Commandino, Federico - Liber de centro gravitatis solidorum

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1metrum habens ed. Quoniam igitur circuli uel ellipſis
aecb grauitatis centrum eſt in diametro be, & portio
nis aec centrum in linea ed: reliquæ portionis, uidelicet
abc centrum grauitatis in ipſa bd conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.

THEOREMA V. PROPOSITIO V.

SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis & ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.

Sit priſma, in quo plana oppoſita ſint triangula abc,
def; axis gh: & ſecetur plano iam dictis planis æquidiſtan
te; quod faciat ſectionem klm; & axi in puncto n occurrat.
Dico klm triangulum æquale eſſe, & ſimile triangulis abc
def; atque eius grauitatis centrum eſſe punctum n. Quo

14[Figure 14]
niam enim plana abc
Klm æquidiſtantia ſecan

tur a plano ae; rectæ li
neæ ab, Kl, quæ ſunt ip
ſorum communes ſectio
nes inter ſe ſe æquidi
ſtant. Sed æquidiſtant
ad, be; cum ae ſit para
lelogrammum, ex priſ
matis diffinitione. ergo
& al parallelogrammum
erit; & propterea linea

kl, ipſi ab æqualis. Si
militer demonſtrabitur
lm æquidiſtans, & æqua
lis bc; & mk ipſi ca.

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