Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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eorum notitia in ſuppoſitione eiuſdem byperbolæ qudaraturæ deficiat;
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<
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dum tenere poterit Lib. </
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<
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byperbolarum ſpeculationem ad oppoſitas ſectiones, & </
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Appolonij opportunè videtur tranſeundum.</
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<
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<
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">oppoſitarum ſectio-
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num ordinatim applicentur rectæ lineæ in eaſdem
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terminatæ, ita vt abſciſſæ per eaſdem ab axibu, vel dia-
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metris verſus vertices ſint æquales erũt iſtæ applicatæ pa-
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rallelogrammi oppoſita latera, quod parallelogrãmum ſi
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compleatur, regula applicatarum altera ſumpta, omnia
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quadrata parallelogrammi conſtituti ad reliquum, dem-
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ptis ab ijſdem omnibus quadratis oppoſitarum hyperbo-
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larum iam ſer dictas ordinatim applicatas conſtitutarum,
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erunt vt rectangulum ſub compoſita ex tranſuerſo latere,
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& </
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<
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">axi, vel diametro alterutrius oppoſitarum hyperbola-
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rum, & </
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ſuerſi lateris, ad rectangulum bis ſub . </
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">tranſuerſi lateris,
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& </
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<
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">eiuſdem tranſuerſi lateris, & </
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<
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vel diamerro alrerutrius oppoſitarum hyperbolarum, cum
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{2/3}. </
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">quadrati eiuſdem axis, vel diametri.</
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<
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">Sint oppoſitæ ſectiones, AMC, BND, quarum latus tranſuer-
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ſum ſit, NM, communis axis, vel diameter earundem, ad quam
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hincinde productam ordinatim applicẽtur, BD, AC, in fectiones
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terminatæ, abicindentes verſus vertices, NM, axes, vel diame-
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tros, FN, ME, hyperbolarum, BND, AMC, (quas pariter oppo-
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ſitas voco) quæ ſint inter ſe æquales, iunganturque, BA, DC, & </
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ſit, O, centrum oppoſitarum ſectionum, BND, AMC: </
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ergo, FN, ME, ſunt æquales, erunt etiam æquales, BD, AC, & </
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ſunt equidiſtantes, quia ad eandem diametrum, velaxim, FE, ſunt
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ex 29. Pri.
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Con.</
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ordinatim applicate, ergo, BA, DC, erunt ęquidiſtantes, &</
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parallelogrammum. </
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<
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">Dico ergo (regula ſumpta altera applica-
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tarum, AC, BD, vt, AC,) omnia quadrata, BC, ad reliquum eo-
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rundem demptis omnibus quadratis oppoſitarum hyperbolarum,
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BND, AMC, eſſe vt rectangulum, NEO, ad rectangulum, </
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