Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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116FED. COMMANDINI quæ quidem in centro conueniunt. idem igitur eſt centrum
circuli centrum.
Sit pentagonum æquilaterum, & æquiangulum in circu-
lo deſcriptum a b c d e:
& iun-
cta b d, bifariamq́;
in ſ diuiſa,
ducatur c f, &
circuli circumferentiam in g;
quæ lineam a e in h ſecet: de-
inde iungantur a c, c e.
Eodem
modo, quo ſupra demonſtra-
bimus angulum b c f æqualem
eſſe angulo d c f;
& angulos
& idcir-
colineam c f g per circuli cen
trum tranſire.
Quoniam igi-
tur latera c b, b a, &
c d, d e æqualia ſunt; & æquales anguli
c b a, c d e:
erit baſis c a baſi c e, & angulus b c a angulo
114. Primi. d c e æqualis.
ergo & reliquus a c h, reliquo e c h. eſt au-
tem c h utrique triangulo a c h, e c h communis.
quare
baſis a h æqualis eſt baſi h e:
& anguli, quiad h recti: ſuntq́;
recti, qui ad f. ergo lineæ a e, b d inter ſe ſe æquidiſtant.
2208. primi. Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
nea fh bifariam diuidantur;
centrum grauitatis ipſius erit
in linea f h, ex ultima eiuſdem libri Archimedis.
Sed trian-
3313. Archi-
medis.
guli b c d centrum grauitatis eſt in linea c f.
linea c h eſt centrum grauitatis trapezij a b d e, &
trian-
guli b c d:
hoc eſt pentagoni ipſius centrum & centrum
circuli.
Rurſus ſi iuncta a d, bifariamq́; ſecta in k, duca-
tur e k l:
demonſtrabimus in ipſa utrumque centrum in
eſſe.
Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
ueniunt, idem ſit centrum circuli, &
centrum grauitatis
pentagoni.
Sit hexagonum a b c d e f æquilaterum, & æquiangulum
in circulo deſignatum:
iunganturq́; b d, a c: & bifariam