Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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dempto quadrato, ME, quia verò tripla, BE, eſt compoſita ex, E
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X, & </
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EN, & </
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<
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xml:space
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MF, &</
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<
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">, ME, remanebit rectangulum ſub compoſita ex ipſa, XE,
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EN, NM, & </
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<
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">ſub, EM, illas ergo tres componentes rationes in has
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duas reſolutas habemus, ſcilicet in eam, quam habet rectangulũ
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ſub, XEN, integra, & </
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EN, NM, & </
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<
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duæ rationes componunt rationem parallelepipedi ſub, NE, & </
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ſub rectangulo integræ, XEN, ductæ in, EN, ideſt parallelepipe-
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note
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di ſub integra, XEN, & </
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ME, & </
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<
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parallelepipedum ſub integra, XE, EN, NM, & </
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<
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ergo 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, HDFG, erunt vt parallelepipedum ſub integra, XEN, & </
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quadrato, NE, ad parallelepipedum ſub integra, XE, EN, NM,
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& </
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ad eiuſdem axim, vel diametrum ordinatim appli-
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catam, cuius omnia quadrata, regula propoſitæ hyperbo-
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læ baſi, ad omnia quadrata trianguli in eadem baſi, & </
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ca eundem axim, vel diametrum cum portione, ſiue hyper-
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bola abſciſſa, exiſtentis, habeant datam rationem, quam
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oportet eſſe quidem maioris inæqualitatis, ſed tamen mi-
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norem ſexquialtera.</
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larus tranſuerſum, CE, cuius ſit, AE, ſexquialtera, baſis, & </
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la, FG, data ratio, quam habet, HR, ad, RL, maioris inæquali-
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tatis, ſed minor ſexquialtera, oportet ergo ab hyperbola, FEG,
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per lineam ad, EM, ordinatim applicatam .</
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<
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FG, parallelam, portionem, ſiue hyperbolam abſcindele, cuius
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omnia quadrata ad omnia quadrata trianguli in eadem baſi, & </
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circa eundem axim, vel diametrum cum ipſa habeant rationem,
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quam habet, HR, ad, RL; </
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nor ſexquialtera, erit minor ea, quam habet, AE, ad, EC, & </
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