Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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mæ abſciſſarum, EM, magnitudines tertij ordinis collectæ iuxta
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tertiam . </
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<
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<
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">iuxta, ME, ad omnes abiciſſas ipſius, ME, magnitudi-
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nes quarti ordinis collectas iuxta quartam . </
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<
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<
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maximisabſciſſarum, EM, & </
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<
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">eiuſdem omnibus abſciſſis, vel recti,
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19. 1. 2.</
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vel eiuſdem obliqui tranſitus; </
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<
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M, duplæ omnium abſciſſarum, EM, recti, vel eiuſdem obliqui
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tranſitus, ergo & </
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<
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">omnia quadrata, EF, erunt dupla omnium qua-
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dratorum ſemiparabolæ, EMF, & </
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<
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quadrata, AF, erunt dupla omnium quadratorum parabolæ, VE
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F; </
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omnia quadrata parabolæ, VEF, erunt tres, ſed quarum partium
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omnia quadrata, AF, ſunt ſex, earum omnia quadrata trianguli,
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EVF, iunt duæ, quia omnia quadrata, AF, iunt tripla omnium
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quadratorum trianguli, EVF, ergo quarum partium omnia qua-
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drata parabolæ, VEF, funttres, earum omnia quadrata triangu-
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li, EVF, erunt duæ, ergo omnia quadrata parabolæ, VEF, erunt
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ſexquialtera omnium quadratorum trianguli, VEF, quæ oſtende-
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re oportebat.</
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applicentur duæ rectæ lineæ parabolas conſtituentes,
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quarum altera ſumatur pro regula, harum parabolarum
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omnia quadrata erunt interſe, vt quadrata axium, vel dia-
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metrorum earundem.</
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CH, duæ vtcunque ordinatim
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applicatæ, FH, OM, parabo-
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las, FCH, OCM, abſcinden-
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tes, ſit autem regula altera ha-
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rum ordinatim applicatarum, vt,
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FH. </
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rabolæ, FCH, ad omnia qua-
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drata parabolæ, OCM, eſſe vt
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quadratum, GC, ad quadratum,
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CI: </
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<
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grammum, AH, in baſi, FH,
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& </
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in baſi, OM, & </
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