Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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ptis omnibus quadratis, HQ, æquatur autem rectangulum, EM
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O, rectangulo ſub, EM, & </
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& </
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<
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xml:space
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">NO, ergo omnia quadrata, SF, ad omnia quadrata fruſti, D
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HGF, demptis omnibus quadratis, HQ, erunt vt rectangulum,
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OEN, ad rectangulum ſub, EM, & </
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<
s
xml:id
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xml:space
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<
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xml:id
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xml:space
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tegra, MN, & </
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<
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xml:space
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</
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<
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<
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">Omnia verò quadrata trianguli, DMF, ad eadem erunt, vt {1/3}.
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</
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<
s
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xml:space
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">rectanguli, OEN, ad rectangulum ſub, EM, & </
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{1/3}. </
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<
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xml:space
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<
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<
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<
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xml:space
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">i. </
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>
<
s
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xml:space
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">vt totum rectangulum ſub, O
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EN, ad rectangulum ſub, EM, & </
s
>
<
s
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xml:space
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MN, &</
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<
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<
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<
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<
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<
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quæ oſtendenda erant.</
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<
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<
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">IN eadem figura, regula eadem retenta, oſtendemus om-
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mnia quadrata, AF, demptis omnibus quadratis hyper-
<
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bolæ, DNF, ad omnia quadrata, SF, demptis omnibus
<
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/>
quadratis fruſti, HDFG, eſſe vt parallelepipedum ſub cõ-
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/>
poſita ex ipſa, XE, EN, & </
s
>
<
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xml:space
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">ſub quadrato, NE, ad parallele-
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pipedum ſub compoſita ex eadem, XE, & </
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<
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& </
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<
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">ſub quadrato, ME.</
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<
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</
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<
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<
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">Quia enim omnia quadrata, AF, ad omnia quadrata hyperbo-
<
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">Is huius.</
note
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læ, DNF, ſunt vt, OE, ad compoſitam ex {1/2}. </
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<
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<
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per conuerſionem rationis, & </
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<
s
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">conuertendo omnia quadrata, AF,
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demptis omnibus quadratis hyperbolæ, DNF, ad omnia quadra-
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ta, AF, erunt vt compoſita ex {1/2}. </
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<
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<
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<
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<
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pta, NE, communialtitudine, vt rectangulum ſub compoſita ex
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{1/2}. </
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<
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<
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verò omnia quadrata, AF, demptis omnibus quadratis hyperbo-
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læ, DNF, ad omnia quadrata, SF, demptis omnibus quadratis
<
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fruſti, DHGF, habent rationem compoſitam ex ea, quam habent
<
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omnia quadrata, AF, demptis omnibus quadratis hyperbolæ, D
<
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<
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1. I.</
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NF, ad omnia quadrata, AF, .</
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<
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<
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ſub compoſita ex {1/2}. </
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<
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<
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lum, NEO; </
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<
s
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xml:space
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">ex ratione, quam habent omnia quadrata,
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AF, ad omnia quadrata, SF, ideſt ex ea, quam habet, NE,
<
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ad, EM, & </
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<
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<
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<
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ad omnia quadrata, SF, demptis omnibus quadratis fruſti, </
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