Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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nes lineas figurę, D, tunc enim comparare continuum ad continuum
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non eſſet niſi ipſa indiuiſibilia comparare; </
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ſum, vel quod, etiamſi verum ſit, tamen legitima ratione ad hoc pro-
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bandum nondum peruenerimus; </
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<
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uiſibilia. </
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<
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vt figuram, A, ad figuram, D. </
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ras, B, C, ſingulas æquales figuræ, A, &</
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omnes lineæ ſingularum figurarum, A, B, C, erunt æquales omni-
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ctd.</
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bus lineis figuræ, A, ſumptis iuxta dictam regulam (quacunque re-
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gula dictæ omnes lineæ ſint aſſumptæ) & </
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poſitum ex figuris, ABC, figuræ, A, totuplex erit compoſitum ex
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omnibus lineis figurarum, ABC, omnium linearum figuræ, A, & </
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ideò habebimus æquè multiplicia primæ, & </
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eſſe figuræ, D, ac compoſitum ex omnibus li-
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neis figurarum, E, D, multiplex eſt omnium
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linearum figuræ, D, quæ ſunt æquè multipli-
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cia ſecundæ, & </
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ergo ſi multiplex primę. </
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ris, ABC, ſuperauerit multiplex ſecundę, ſci-
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licet compoſitum ex figuris, DE, etiam mul-
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tiplex tertiæ. </
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figurarum, ABC, ſuperabit multiplex quartæ
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.</
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<
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ex antec.</
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mæ fuerit æquale multiplici ſecundæ, etiam multiplex tertię erit æ-
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quale multiplici quarte, ſcilicet ſi compoſitum ex figuris, ABC,
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fuerit æquale compoſito ex figuris, DE, etiam eorundem compo-
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ſitorum omnes lineæ erunt æquales, & </
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Qui. El.</
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ad ſecundam erit, vt tertia ad quartam, ſcilicet figura, A, ad figu-
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ram, D, erit vt omnes lineæ figuræ, A, ad omnes lineas figuræ, D,
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ſumptas iuxta datas regulas. </
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huius.</
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planis erat oſtendendum.</
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C, B, ſingulas æquales ipſi, A, &</
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poſitum ex figuris, ABC, tam multiplex eſſe figurę, A, ac compo-
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ſitum ex omnibus planis figurarum, A, B, C, multiplex eſt omnium
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planorum figurę, A, & </
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tiplex eſſe figuræ, D, ac compoſitum ex omnibus planis figurarum,
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DE, multiplex eſt omnium planorum figuræ, D, & </
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<
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antecedentem Propoſitionem oſtendemus, ſi multiplex primæ ſupe-
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rauerit multiplex ſecundę, etiam multiplex tertiæ ſuperaturum mul-
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tiplex quartæ, & </
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