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

Table of figures

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            <s xml:id="echoid-s7617" xml:space="preserve">Quoniam ergo, OF, eſt diſtantia parallelarum axi ductarum à
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            punctis, BF, abſcindatur à, BF, recta, FE, æqualis diſtantiæ, F
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            O, inſuper intelligatur adhuc ipſa, CD, ducta vtcunque parallela
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            rectæ, BF, terminans in puncta, CD, curuæ parabolæ, & </s>
            <s xml:id="echoid-s7618" xml:space="preserve">cum
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            ſit, VG, diſtantia parallelarumaxi, quæ à punctis, CD, ducun-
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            tur, abſcindatur ab ipſa, CD, verſus, D, ipſa, DZ, æqualis di-
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            ſtantiæ, VG; </s>
            <s xml:id="echoid-s7619" xml:space="preserve">ſic ductis in portione, BCDF, omnibus lineis, regu-
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            la, BF, in earundem ſingulis intell gantur ſumptæ diſtantiæ, ſicut
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            acceptæ ſuerunt, EF, ZD, quarum extrema puncta ſint in curua
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            parabolica, FDCB, ſint autem in huius curuæ ea parte, in qua
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            ſunt puncta, DF, patet ergo ſi fumamus punctum, S, verticem
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            portionis, BSF, quod dictarum omnium linearum extrema puncta
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            erunt in curua parabolica, quæ incipit a vertice, S, & </s>
            <s xml:id="echoid-s7620" xml:space="preserve">deſinit in, F;
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            </s>
            <s xml:id="echoid-s7621" xml:space="preserve">
              <figure xlink:label="fig-0336-01" xlink:href="fig-0336-01a" number="226">
                <image file="0336-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0336-01"/>
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            per alia ergo extrema puncta earundem
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            diſtantiarum intelligatur ducta linea, S
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            ZE. </s>
            <s xml:id="echoid-s7622" xml:space="preserve">Dico figuram, SFE, compre-
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            henſam recta, EF, curua parabolica,
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            SDF, & </s>
            <s xml:id="echoid-s7623" xml:space="preserve">linea, SZE, eſſe huiuſmo-
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            di, quod, ſi duxerimus intra ipſam vt-
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            cunq; </s>
            <s xml:id="echoid-s7624" xml:space="preserve">ipſi, BF, parallelam, quæ pro-
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            ducatur vſq; </s>
            <s xml:id="echoid-s7625" xml:space="preserve">ad curuam parabolicam,
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            huius portio manens in figura, SEF, erit diſtantia parallelarum
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            axi, quæ ducuntur ab extremis punctis ab eadem producta in curua
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            parabolica ſignatis. </s>
            <s xml:id="echoid-s7626" xml:space="preserve">Intelligatur ergo ducta vtcunque, DZ, ipſi, B
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            F, parallela, & </s>
            <s xml:id="echoid-s7627" xml:space="preserve">producta vſq; </s>
            <s xml:id="echoid-s7628" xml:space="preserve">ad curuam parabolicam incidens illi
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            in puncto, C, quoniam ergo, CD, eſt vna earum, quæ dicuntur
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            omnes lineæ figurę, BSF, portio eiuſdem manens intra figuram,
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            SEF, erit diſtantia parallelarum axi, quę ab eiuſdem extremis pun-
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            ctis ductæ intelliguntur, & </s>
            <s xml:id="echoid-s7629" xml:space="preserve">hoc per conſtructionem patet, quoniam
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            abipſa, CD, abſciſſa eſt, DZ, quę terminat in lineam, SZE, æ-
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            qualis dictę diſtantię, ergo figura, SEF, deſcripta eſt, qualem pro-
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            blema poſtulabat; </s>
            <s xml:id="echoid-s7630" xml:space="preserve">quę vocetur figura diſtantiarum portionis, ſiue pa-
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            rabolę, BSF.</s>
            <s xml:id="echoid-s7631" xml:space="preserve"/>
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        <div xml:id="echoid-div757" type="section" level="1" n="446">
          <head xml:id="echoid-head466" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s7632" xml:space="preserve">_Q_Via verò oſtenſum eſt, BF, ad diſtantiam parallelarum axià, B,
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            F, ductarum, eſſe vt, CD, ad diſtantiam parallelarum axi à
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            punctis, C, D, ductarum, ſunt autem, EF, ZD, æquales dictis diſtan-
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            tijs, ideò erit, BF, ad, FE, vt, CD, ad, DZ, & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">ſic erit quælibet du-
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            cta in portione, BSF, parallelaipſi, BF, adeiuſdem partemincluſam@
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            figura, SEF, vt, BF, ad, FE.</s>
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