod percuſsione, vel ictu pondus aliquod irruens
in nucem feciſſet, id vectes compreßi certius faciunt. Sæpè
enim ictum ob ſui rotunditatem nux eludit. Nam cum nux
ſit rotunda, inſiſtat autem plano attingens ipſam puncto,
& à plano mallei in puncto attingatur, facile elabitur, niſi
ictus kat' i)/cin incidat in rectam, quæ coniungit hæc duo
puncta.
quia duplicatus eſt vectis, vnum hypomochlium, vt in A
commiſſura habentibus. Diductis enim B C extremis
vectium E A B & F A C à viribus in E & F.
alteris vectium extremis exiſtentibus, ſi ipſa compriman
tur etiam B & C comprimentur. Quare & nux D in
terpoſita, & valide compreſſa frangitur, tantò celerius:
quantò extrema B & C minus diſtabunt ab hypomoch
lio A. Sic enim aliæ partes vectium ab ipſo diſtantes
maiorem rationem habebunt. Et proinde facilius moue
bunt pondus mouendum, vt ante ſæpius eſt declaratum,
Quare quod percuſsione, vel ictu pondus aliquod irruens
in nucem feciſſet, id vectes compreßi certius faciunt. Sæpè
enim ictum ob ſui rotunditatem nux eludit. Nam cum nux
ſit rotunda, inſiſtat autem plano attingens ipſam puncto,
& à plano mallei in puncto attingatur, facile elabitur, niſi
ictus kat' i)/cin incidat in rectam, quæ coniungit hæc duo
puncta.
Itaque nucifrangibulum nucem facile ſine ictu franget.
Quantò igitur.] Repetitio eſt eiuſdem ſuperflua.
24. *dia\ ti/ e)n tw=| r(o/mbw| e(ka/
teron tw=n a)/krwn shmei/wn ou)
th\n i)/shn eu)qei=an die/rxetai.
teron tw=n a)/krwn shmei/wn ou)
th\n i)/shn eu)qei=an die/rxetai.
24. Cur in Rhombo alterum
punctorum extremorum
non æqualem rectam
tranſit.
punctorum extremorum
non æqualem rectam
tranſit.
*dia\ ti/ ferome/nwn du/o fora\s e)n tw=| r(o/mbw| tw=n a)/krwn
shmei/wn a)mfote/rwn, ou) th\n i)/shn e(ka/teron au)tw=n eu)qei=an die/rxetai,
a)lla\ pollaplasi/an qa/teron; o( au)to\s de\ lo/gos kai\
dia\ ti/ to\ e)pi\ th=s pleura=s fero/menon e)la/ttw die/rxetai th=s
pleura\s. to\ me\n ga\r th\n e)la/ttw dia/metron, h( de\ th\n
pleura\n mei/zw, kai\ h( me\n mi/an, to\ de\ du/o fe/retai
fora/s. fere/sqw ga\r e)pi\ th=s *a*b, to\ me\n *a pro\s to\ *b, to\
de\ *b pro\s to\ *d, tw=| au)tw=| ta/xei: fere/sqw de\ kai\ h( *a*b
e)pi\ th=s *a*g, para\ th\n *g*d tw=| au)tw=| ta/xei tou/tois. a)na/gkh
dh\ to\ me\n *a e)pi\ th=s *a*d diame/trou fe/resqai. to\ de\ *b e)pi\
th=s *b*g, kai\ a(/ma dielhluqe/nai e(kate/ran, kai\ th\n *a*b th\n
*a*g pleura/n. kai\ th\n *b*d th\n *b*a. e)nhne/xqw ga\r to\ me\n *a, th\n *a*e, h( de\ *a
*b, th\n *a*z, kai\ e)/stw e)kbeblhme/nh h( *z*h para\ th\n *a*b,
kai\ a)po\ tou= *e peplhrw/sqw. o(/moion ou)=n gi/netai to\ paraplhrwqe\n
tw=| o(/lw|. i)/sh a)/ra h( *a*z th=| *a*e: h( de\ *a*b th\n *a*z,
ei)/h a)\n e)nhnegme/nh. e)/stai a)/ra e)pi\ th=s diame/trou kata\ to\ *q.
kai\ ai)ei\ de\ a)na/gkh au)to\ fe/resqai kata\ th\n dia/metron.
kai\ a(/ma h( pleura\ h( *a*b, th\n pleura\n th\n *a*g di/eisi,
kai\ to\ *a th\n dia/metron di/eisi th\n *a*d. o(moi/ws de\ deixqh/setai
kai\ to\ *b e)pi\ th=s *a*g diame/trou fero/menon. i)/sh
ga/r e)stin h( *b*e, th=| *b*h. paraplhrwqe/ntos ou)=n a)po\ tou= *h,
o(/moio/n e)sti tw=| o(/lw| to\ e)nto/s: kai\ to\ *b e)pi\ th=s diame/trou
e)/stai kata\ th\n su/nayin tw=n pleurw=n, kai\ a(/ma di/eisin h(/
te pleura\ th\n pleura\n, kai\ to\ *b th\n *b*g dia/metron.
