Valerio, Luca, De centro gravitatis solidorvm libri tres

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1quadrupla igitur BC ipſius DK: cum igitur BC ſit
dupla ipſius KH, erit DK dimidia eiuſdem KH, & ſecta
bifariam KH in puncto D: ſed recta AG ſecabat eandem
KH bi fariam; per punctum igitur D tranſibit AG. Quo­
niam igitur parabola ADC, cuius vertex D, ſeſquiter­
tia eſt per Archimedem trianguli ADB, cuius duplum
eſt triangulum ABG, ſicut & huius triangulum ABC;
triangulum ABC quadruplum erit trianguli ADB: qua­
lium igitur partium æqualium eſt triangulum ABC duo­
decim, talium erit triangulum ADB trium, & parabola
ADB, cuius ver­
tex D quatuor: du
plum igitur erit tri­
angulum ABC
mixtum parabolæ
ADB, cuius ver­
tex D, & cen­
trum grauitatis M:
ſed trianguli ABC
rectilinei eſt cen­
trum grauitatis N,
& F trianguli ABC
mixti; dupla igitur
erit MN ipſius N
F, & MD ipſius
163[Figure 163]
OF, & DN ipſius NO, propter ſimilitudinem triangulo­
rum: ſed & tota AN dupla eſt totius NG, ob centrum
grauitatis N rectilinei trianguli ABC; reliqua igitur AD
dupla eſt reliquæ GO. cum igitur AG ſit dupla ipſius
AD, quadrupla erit AG ipſiuſque GO. quare & quadru
pla AE ipſius FE ob parallelas: tripla igitur AF ipſius FE.
Rurſus quoniam ex Archimede ſeſquialtera eſt DM ipſius
MH, erit tota DH ad DM vt quinque ad tria, hoc eſt
vt decem ad ſex: ſed MD erat dupla ipſius OF; tota igi-

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