Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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metro figuræ, EAG, vna ex ijs, quæ dicuntur omnes lineæ figurę,
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EAG, &</
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<
s
xml:id
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">, NS, clauſa perimetro figuræ, GOS, vna ex omnibus
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lineis figurę, GOQ, ſumptis omnibus lineis iam dictis, regula com-
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muni, EQ, & </
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<
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">recti tranſitus, vti ſemper intelligemus, niſi aliter ex-
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plicetur, etiamſi id non exprimatur. </
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<
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">Quoniam igitur ſi recta, NS,
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ſit minor recta, LM, poteſt indefinitè producta aliquando fieri ma-
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ior, ſi hoc intelligamus fieri de cæteris lineis, quæ ab altitudinibus
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portiones abſcindunt ęquales verſus regulas, EG, GQ, patet, quod
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ſingulę, quę erunt in figura, GOQ, productę fient maiores ijs, quę
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erunt in figura, EAG, ſit autem ita facta productio cuiuſuis om-
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nium linearum figuræ, GOQ, regula, EQ, vt quæ illi in directum
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conſtituitur in figura, EAG, ſit portio eiuſdem productæ, vt ex. </
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<
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</
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<
s
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">ita ſit producta, SN, verſus, ML, vt ipſam pertranſeat perueniens
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verbi gratia vſque ad, T, ita vt, LM, ſit portio ipſius, TS, patet
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ergo, quod omnes lineæ figuræ, EAG, erunt pars omnium linea-
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rum figuræ, GOQ, ſic productarum, & </
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<
s
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">iſtę erunt totum, nam illę
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iſtis claudentur, ſiue in his totæ reperientur, & </
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<
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">aliquid amplius .</
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quod de omnibus lineis figuræ, GOQ, ſic productis manet extra fi-
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guram, EAG, totum autem eſt maius ſua parte, ergo omnes lineę
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figuræ, GOQ, ſic productę fuerunt, vt maiores effectę fuerint om-
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nibus lineis figuræ, EAG; </
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<
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">eadem methodo omnes lineas figurę, E
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AG, ſic producemus, vt complectantur omnes lineas figuræ, GO
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Q, iam productas, vt dictum eſt, & </
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<
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">ideò maiores eiſdem fiant, ma-
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gnitudines autem rationem habere inter ſe dicuntur, quæ multipli-
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<
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">Diffin. 4.
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1. 5. Elem.</
note
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catæ ſe inuicem ſuperare poſiunt, ergo patet omnes lineas figura-
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rum, EAG, GOQ, cum altitudines, A ℟, OP, fuerint æquales,
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inter ſe rationem habere.</
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<
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">Non ſint autem æquales, ſed altitudo, A ℟, ſit maior altitudine,
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OP, & </
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">ab, A ℟, ſit abſciſſa verſus, EG, ipſa, C ℟, ęqualis ipſi, O
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P, & </
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<
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">per, C, ducta, BD, parallela, EG, intelligatur per, BD, à
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figura, EAG, abſciſſa figura, BAD, & </
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<
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">ea conſtituta, vt, HFE,
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ita vt ſit in eodem plano ad eandem partem cum figuris, EBDG,
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(quæ remanſit) &</
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<
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">, GOQ, exiſtente, HE, in directum ipſi, EQ,
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quod ſi adhuc altitudo, FX, ſit maior altitudine, OP, abſcindatur
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illi æqualis, & </
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<
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">diſponantur figuræ reſiduæ, vt ea-
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rum baſes ſint in directum ipſi, EQ, & </
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<
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">figuræ conſtitutæ in eodem
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plano, & </
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">ad eandem partem cum figuris, EAG, GOQ, in altitu-
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dinibus vel ęqualibus, vel non maioribus altitudine, OP, Intelliga-
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tur nunc ducta vtcumque in figura, GOQ, recta, NS, parallela,
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GQ, quæ erit vna ex omnibus lineis figura, GOQ, regula, GQ,
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producaturq; </
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<
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