Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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              <pb o="109" file="0129" n="129" rhead="LIBER II."/>
            metro figuræ, EAG, vna ex ijs, quæ dicuntur omnes lineæ figurę,
              <lb/>
            EAG, &</s>
            <s xml:id="echoid-s2598" xml:space="preserve">, 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, & </s>
            <s xml:id="echoid-s2599" xml:space="preserve">recti tranſitus, vti ſemper intelligemus, niſi aliter ex-
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            plicetur, etiamſi id non exprimatur. </s>
            <s xml:id="echoid-s2600" xml:space="preserve">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
              <lb/>
            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. </s>
            <s xml:id="echoid-s2601" xml:space="preserve">gr.
              <lb/>
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            <s xml:id="echoid-s2602" xml:space="preserve">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, & </s>
            <s xml:id="echoid-s2603" xml:space="preserve">iſtę erunt totum, nam illę
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            iſtis claudentur, ſiue in his totæ reperientur, & </s>
            <s xml:id="echoid-s2604" xml:space="preserve">aliquid amplius .</s>
            <s xml:id="echoid-s2605" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">
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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; </s>
            <s xml:id="echoid-s2607" xml:space="preserve">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, & </s>
            <s xml:id="echoid-s2608" xml:space="preserve">ideò maiores eiſdem fiant, ma-
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            gnitudines autem rationem habere inter ſe dicuntur, quæ multipli-
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              1. 5. Elem.</note>
            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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            <s xml:id="echoid-s2610" xml:space="preserve">Non ſint autem æquales, ſed altitudo, A ℟, ſit maior altitudine,
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            OP, & </s>
            <s xml:id="echoid-s2611" xml:space="preserve">ab, A ℟, ſit abſciſſa verſus, EG, ipſa, C ℟, ęqualis ipſi, O
              <lb/>
            P, & </s>
            <s xml:id="echoid-s2612" xml:space="preserve">per, C, ducta, BD, parallela, EG, intelligatur per, BD, à
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            figura, EAG, abſciſſa figura, BAD, & </s>
            <s xml:id="echoid-s2613" xml:space="preserve">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) &</s>
            <s xml:id="echoid-s2614" xml:space="preserve">, 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, & </s>
            <s xml:id="echoid-s2615" xml:space="preserve">ſic ſemper fiat, & </s>
            <s xml:id="echoid-s2616" xml:space="preserve">diſponantur figuræ reſiduæ, vt ea-
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            rum baſes ſint in directum ipſi, EQ, & </s>
            <s xml:id="echoid-s2617" xml:space="preserve">figuræ conſtitutæ in eodem
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            plano, & </s>
            <s xml:id="echoid-s2618" xml:space="preserve">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; </s>
            <s xml:id="echoid-s2619" xml:space="preserve">ita, vt pertranſeat omnes ſic diſpoſitas figuras, vt vſq;
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            <s xml:id="echoid-s2620" xml:space="preserve">in, Z, complectetur ergo, SZ, ipſas, LM, YT, & </s>
            <s xml:id="echoid-s2621" xml:space="preserve">ſic quæuis </s>
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