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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