Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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ro ita demonſtrabitur. </
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">Ducatur à puncto b ad planum ba-
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ſis a c perpendicularis linea b h, quæ ipſam e fin K ſecet.
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</
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<
s
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xml:space
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">erit b h altitudo coni, uel coni portionis a b c: </
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<
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echoid-s5085
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xml:space
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">& </
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<
s
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echoid-s5086
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xml:space
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">b K altitu
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cimi.</
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do e f g. </
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<
s
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">Quod cum lineæ a c, e f inter ſe æ quidiſtent, ſunt
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enim planorum æ quidiſtantium ſectiones: </
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<
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echoid-s5088
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xml:space
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">habebit d b ad
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">4 ſexti.</
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b g proportionem ean dem, quam h b ad b k. </
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<
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xml:space
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">quare por-
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tio conoidis a b c ad portionem e f g proportionem habet
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compoſitam ex proportione baſis a c ad baſim e f; </
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<
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xml:space
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">& </
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<
s
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">ex
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proportione d b axis ad axem b g. </
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<
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">Sed circulus, uel
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">2. duode
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cimi</
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ellipſis circa diametrum a c ad circulum, uel ellipſim
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<
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xlink:label
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">7. de co-
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noidibus
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& ſphæ-
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roidibus</
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circa e f, eſt ut quadratum a c ad quadratum e f; </
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<
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">hoc eſt ut
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quadratũ a d ad quadratũ e g. </
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<
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xml:space
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">& </
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<
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xml:id
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xml:space
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">quadratum a d ad quadra
<
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tum e g eſt, ut linea d b ad lineam b g. </
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<
s
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xml:space
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">circulus igitur, uel el
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lipſis circa diametrum a c ad circulũ, uel ellipſim circa e f,
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<
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xlink:label
="
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">15. quinti</
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hoc eſt baſis ad baſim eandem proportionem habet, quã
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xlink:label
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">20. primi
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conicorũ</
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d b axis ad axem b g. </
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<
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">ex quibus ſequitur portionem a b c
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ad portionem e b f habere proportionem duplam eius,
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quæ eſt baſis a c ad bafim e f: </
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<
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xml:id
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xml:space
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">uel axis d b ad b g axem. </
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<
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">quod
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demonſtrandum proponebatur.</
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<
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">THEOREMA XXV. PROPOSITIO XXXI.</
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<
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">Cuiuslibet fruſti à portione rectanguli conoi
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dis abſcisſi, centrum grauitatis eſt in axe, ita ut
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demptis primum à quadrato, quod fit ex diame-
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tro maioris baſis, tertia ipſius parte, & </
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<
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tertiis quadrati, quod fit ex diametro baſis mino-
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ris: </
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<
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xml:space
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">deinde à tertia parte quadrati maioris baſis
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rurſus dempta portione, ad quam reliquum qua
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drati baſis maioris unà cum dicta portione duplã
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proportionem habeat eius, quæ eſt quadrati </
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