Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ſemiportio verò. </
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<
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<
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xml:space
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">{1/2}, excedit, {2/3}, paral-
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lelogrammi, OV, ſcilicet 14. </
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<
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">per 2 {1/2}, ſi ergo ſemiportioni, OCD,
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quæ eſt proximè 16 {1/2}, iunxerimus exceſſum eiuſdem ſemiportionis
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ſuper, {2/3}, parallelogrammi, OV, .</
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<
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<
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ximè 19. </
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<
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21. </
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<
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<
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">erit ergo parallelogrammum, OV, ad hoc reſi-
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duum proximè, vt 21. </
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<
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<
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">omnia quadrata parallelogram-
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mi, OV, ad omnia quadrata trilinei, DCV, erunt proximè vt 21.
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</
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<
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<
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">_H_INC patet, ſi nos præcisè ſciamus, quam rationem habeant om-
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nia quadrata parallelogrammi, OV, ad omnia quadrata trilinei,
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DCV, quia etiam ſcimus, quam rationem habeant omnia quadrata, C
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D, ad omnia quadrata ſemiportionis, OCD, ſciemus etiam, quam ra-
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tionem habeant eadem ad rectangula ſub ſemiportione, OCD, & </
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<
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neo, DCV, bis ſumpta, & </
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<
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">item nota erit ratio ad eadem ſemel ſum-
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pta, quæ ſi iungantur omnibus quadratis ſemiportionis, OCD, compo-
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_lib.2._</
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nentur rectangula ſub para lelogrammo, OV, & </
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OCD, & </
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ſub parallelogrammo, OV, & </
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_26.lib.2._</
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ei, quam habet parallelogrammum OV, ad ſemiportionem, OCD,
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& </
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<
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">ideò hęc erit nota, ſicut etiam erit nota ratio parallelogrammi cir-
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culo, vel ellipſi, ABCD, circumſcripti, habentis latera parallela
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ipſis, AC, BD, ad eundem circulum, vel ellipſim, ABCD, & </
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<
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tur circuli quadratura; </
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<
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">ideò quærendum eſt, quam rationem habeant præ-
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cise omnia quadrata, OV, ad omnia quadrata trilinei, CDV; </
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<
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que nec alijs, nec mibi compertum eſſe potuit.</
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<
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">SI circa parallelogrammi rectanguli quodlibet laterum,
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tamquam circa diametrum integrorum, ſemicirculus,
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vel ſemiellipſis, etiam ipſo non exiſtente rectangulo, deſ-
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cripti fuerint, circumferentia autem circuli, vel curua elli-
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pſis non pertingant, neque ſecet oppoſitum prædicto latus,
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ſit autem regula parallelogrammi baſis: </
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dicti parallelogrammi ad omnia quadrata figuræ, quæ reli-
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quis tribus parallelogrammi lateribus (dempto eo, </
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