Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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176FED. COMMANDINI pyramidem, uel conum, uel coni portionem candem pro-
portionem habet, quam baſes ab, cd unà cum e ſ ad ba-
ſim a b.
quod demonſtrare uolebamus.
Fruſtum uero a d æquale eſſe pyramidi, uel co
no, uel coni portioni, cuius baſis conſtat ex baſi-
bus a b, c d, e f, &
altitudo fruſti altitudini eſt æ-
qualis, hoc modo oſten demus.
Sit fruſtum pyramidis a b c d e f, cuius maior baſis trian-
gulum a b c;
minor d e f: & ſecetur plano baſibus æquidi-
ſtante, quod ſectionem faciat triangulum g h k inter trian-
gula a b c, d e f proportionale.
Iam ex iis, quæ demonſtrata
ſuntin 23.
huius, patet ſruſtum a b c d e f diuidi in tres pyra
mides proportionales;
& earum maiorem eſſe pyramidẽ
a b c d minorẽ uero d e f b.
ergo pyramis à triangulo g h k
conſtituta, quæ altitudinem habeat ſruſti altitudini æqua-
lem, proportionalis eſtinter pyramides a b c d, d e f b:
&
idcirco fruſtum a b c d e f tribus dictis pyramidibus æqua
le erit.
Itaque ſi intelligatur alia pyra-
131[Figure 131] mis æque alta, quæ baſim habeat ex tri
bus baſibus a b c, d e f, g h k conſtan-
tem;
perſpicuum eſtipſam eiſdem py-
ramidibus, &
propterea ipſi fruſto æ-
qualem eſſe.
Rurſus ſit ſruſtum pyramidis a g, cu
ius maior baſis quadrilaterum a b c d,
minor e f g h:
& ſecetur plano baſi-
bus æquidiſtante, ita ut fiat ſectio qua-
drilaterum K lm n, quod ſit proportio
nale inter quadrilatera a b c d, e f g h.
Dico pyramidem,
cuius baſis ſit æqualis tribus quadrilateris a b c d, _k_ l m n,
e f g h, &
altitudo æqualis altitudini fruſti, ipſi fruſto a g
æqualem eſſe.
Ducatur enim planum per lineas f b, h

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