Full text: Archimedes: Archimedis De iis qvae vehvntvr in aqva libri dvo

FED. COMMANDINI Dico eas proportion ales eſſe in proportione, quæ eſt la-
teris a b adlatus d e, itaut earum maior ſit a b c e, me-
dia a d c e, & minor d e f c. Quoniam enim lineæ d e,
a b æquidiſtant; & interipſas ſunt triangula a b e, a d e; erit triangulum a b e
ad triangulum a d e,
ut linea a b ad lineam
d e. ut autem triangu
lum a b e ad triangu-
lum a d e, ita pyramis
a b e c ad pyramidem
a d e c: habent enim
altitudinem eandem,
quæ eſt à puncto c ad
planum, in quo qua-
drilaterum a b e d. er-
go ut a b ad d e, ita pyramis a b e c ad pyramidem a d e c. Rurſus quoniam æquidiſtantes ſunt a c, d f; erit eadem
ratione pyramis a d c e ad pyramidem c d f e, ut a c ad
d f. Sed ut a c a l d f, ita a b ad d e, quoniam triangula
a b c, d e f ſimilia ſunt, ex nona huius. quare ut pyramis
a b c e ad pyramidem a d c e, ita pyramis a d c e ad ipſam
d e f c. fruſtum igitur a b c d e f diuiditur in tres pyramides
proportionales in ea proportione, quæ eſt lateris a b ad d e
latus, & earum maior eſt c a b e, media a d c e, & minor
d e f c. quod demonſtrare oportebat.

88.1.

0172-01
1. ſextí.
5. duodeci
mi.
11. quinti.
4 ſexti.

89. PROBLEMA V. PROPOSITIO XXIIII.

Qvodlibet fruſtum pyramidis, uel coni,
uel coni portionis, plano baſi æquidiſtanti ita ſe-
care, ut ſectio ſit proportionalis inter maiorem,
& minorem baſim.

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