Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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Dico eas proportion ales eſſe in proportione, quæ eſt la-
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teris a b adlatus d e, itaut earum maior ſit a b c e, me-
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dia a d c e, & </
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<
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">Quoniam enim lineæ d e,
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a b æquidiſtant; </
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">& </
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<
s
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">interipſas ſunt triangula a b e, a d e;
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">erit triangulum a b e
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0172-01
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">1. ſextí.</
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ad triangulum a d e,
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ut linea a b ad lineam
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d e. </
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">ut autem triangu
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lum a b e ad triangu-
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lum a d e, ita pyramis
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">5. duodeci
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mi.</
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a b e c ad pyramidem
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a d e c: </
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<
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">habent enim
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altitudinem eandem,
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quæ eſt à puncto c ad
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planum, in quo qua-
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drilaterum a b e d. </
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<
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">er-
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<
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">11. quinti.</
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go ut a b ad d e, ita pyramis a b e c ad pyramidem a d e c.
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<
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">erit eadem
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ratione pyramis a d c e ad pyramidem c d f e, ut a c ad
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xlink:label
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d f. </
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<
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">Sed ut a c a l d f, ita a b ad d e, quoniam triangula
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a b c, d e f ſimilia ſunt, ex nona huius. </
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<
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">quare ut pyramis
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a b c e ad pyramidem a d c e, ita pyramis a d c e ad ipſam
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d e f c. </
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>
<
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">fruſtum igitur a b c d e f diuiditur in tres pyramides
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proportionales in ea proportione, quæ eſt lateris a b ad d e
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latus, & </
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<
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">earum maior eſt c a b e, media a d c e, & </
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d e f c. </
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<
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fruſtum pyramidis, uel coni,
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uel coni portionis, plano baſi æquidiſtanti ita ſe-
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care, ut ſectio ſit proportionalis inter maiorem,
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& </
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