Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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rum hyperbol arum, FAD, EVC, ad omnia quadrata, TN, dem-
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ptis omnibus quadratis oppoſitarum hyperbolarum, TAY, MVN,
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quod, &</
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demus omnia quad. </
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<
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">FADCVE, ad omnia quadra-
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ta figuræ, TAYNVM, eſſe vt paralle lepipedum ſub, XL, & </
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quadrato, RZ, cum duplo quadrati, AV, ad parallelepipe-
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dum ſub, HG, & </
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<
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">quadrato, BS, cum duplo quadrati, AV.</
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<
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<
s
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">Omnia namque quadrata figuræ, FADCVE, ad omnia quadra-
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ta figuræ, TAYNVM, habent rationem compoſitam ex ea, quam
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habent omnia quadrata figuræ, FADCVE, ad omnia quadrata,
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FC, .</
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<
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">i. </
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<
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">ex ratione quadrati, AV, cum {1/3}. </
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<
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">quadrati, KI, (quæ ſit
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portio, DC, capta inter aſymptotos, qui ſint, PI, KQ, ducti per,
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O, ſecantes, YN, in, &</
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<
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<
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">, TM, in, Ω, Π) ad
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quadratum, DC, & </
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<
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">ex ratione omnium quadratorum, FC, ad om-
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nia quadrata, TN, quæ eſt compoſita ex ea, quam habet quadra-
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tum, DC, ad quadratum, YN, & </
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<
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">ex ea, quam habet, EC, ad, MN,
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& </
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<
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">tandem ex ratione omnium quadratorum, TN, ad omnia qua-
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drata figuræ, TAYNVM, .</
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<
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">i. </
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<
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">ex ratione quadrati, YN, ad quadra-
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tum, AV, cum {1/3}. </
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<
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">℟, porrò ex his rationibus compo-
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nentibus ea, quam habet quadratum, AV, cum {1/3}. </
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<
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quadratum, DC, item quadratum, DC, ad quadratum, YN, & </
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quadratum, YN, ad quadratum, AV, cum {1/3}. </
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<
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ponunt rationem quadrati, AV, cum {1/3}. </
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<
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">quadrati, KI, ad quadra-
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tum, AV, cum {1/3}. </
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<
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">℟, vel triplicatis terminis, compo-
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nunt rationem trium quadratorum, AV, cum quadrato, KI, ad
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tria quadrata, AV, cum quadrato, & </
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l. 1.</
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trium quadratorum, OV, cum quadrato, LI, ad tria quadrata, O
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V, cum quadrato, G ℟; </
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gulo, OVZ, bis cum quadrato, VZ, & </
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rectangulo, OVZ, bis cum quadrato, VS; </
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I, ex prop. </
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rectangulum, KCI, cum quadrato, IL, æquatur quadrato. </
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quadrato, OZ, vnde quadratum, LI, remanet æquale rectangulo
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ſub, OVZ, bis cum quadrato, VZ; </
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concludetur æquale eſſe rectangulo bis ſub, OVS, cum </
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