Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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">_H_Inc patet, quod, diuidendo, portio parabolæ, SGAT, ad por-
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tionem, SHT, erit bt omnia quadrata ſemiportionis, AMVT,
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ad omnia quadrata ſemiportionis, HVT, .</
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<
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xml:space
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">bt parallelepipedum ſub
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altitudine linea compoſita ex, OH, HT, baſi quadrato, TA, ad paral-
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lelepipedum ſub altitudine, XT, baſi quadrato, HT, bt patet in Coroll.
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<
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<
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<
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">SI duæ ad baſim parabolæ applicentur vtcunque rectæ li-
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neæ, abſciſſæ portiones parabolæ eruntinterſe, vt pa-
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rallelepipeda ſub baſibus quadratis abſciſſarum à baſi per
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eaſdem applicatas ab eadem extremitate, à qua portiones
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abſciſſæ intelliguntur, altitudinibus compoſitis ex reſiduis
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dictæ baſis (demptis abſciſſis) & </
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<
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plicentur duæ vtcunque lineæ, ST, RV, abſcindentes portiones, R
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HV, SHT. </
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portionem, SHT, eſſe (ſi producatur, AX,
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æqualis ipſius baſis, AH, medietati) vt pa-
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rallelepipedum ſub altitudine, XV, baſi qua-
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drato, VH, ad parallelepipedum ſub altitudi-
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ne, XT, baſi quadrato, TH. </
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tio, RHV, ad parabolam, AGH, vt paral-
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lelepipedum ſub altitudine, XV, baſi quadra-
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to, VH, ad parallelepipedum ſub altitudine,
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XA, baſi quadrato, AH, item parabola, A
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GH, ad portionem, HST, eſt vt parallele-
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pipedum ſub altitudine, XA, baſi quadrato,
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AH, ad parall elepipedum ſub altitudine, XT,
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baſi quadrato, TH, ergo exæquali portio, R
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HV, ad portionem, SHT, eſt vt parallele-
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pipedum ſub altitudine, XV, baſi quadrato,
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VH, ad parallelepipedum ſub altitudine, X
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T, baſi quadrato, TH, quod oſtendere opor-
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tebar.</
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