Valerio, Luca, De centro gravitatis solidorvm libri tres

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1Rurſus quia puncta K, H, ſunt centra grauitatis triangu­
lorum ABC, CDA, erunt EH, EK, axes pyramidum
ABCE, ACDA: quorum EL, eſt tripla ipſius LH,
nec non EN, tripla ipſius EK; pyramidis igitur ABCE,
centrum grauitatis erit L, ſicut & K, pyramidis ACDE.
Rurſus, quoniam totius quadrilateri ABCD, eſt cen­
trum grauitatis F, cuius magnitudinis partium triangu­
lorum ABC, CDA, centra grauitatis ſunt K, H; recta
KH, à puncto F, ſic
diuiditur, vt ſit HF, ad
FK, vt triangulum
ACD, ad triangulum
ABC, hoc eſt, vt py­
ramis ACDE, ad py
ramidem ABCE. ſed
vt HF, ad FK, ita
eſt LM, ad MN; vt
igitur eſt pyramis AC
DE, ad pyramidem
ABCE, ita erit LM,
ad MN. Sed N, eſt
centrum grauitatis py­
47[Figure 47]
ramidis ACDE, & L pyramidis ABCE; punctum
igitur M, erit centrum grauitatis pyramidis ABCDE.
Quod ſi pyramis habeat baſim quinquelateram; poſito
rurſus axe totius pyramidis, & baſi ſecta in triangulum,
& quadrilaterum, poſitis vtriuſque proprijs centris graui­
tatis, eadem demonſtratione propoſitum concludetur.
Quemadmodum ſi baſis ſit ſex laterum, ſecta ea in quinque
laterum, & triangulum, & reliquis vt antea poſitis: & ſic ſem
per deinceps. Manifeſtum eſt igitur propoſitum.

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