Eſto A B C, peripheria ſemidiametri maioris A E: item
D F G, peripheria ſemidiametri D H minoris. Dico periphe
riam A B C maiorem peripheria D F G. Producatur enim A E
recta vt ſit A C
diameter poſtul.
8[Figure 8]
2. item D H vt ſit
& D G diame
ter. Quia igi
tur vt diameter
A C ad ſuam pe
ripheriam A B C:
ita & D G diameter ad ſuam peripheriam D F G, per ea quæ
demonſtrata ſunt ab Archimede prop. 3. lib. de dimenſ. circuli, &
vicißim proportionales erunt A C diameter ad D G diametrum:
vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. &
quia A E & D H partes ſunt pariter multiplicium A C, D G
vtpote ſemidiametri ſuarum diametrorum, erit A E ad D H vt
A C ad D G prop. 15. lib. 5. ergo & peripheria A B C ad peri
pheriam D F G: vt A E ad D H prop. 11. lib. eiuſdem. Eſt
autem A E maior: quam D H ex hypotheſi. Erit igitur peri
pheria A B C maior: quam peripheria D F G. Et ſic peripheria
remotioris puncti à centro maior eſt peripheria puncti centro pro
pinquioris, quod fuit demonſtrandum.
D F G, peripheria ſemidiametri D H minoris. Dico periphe
riam A B C maiorem peripheria D F G. Producatur enim A E
recta vt ſit A C
diameter poſtul.
8[Figure 8]2. item D H vt ſit
& D G diame
ter. Quia igi
tur vt diameter
A C ad ſuam pe
ripheriam A B C:
ita & D G diameter ad ſuam peripheriam D F G, per ea quæ
demonſtrata ſunt ab Archimede prop. 3. lib. de dimenſ. circuli, &
vicißim proportionales erunt A C diameter ad D G diametrum:
vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. &
quia A E & D H partes ſunt pariter multiplicium A C, D G
vtpote ſemidiametri ſuarum diametrorum, erit A E ad D H vt
A C ad D G prop. 15. lib. 5. ergo & peripheria A B C ad peri
pheriam D F G: vt A E ad D H prop. 11. lib. eiuſdem. Eſt
autem A E maior: quam D H ex hypotheſi. Erit igitur peri
pheria A B C maior: quam peripheria D F G. Et ſic peripheria
remotioris puncti à centro maior eſt peripheria puncti centro pro
pinquioris, quod fuit demonſtrandum.
dia\ de\ to\
ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\
me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen
kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen
kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous
a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n
toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.
ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(=
*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou
ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou
tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/. ei)s
tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f'
ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s
tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an. to\n au)to\n de\
tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.
tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n
fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes
th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\
qaumasto/n, to\ d' ai)/tion a)/dhlon.
ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\
me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen
kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen
kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous
a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n
toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.
ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(=
*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou
ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou
tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/. ei)s
tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f'
ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s
tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an. to\n au)to\n de\
tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.
tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n
fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes
th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\
qaumasto/n, to\ d' ai)/tion a)/dhlon.