Valerio, Luca, De centro gravitatis solidorvm libri tres

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ALITER.
Dico hemiſphærij, vel hemiſphæroidis ABC cen­
trum grauitatis eſſe G. In plano enim ſemicirculi, vel ſe­
miellipſis per axem BD deſcriptæ intelligantur duæ pa­
rabolæ, quarum diametri AD, DC, & communiter
ad vtranque ordinatim applicata ſit BD: & connectun­
tur rectæ AB, BC: ſumptis autem in BD tribus qui­
buslibet punctis, æqualia axis ſegmenta XF, FY interci­
pientibus, ſecent per ea puncta tres figuras hemiſphærium,
vel hemiſphæroides ABC, & ſemicirculum, vel ſemielli­
177[Figure 177]
pſim per axem, & figuram planam ARBSC, quæ lineis pa
rabolicis ARB, BSC, & recta AC continetur, pla­
na quædam baſi hemiſphærij, vel hemiſphæroidis paralle­
la. Erunt igitur ſectiones hemiſphærij, vel hemiſphæroidis
circuli, vel ellipſes ſimiles baſi, quarum diametri ſint KXH,
LFM, NΥO: figuræ autem ARBSC ſectiones rectæ
lineæ PXQ, RFS, TYV. Quoniamigitur per IV hu­
ius eſt vt KH ad LM potentia, ita KQ ad FS hoc
eſt in earum duplis PQ ad RS longitudine; erit vt PQ
ad RS, ita circulus, vel ellipſis KH ad circulum vel ſi­
milem ellipſim LM. Eadem ratione erit vt RS ad
TV, ita circulus, vel ellipſis LM ad circulum, vel

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