a(/ma a)/ra kai\ to\ *a th\n pollaplasi/an th=s *b*g di/eisi,
kai\ h( pleura\ th\n e)la/ttona pleura\n tw=| au)tw=| ta/xei fero/mena,
kai\ h( pleura\ *b*d mei/zw pleura\n tou= *b*g dielh/luqe mi/an fora\n
ferome/nh. o(/sw| ga\r a)\n o)cu/teros ge/nhtai o( r(o/mbos, h(
me\n dia/metros *a*g, h( e)la/ttwn gi/netai, h( de\ *a*d mei/zwn, h( de\
pleura\ th=s *b*g mei/zwn.
shmei/wn a)mfote/rwn, ou) th\n i)/shn e(ka/teron au)tw=n eu)qei=an die/rxetai,
a)lla\ pollaplasi/an qa/teron; o( au)to\s de\ lo/gos kai\
dia\ ti/ to\ e)pi\ th=s pleura=s fero/menon e)la/ttw die/rxetai th=s
pleura\s. to\ me\n ga\r th\n e)la/ttw dia/metron, h( de\ th\n
pleura\n mei/zw, kai\ h( me\n mi/an, to\ de\ du/o fe/retai
fora/s. fere/sqw ga\r e)pi\ th=s *a*b, to\ me\n *a pro\s to\ *b, to\
de\ *b pro\s to\ *d, tw=| au)tw=| ta/xei: fere/sqw de\ kai\ h( *a*b
e)pi\ th=s *a*g, para\ th\n *g*d tw=| au)tw=| ta/xei tou/tois. a)na/gkh
dh\ to\ me\n *a e)pi\ th=s *a*d diame/trou fe/resqai. to\ de\ *b e)pi\
th=s *b*g, kai\ a(/ma dielhluqe/nai e(kate/ran, kai\ th\n *a*b th\n
*a*g pleura/n. kai\ th\n *b*d th\n *b*a. e)nhne/xqw ga\r to\ me\n *a, th\n *a*e, h( de\ *a
*b, th\n *a*z, kai\ e)/stw e)kbeblhme/nh h( *z*h para\ th\n *a*b,
kai\ a)po\ tou= *e peplhrw/sqw. o(/moion ou)=n gi/netai to\ paraplhrwqe\n
tw=| o(/lw|. i)/sh a)/ra h( *a*z th=| *a*e: h( de\ *a*b th\n *a*z,
ei)/h a)\n e)nhnegme/nh. e)/stai a)/ra e)pi\ th=s diame/trou kata\ to\ *q.
kai\ ai)ei\ de\ a)na/gkh au)to\ fe/resqai kata\ th\n dia/metron.
kai\ a(/ma h( pleura\ h( *a*b, th\n pleura\n th\n *a*g di/eisi,
kai\ to\ *a th\n dia/metron di/eisi th\n *a*d. o(moi/ws de\ deixqh/setai
kai\ to\ *b e)pi\ th=s *a*g diame/trou fero/menon. i)/sh
ga/r e)stin h( *b*e, th=| *b*h. paraplhrwqe/ntos ou)=n a)po\ tou= *h,
o(/moio/n e)sti tw=| o(/lw| to\ e)nto/s: kai\ to\ *b e)pi\ th=s diame/trou
e)/stai kata\ th\n su/nayin tw=n pleurw=n, kai\ a(/ma di/eisin h(/
te pleura\ th\n pleura\n, kai\ to\ *b th\n *b*g dia/metron.
a(/ma a)/ra kai\ to\ *a th\n pollaplasi/an th=s *b*g di/eisi,
kai\ h( pleura\ th\n e)la/ttona pleura\n tw=| au)tw=| ta/xei fero/mena,
kai\ h( pleura\ *b*d mei/zw pleura\n tou= *b*g dielh/luqe mi/an fora\n
ferome/nh. o(/sw| ga\r a)\n o)cu/teros ge/nhtai o( r(o/mbos, h(
me\n dia/metros *a*g, h( e)la/ttwn gi/netai, h( de\ *a*d mei/zwn, h( de\
pleura\ th=s *b*g mei/zwn.
Cur amborum extremo
rum punctorum duabus la
tionibus in rhombo lato
rum, alterum non tranſit
æqualem rectam. ſed alte
rum punctorum duabus la
tionibus in rhombo lato
rum, alterum non tranſit
æqualem rectam. ſed alte