Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s6966" xml:space="preserve">Iam cum portio V M T æqualis ſit portioni I X H, erit baſis V T ad
              <note symbol="a" position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">45. h.</note>
            I H reciprocè vt altitudo X Z ad altitudinem M K, ſed eſt V T maior I H,
              <lb/>
            cum ipſa V T ſit contingentium _MAXIMA_, ergo, & </s>
            <s xml:id="echoid-s6967" xml:space="preserve">X Z erit maior M K;</s>
            <s xml:id="echoid-s6968" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0252-02" xlink:href="note-0252-02a" xml:space="preserve">47. h.</note>
            facta igitur X Y æquali ipſi M K, applicataque S Y R, erunt portiones V M
              <lb/>
            T, R X S æqualium altitudinum, ſed eſt portio R X S minor portione I X H,
              <lb/>
            pars ſuo toto, ergo ipſa R X S minor quoque erit portione V M T, & </s>
            <s xml:id="echoid-s6969" xml:space="preserve">hoc ſem-
              <lb/>
            per, &</s>
            <s xml:id="echoid-s6970" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6971" xml:space="preserve">Quare portio V M T eſt _MAXIMA_ portionum eiuſdem Ellipſis, & </s>
            <s xml:id="echoid-s6972" xml:space="preserve">
              <lb/>
            æqualium altitudinum. </s>
            <s xml:id="echoid-s6973" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s6974" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div731" type="section" level="1" n="292">
          <head xml:id="echoid-head301" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6975" xml:space="preserve">PRoxima quatuor præcedentia Theoremata, ſuper hoc ipſo Diagrammate,
              <lb/>
            facilè ſimul, tanquam Conſectaria demonſtrabuntur, ſi tamen hæ tres
              <lb/>
            concluſiones notatu dignæ præmittantur, à quibus ipſa ortum ducant. </s>
            <s xml:id="echoid-s6976" xml:space="preserve">Nimirũ.</s>
            <s xml:id="echoid-s6977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6978" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6979" xml:space="preserve">INter diametros æqualium portionum eiuſdem anguli, vel Hyperbolæ, aut
              <lb/>
            Ellipſis, _MINIMA_ eſt ea illius portionis, cuius diameter ſimul ſit ſegmentũ
              <lb/>
            axis dati anguli, vel Hyperbolæ: </s>
            <s xml:id="echoid-s6980" xml:space="preserve">ſed in Ellipſi, quæ ſit ſegmentum minoris
              <lb/>
            axis, & </s>
            <s xml:id="echoid-s6981" xml:space="preserve">_MAXIMA_, quæ ſit ſegmentum maioris.</s>
            <s xml:id="echoid-s6982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6983" xml:space="preserve">Etenim in prima figura angulum ex-
              <lb/>
              <figure xlink:label="fig-0252-01" xlink:href="fig-0252-01a" number="208">
                <image file="0252-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0252-01"/>
              </figure>
            hibente, in portionibus A B C, H O I,
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            quæ ſunt æquales, (eò quod
              <note symbol="c" position="left" xlink:label="note-0252-03" xlink:href="note-0252-03a" xml:space="preserve">45. h.</note>
            baſes contingant eandem ſimilem con-
              <lb/>
            cẽtricam Hyperbolen interiorem) dia-
              <lb/>
            meter B D, quæ eſt axis dati anguli,
              <lb/>
            minor eſt diametro O F, cum ſit B D
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            ſemi-tranſuerſorum _MINIMA_. </s>
            <s xml:id="echoid-s6984" xml:space="preserve">Et
              <note symbol="d" position="left" xlink:label="note-0252-04" xlink:href="note-0252-04a" xml:space="preserve">24. h.</note>
            ſecunda, Hyperbolen repræſentante,
              <lb/>
            in portionibus item A B C, H O I, quę
              <lb/>
            ob eandem rationem æquales ſunt, dia-
              <lb/>
            meter B D, quæ eſt ſegmentum axis
              <lb/>
            Hyperbolæ, minor eſt diametro O F,
              <lb/>
            cum ſit B D ad O F, vt ſemi - axis per-
              <lb/>
            tingens ad B ex centro exterioris Hy-
              <lb/>
            perbole, A B C, ad ſemi-tranſuerſum
              <lb/>
            pertingens ad O ex eodem centro, vt
              <lb/>
            ſatis conſtat ex 44. </s>
            <s xml:id="echoid-s6985" xml:space="preserve">huius, at ſemi-axis,
              <lb/>
            minor eſt ſemi-tranſuerſo, quare pa-
              <lb/>
            tet, &</s>
            <s xml:id="echoid-s6986" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6987" xml:space="preserve">In tertia denique in portioni-
              <lb/>
            bus T L V, H O I, A B C interſe pariter æqualibus, diameter L K portionis
              <lb/>
            T L V, quæ eſt ex minori axe datæ Ellipſis, minor eſt diametro O F portionis
              <lb/>
            H O I, atque minor diametro B D portionis A B C, & </s>
            <s xml:id="echoid-s6988" xml:space="preserve">ſic de ſingulis, quoniam
              <lb/>
            E K ad K L eſt vt E F ad F O, & </s>
            <s xml:id="echoid-s6989" xml:space="preserve">vt E D ad D B, eſtque antecedens E K minor
              <lb/>
            qualibet alia antecedentium, cum ea ſit ſemi-tranſuerſorum _MINIMA_, & </s>
            <s xml:id="echoid-s6990" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-0252-05" xlink:href="note-0252-05a" xml:space="preserve">ibidem.</note>
            D maior eſt ipſarum antecedentiũ, cum ſit ſemi-trãſuerſorum _MAXIMA_, qua-
              <lb/>
            re & </s>
            <s xml:id="echoid-s6991" xml:space="preserve">K L erit _MINIMA_, & </s>
            <s xml:id="echoid-s6992" xml:space="preserve">D B _MAXIMA_, &</s>
            <s xml:id="echoid-s6993" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6994" xml:space="preserve">idemque dicetur de æqualibus
              <lb/>
            portionibus ſemi-Ellipſi maioribus. </s>
            <s xml:id="echoid-s6995" xml:space="preserve">Verùm inter diametros æqualium por-
              <lb/>
            tionum eiuſdem Parabolæ non datur _MAXIMA_, cum omnes æquales ſint.</s>
            <s xml:id="echoid-s6996" xml:space="preserve"/>
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