Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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pra demonſtratum eſt, ita eſſe cylindrum, uel cylindri por-
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tionem ad priſina, cuius baſis rectilinea figura, & </
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lis altitudo. </
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<
s
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xml:space
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">ergo per conuerſionem rationis, ut circulus,
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uel ellipſis ad portiones, ita conus, uel coni portio ad por-
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tiones ſolidas. </
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<
s
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echoid-s4281
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xml:space
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">quare conus uel coni portio ad portiones
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ſolidas maiorem habet proportionem, quam g e ad 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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xml:space
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<
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diuidendo, pyramis ad portiones ſolidas maiorem pro-
<
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portionem habet, quam g f ad f e. </
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<
s
xml:id
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xml:space
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">ſiat igitur q f ad f e
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ut pyramis ad dictas portiones. </
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<
s
xml:id
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xml:space
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">Itaque quoniam à cono
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uel coni portione, cuius grauitatis centrum eſt f, aufer-
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tur pyramis, cuius centrum e; </
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<
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xml:space
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">reliquæ magnitudinis,
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quæ ex ſolidis portionibus conſtat, centrum grauitatis
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erit in linea e f protracta, & </
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<
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non poteft: </
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">eſt enim centrum grauitatis intra. </
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<
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xml:space
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igitur coni, uel coni portionis grauitatis centrum eſſe pun
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ctum e. </
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<
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<
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<
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fruſtum à pyramide, quæ
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triangularem baſim habeat, abſciſſum, diuiditur
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in tres pyramides proportionales, in ea proportio
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ne, quæ eſt lateris maioris baſis ad latus minoris
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ipſi reſpondens.</
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<
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">Hoc demonſtrauit Leonardus Piſanus in libro, qui de-
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praxi geometriæ inſcribitur. </
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">Sed quoniam is adhucim-
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preſſus non eſt, nos ipſius demonſtrationem breuíter
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perſtringemus, rem ipſam ſecuti, non uerba. </
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xml:space
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ſtum pyramidis a b c d e f, cuíus maior baſis triangulum
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a b c, minor d e f: </
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xml:space
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<
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xml:space
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">iunctis a e, e c, c d, per line-
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as a e, e c ducatur planum ſecans fruſtum: </
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<
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lineas e c, c d; </
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">per c d, d a alia plana ducantur, quæ,
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diuident fruſtum in tres pyramides a b c e, a d c e, d e f c.</
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