Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
quod diuidat fruſtum in duo fruſta triangulares baſes ha-
bentia, uidelicet in fruſtum a b d e f h, &
in fruſtũ b c d f g h.
erit triangulum k l n proportionale inter triangula a b d,
e f h:
& triangulum l m n proportionale inter b c d, f g h.
ſed pyramis æque alta, cuius baſis conſtat ex tribus trian-
gulis a b d, k l n, e f h, demonſtrata
Figure: /permanent/library/4E7V2WGH/figures/0177-01 not scanned
[Figure 132]
eſt ſruſto a b d e f h æqualis.
& ſi-
militer pyramis, cuius baſis con-
ſtat ex triangulis b c d, l m n, f g h
æqualis fruſto b c d f g h:
compo-
nuntur autem tria quadrilatera a
b c d, _k_ l m n, e f g h è ſex triangu-
lis iam dictis.
pyramis igitur ba-
ſim habens æqualem tribus qua-
drilateris, &
altitudinem eandem
ipſi fruſto a g eſt æqualis.
Eodem
modo illud demõſtrabitur in aliis
eiuſmodi fruſtis.
Sit fruſtum coni, uel coni, uel coni portionis a d; cuius maior ba-
ſis circulus, uel ellipſis circa diametrum a b;
minor circa
c d:
& ſecetur plano, quod baſibus æquidiſtet, faciatq; ſe-
ctionem circulum, uel ellipſim circa diametrum e f, ita ut
inter circulos, uel ellipſes a b, c d ſit proportionalis.
Dico
conum, uel coni portionem, cuius baſis eſt æqualis tribus
circulis, uel tribus ellipſibus a b, e f, c d;
& altitudo eadem,
quæ fruſti a d, ipſi fruſto æqualem eſſe.
producatur enim
fruſti ſuperficies quouſque coeat in unum punctum, quod
ſit g:
& coni, uel coni portionis a g b axis ſit g h, occurrens
planis a b, e f, c d in punctis h _k_ l:
circa circulum uero de-
ſcribatur quadratum m n o p, &
circa ellipſim rectangulũ
m n o p, quod ex ipſius diametris conſtat:
iunctisq; g m,
g n, g o, g p, ex eodem uertice intelligatur pyramis baſim
habens dictum quadratum, uel rectangulum:
& plana in
quibus ſunt circuli, uel ellipſes e f, c d uſque ad eius latera

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