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

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        <div xml:id="echoid-div623" type="section" level="1" n="245">
          <p style="it">
            <s xml:id="echoid-s6036" xml:space="preserve">
              <pb o="34" file="0216" n="216" rhead=""/>
            factum, tunc ex dictis binis contingentibus, quæ ad partem axis ducitur ſem-
              <lb/>
            per altera contingente ad oppofitam axis partem minor erit, atq; </s>
            <s xml:id="echoid-s6037" xml:space="preserve">hæc erit MA-
              <lb/>
            XIMA. </s>
            <s xml:id="echoid-s6038" xml:space="preserve">Si verò punctum fuerit extra Ellipſim inter axes, tunc contingens
              <lb/>
            ad partem maioris axis ducta, minor erit altera contingente ad partem mino-
              <lb/>
            ris, pariterque hæc erit MAXIMA ad conuexam Ellipſis peripheriã. </s>
            <s xml:id="echoid-s6039" xml:space="preserve">Quæ
              <lb/>
            omnia facili negotio demonſtrabuntur ſi animaduertatur, quod in quocunque
              <lb/>
            triangulo, cuius vnum latus altero ſit maius, hoc ipſum eſſe MAXIMIAM
              <lb/>
            linearum omnium à vertice anguli ab ipſis lateribus comprehenſi, ad puncta
              <lb/>
            baſis prædicti trianguli ducibilium, (tale enim triangulum eſt, quod a prædi-
              <lb/>
            ctis contingentibus tanquam lateribus, & </s>
            <s xml:id="echoid-s6040" xml:space="preserve">à recta puncta contactuum iungen-
              <lb/>
            te, tanquam baſi efficitur, in quo idem maius latus, ſiue contingentium ma-
              <lb/>
            ior eò magis erit MAXIMA ad incluſam ſectionis peripheriam.) </s>
            <s xml:id="echoid-s6041" xml:space="preserve">Si tandem
              <lb/>
            punctum fuerit in angulo ad verticem aſymptotalis, aut in aſymptotis eum
              <lb/>
            comprehendentibus, tunc vllam contingentium ducere imposſibile eſt, & </s>
            <s xml:id="echoid-s6042" xml:space="preserve">du-
              <lb/>
            cibiles lineæ ad conuexam Hyperbolæ peripheriam ſemper augentur, ideoque
              <lb/>
            non datur MAXIMA; </s>
            <s xml:id="echoid-s6043" xml:space="preserve">& </s>
            <s xml:id="echoid-s6044" xml:space="preserve">cum eſt in altero angulorum, qui deinceps ſunt
              <lb/>
            aſymptotali, vel in ipſis aſymptotis Hyperbolen continentilem
              <unsure/>
            , tunc vnica
              <lb/>
            tantùm contingens linea ab eo duci poteſt, & </s>
            <s xml:id="echoid-s6045" xml:space="preserve">hæc ad partem axis, quæ erit
              <lb/>
            MAXIMA ad eandem partem ducibilium; </s>
            <s xml:id="echoid-s6046" xml:space="preserve">ſed ad oppoſitam, ipſæ ducibiles
              <lb/>
            ad Hyperbolæ conuexam peripheriam perpetuò pariter augentur. </s>
            <s xml:id="echoid-s6047" xml:space="preserve">Sed in re
              <lb/>
            haud difficilis inueſtigationis ne ampliùs quæſo immoremur.</s>
            <s xml:id="echoid-s6048" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div624" type="section" level="1" n="246">
          <head xml:id="echoid-head254" xml:space="preserve">THEOR. XVI. PROP. XXIV.</head>
          <p>
            <s xml:id="echoid-s6049" xml:space="preserve">Tranſuerſorũ laterũ in Hyperbola, MINIMVM eſt axis; </s>
            <s xml:id="echoid-s6050" xml:space="preserve">in Elli-
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            pſi autẽ, MAXIMVM eſt axis maior, MINIMVM verò axis minor.</s>
            <s xml:id="echoid-s6051" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6052" xml:space="preserve">SIt Hyperbole A B C, cuius axis tranſuerſus D B, centrum E. </s>
            <s xml:id="echoid-s6053" xml:space="preserve">Dico D
              <lb/>
            B omnium tranſuerſorum eſſe _MINIMVM._</s>
            <s xml:id="echoid-s6054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6055" xml:space="preserve">Sit quodcunque aliud H
              <lb/>
              <figure xlink:label="fig-0216-01" xlink:href="fig-0216-01a" number="177">
                <image file="0216-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0216-01"/>
              </figure>
            E A, & </s>
            <s xml:id="echoid-s6056" xml:space="preserve">per B axi applicetur
              <lb/>
            G B F, quę axi perpendicu-
              <lb/>
            laris erit, ac ſectionem con-
              <lb/>
            tinget in B. </s>
            <s xml:id="echoid-s6057" xml:space="preserve">Erit ergo per-
              <lb/>
            pendicularis E B _MINIMA_
              <lb/>
            ad peripheriam A B C:</s>
            <s xml:id="echoid-s6058" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">10. h.</note>
            quare E B minor erit E A,
              <lb/>
            & </s>
            <s xml:id="echoid-s6059" xml:space="preserve">duplum D B maius du-
              <lb/>
            plo H A: </s>
            <s xml:id="echoid-s6060" xml:space="preserve">ex quo D B erit
              <lb/>
            tranſuerſorum _MINIMVM._</s>
            <s xml:id="echoid-s6061" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6062" xml:space="preserve">In Ellipſi verò A B C,
              <lb/>
            cuius centrum E, & </s>
            <s xml:id="echoid-s6063" xml:space="preserve">B D ſit
              <lb/>
            axis maior, & </s>
            <s xml:id="echoid-s6064" xml:space="preserve">A C minor: </s>
            <s xml:id="echoid-s6065" xml:space="preserve">patet B D eſſe tranſuerſorum _MAXIMVM_, & </s>
            <s xml:id="echoid-s6066" xml:space="preserve">
              <lb/>
            A C _MINIMVM_, ex primo Coroll. </s>
            <s xml:id="echoid-s6067" xml:space="preserve">86. </s>
            <s xml:id="echoid-s6068" xml:space="preserve">primihuius. </s>
            <s xml:id="echoid-s6069" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s6070" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6071" xml:space="preserve"/>
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