Commandino, Federico - Liber de centro gravitatis solidorum

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1cta bd in g puncto, ducatur cg; & protrahatur ad circuli
uſque circumferentiam; quæ ſecet ae in h. Similiter conclu
demus cg per centrum circuli tranſire: & bifariam ſecate
lineam ae; itemque; lineas bd, ae inter ſe æquidiſtantes eſſe.
Cum igitur cg per centrum circuli tranſeat; & ad punctum
f perueniat neceſſe eſt: quòd cdef ſit dimidium circumfe

5[Figure 5]

rentiæ circuli. Quare in eadem
diametro cf erunt centra gra
uitatis triangulorum bcd,
afe, & quadrilateri abde, ex
quibus conſtat hexagonum ab
cdef. perſpicuum eſt igitur in
ipſa cf eſſe circuli centrum, &
centrum grauitatis hexagoni.
Rurſus ducta altera diametro
ad, eiſdem rationibus oſtende
mus in ipſa utrumque centrum
ineſſe. Centrum ergo grauita
tis hexagoni, & centrum circuli idem erit.

13 Archi
medis.
9. eiusdem
m

Sit heptagonum abcdefg æquilaterum atque æquian

6[Figure 6]
gulum in circulo deſcriptum:
& iungantur ce, bf, ag: di
uiſa autem ce bifariam in pun
cto h: & iuncta dh produca
tur in k. non aliter demon
ſtrabimus in linea dk eſſe cen
trum circuli, & centrum gra
uitatis trianguli cde, & tra
peziorum bcef, abfg, hoc
eſt centrum totius heptago
ni: & rurſus eadem centra in
alia diametro cl ſimiliter du
cta contineri. Quare & centrum grauitatis heptagoni, &
centrum circuli in idem punctum conueniunt. Eodem

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