1rectos angulos ef
50[Figure 50]
ficit ex def. 3. lib.
11. vt A B dia
meter ad B O, B D,
B E, B F. Et A B
quia diameter eſt
circulum ſuum bi
fariam diuidit ex
def. 17. lib. 1. Sic
que tanta pars eſt
ad G, quanta ad H. Similiter maximus in ſphæra circulus recta
inſiſtens ſphæram bifariam diſpeſcit.
50[Figure 50]ficit ex def. 3. lib.
11. vt A B dia
meter ad B O, B D,
B E, B F. Et A B
quia diameter eſt
circulum ſuum bi
fariam diuidit ex
def. 17. lib. 1. Sic
que tanta pars eſt
ad G, quanta ad H. Similiter maximus in ſphæra circulus recta
inſiſtens ſphæram bifariam diſpeſcit.
e)/ti le/gousi/
tines o(/ti kai\ h( grammh\ h( tou= ku/klou, e)n fora=| e)sti\n
a)ei/, w(/sper ta\ me/nonta, dia\ to\ a)nterei/dein, oi(=on kai\ toi=s
mei/zosi ku/klois u(pa/rxei pro\s tou\s e)la/ttonas. qa=tton ga\r
u(po\ th=s i)/shs i)sxu/os kinou=ntai oi( mei/zous kai\ ta\ ba/rh kinou=si,
dia\ to\ r(oph/n tina e)/xein th\n gwni/an th\n tou= mei/zonos
ku/klou pro\s th\n tou= e)la/ttonos, kai\ ei)=nai o(/per h( dia/metros
pro\s th\n dia/metron. a)lla\ mh\n pa=s ku/klos mei/zwn pro\s
e)la/ttona. a)/peiroi ga\r oi( e)la/ttones. ei) de\ kai\ pro\s e(/teron
e)/xei r(oph\n o( ku/klos, o(moi/ws de\ eu)ki/nhtos, kai\ a)/llhn a)\n
e)/xoi r(oph\n o( ku/klos kai\ ta\ u(po\ ku/klou kinou/mena, ka)\n mh\
th=| a(yi/di a(/pthtai tou= e)pipe/dou, a)ll' h)\ para\ to\ e)pi/pedon,
h)\ w(s ai( troxile/ai. kai\ ga\r ou(/tws e)/xonta, r(a=|sta kinou=ntai
kai\ kinou=si to\ ba/ros, h)\ ou) tw=| kata\ mikro\n a(/ptesqai kai\
proskrou/ein, a)lla\ di' a)/llhn ai)ti/an. au(/th de/ e)stin h( ei)rhme/nh
pro/teron, o(/ti e)k du/o forw=n gege/nhtai o( ku/klos, w(/ste
mi/an au)tw=n ai)ei\ e)/xein r(oph/n, kai\ oi(=on fero/menon au)to\n
ai)ei\, kinou=sin oi( kinou=ntes, o(/tan kinw=sin kata\ th\n perife/reian
o(pwsou=n. ferome/nhn ga\r au)th\n kinou=sin: th\n me\n ga\r ei)s
to\ pla/gion au)tou= ki/nhsin, w)qei= to\ kinou=n, th\n de\ e)pi\ th=s
diame/trou, au)to\s kinei=tai.
tines o(/ti kai\ h( grammh\ h( tou= ku/klou, e)n fora=| e)sti\n
a)ei/, w(/sper ta\ me/nonta, dia\ to\ a)nterei/dein, oi(=on kai\ toi=s
mei/zosi ku/klois u(pa/rxei pro\s tou\s e)la/ttonas. qa=tton ga\r
u(po\ th=s i)/shs i)sxu/os kinou=ntai oi( mei/zous kai\ ta\ ba/rh kinou=si,
dia\ to\ r(oph/n tina e)/xein th\n gwni/an th\n tou= mei/zonos
ku/klou pro\s th\n tou= e)la/ttonos, kai\ ei)=nai o(/per h( dia/metros
pro\s th\n dia/metron. a)lla\ mh\n pa=s ku/klos mei/zwn pro\s
e)la/ttona. a)/peiroi ga\r oi( e)la/ttones. ei) de\ kai\ pro\s e(/teron
e)/xei r(oph\n o( ku/klos, o(moi/ws de\ eu)ki/nhtos, kai\ a)/llhn a)\n
e)/xoi r(oph\n o( ku/klos kai\ ta\ u(po\ ku/klou kinou/mena, ka)\n mh\
th=| a(yi/di a(/pthtai tou= e)pipe/dou, a)ll' h)\ para\ to\ e)pi/pedon,
h)\ w(s ai( troxile/ai. kai\ ga\r ou(/tws e)/xonta, r(a=|sta kinou=ntai
kai\ kinou=si to\ ba/ros, h)\ ou) tw=| kata\ mikro\n a(/ptesqai kai\
proskrou/ein, a)lla\ di' a)/llhn ai)ti/an. au(/th de/ e)stin h( ei)rhme/nh
pro/teron, o(/ti e)k du/o forw=n gege/nhtai o( ku/klos, w(/ste
mi/an au)tw=n ai)ei\ e)/xein r(oph/n, kai\ oi(=on fero/menon au)to\n
ai)ei\, kinou=sin oi( kinou=ntes, o(/tan kinw=sin kata\ th\n perife/reian
o(pwsou=n. ferome/nhn ga\r au)th\n kinou=sin: th\n me\n ga\r ei)s
to\ pla/gion au)tou= ki/nhsin, w)qei= to\ kinou=n, th\n de\ e)pi\ th=s
diame/trou, au)to\s kinei=tai.
*e)/xh
Præterea nonnulli di
cunt lineam circuli in per
petuo motu eſſe, vt quæ
manent, propter renixum.
Vt maioribus circulis eue
nit reſpectu minorum. Ce
lerius enim ab æquali vi
maiores mouentur, & pon
dera mouent. quia maioris
circuli angulus nutum quen
dam habet ad minoris an
gulum. Et eſt vt diameter
ad diametrum: ſic omnis ma
ior circulus ad minorem.
Infiniti autem ſunt mino
res. Si verò etiam circulus
nutum habet ad alterum.
Similiter verò facile mobi
lis alium nutum habet circulus,
& quæ à circulo mouentur,
etiamſi ſua curuatura planum
non contingat: ſed vel propè
planitiem, vel vt trochleæ.
cunt lineam circuli in per
petuo motu eſſe, vt quæ
manent, propter renixum.
Vt maioribus circulis eue
nit reſpectu minorum. Ce
lerius enim ab æquali vi
maiores mouentur, & pon
dera mouent. quia maioris
circuli angulus nutum quen
dam habet ad minoris an
gulum. Et eſt vt diameter
ad diametrum: ſic omnis ma
ior circulus ad minorem.
Infiniti autem ſunt mino
res. Si verò etiam circulus
nutum habet ad alterum.
Similiter verò facile mobi
lis alium nutum habet circulus,
& quæ à circulo mouentur,
etiamſi ſua curuatura planum
non contingat: ſed vel propè
planitiem, vel vt trochleæ.