Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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1 34[Figure 34]
THEOREMA X. PROPOSITIO XIIII.
Cuiuslibet pyramidis, & cuiuslibet coni, uel
coni portionis, centrum grauitatis in axe conſiſtit.
SIT pyramis, cuius baſis triangulum abc: & axis de.
Dico in linea de ipſius grauitatis centrum ineſſe. Si enim
fieri poteſt, ſit centrum f: & ab f ducatur ad baſim pyrami
dis linea fg, axi æquidiſtans: iunctaque eg ad latera trian­
guli abc producatur in h.
quam uero proportionem ha­
bet linea he ad eg, habeat pyramis ad aliud ſolidum, in
quo K: inſcribaturque in pyramide ſolida figura, & altera cir
cumſcribatur ex priſmatibus æqualem habentibus altitu­
dinem, ita ut circumſcripta inſcriptam exuperet magnitu­
dine, quæ ſolido k ſit minor.
Et quoniam in pyramide pla
num baſi æquidiſtans ductum ſectionem facit figuram ſi­
milem ei, quæ eſt baſis; centrumque grauitatis in axe haben
tem: erit priſmatis st grauitatis centrum in linea rq ;
matis ux centrum in linea qp, priſmatis yz in linea po;
priſmatis ηθ in linea on; priſmatis λμ in linea nm; priſ­
matis νπ in ml; & denique priſmatis ρσ in le.
quare

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