Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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culi, uel ellipſes c d, e ſ a b ad circulum, uel ellipſim a b. </
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<
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telligatur pyramis q baſim habens æqualem tribus rectan
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gulis a b, e f, c d; </
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<
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">& </
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<
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xml:space
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">altitudinem eãdem, quam fruſtum a d.
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</
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<
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xml:space
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">intelligatur etiam conus, uel coni portio q, eadem altitudi
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ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus a b,
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e f, c d æqualis. </
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<
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baſis ſit rectangulum m n o p, & </
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<
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ſti: </
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<
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">itemq, intelligatur conus, uel coni portio a l b, cuius
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baſis circulus, uel ellipſis circa diametrum a b, & </
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<
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">eadem al
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titudo. </
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<
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">ut igitur rectangula a b, e f, c d ad rectangulum a b,
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decimi</
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ita pyramis q ad pyramidem a l b; </
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<
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xml:space
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">ut circuli, uel ellip-
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ſes a b, e f, c d ad a b circulum, uel ellipſim, ita conus, uel co
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ni portio q ad conum, uel coni portionem a l b. </
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<
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igitur, uel coni portio q ad conum, uel coni portionem
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a l b eſt, ut pyramis q ad pyramidem a l b. </
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<
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a l b ad pyramidem a g b eſt, ut altitudo ad altitudinem, ex
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20. </
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xml:space
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<
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">ita eſt conus, uel coni portio al b ad conum,
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uel coni portionem a g b ex 14. </
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<
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& </
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">ex iis, quæ nos demonſtrauimus in commentariis in un-
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decimam de conoidibus, & </
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quarta. </
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tionem habet compoſitam ex proportione baſium & </
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portione altitudinum, ex uigeſima prima huius: </
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<
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ter conus, uel coni portio a g b a d conum, uel coni portio-
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nem c g d proportionem habet compoſitã ex eiſdem pro-
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portionibus, per ea, quæ in dictis commentariis demon-
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ſtrauimus, propoſitione quinta, & </
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utriſque eadem eſt, & </
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portionem. </
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<
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">ergo ut pyramis a g b ad pyramidem c g d, ita
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eſt conus, uel coni portio a g b ad a g d conum, uel coni
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portionem: </
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<
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">per conuerſionẽ rationis, ut pyramis a g b
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ad fruſtū à pyramide abſciſſum, ita conus uel coni portio
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a g b ad fruſtum a d. </
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<
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ſtum à pyramide abſciſſum, ita conus uel coni portio q </
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