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