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

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        <div xml:id="echoid-div577" type="section" level="1" n="233">
          <head xml:id="echoid-head241" xml:space="preserve">THEOR. X. PROP. XIV.</head>
          <p>
            <s xml:id="echoid-s5574" xml:space="preserve">Si in Hyperbola ſumpta fuerint duo quælibet puncta, è quo-
              <lb/>
            rum vno ducta ſit recta linea, alteri aſymptoto æquidiſtans,
              <lb/>
            aliamque ſecans; </s>
            <s xml:id="echoid-s5575" xml:space="preserve">ex reliquo verò alia vtranque aſymptoton di-
              <lb/>
            uidens in angulo, qui aſymptotali deinceps eſt, à qua, producta
              <lb/>
            in angulo ad verticem aſymptotalis, ſumatur ęqualis ei, quę ex
              <lb/>
            ipſa inter prædictum punctum, & </s>
            <s xml:id="echoid-s5576" xml:space="preserve">alteram aſymptoton interci-
              <lb/>
            pitur, atque ex ſumptæ termino ducta ſit parallela ei aſympto-
              <lb/>
            to, cui prima eductarum occurrit, hanc ipſam ſecans: </s>
            <s xml:id="echoid-s5577" xml:space="preserve">recta li-
              <lb/>
            nea huiuſmodi interſectionem iungens cum puncto, in quo ſe-
              <lb/>
            cunda eductarum eam aſymptoton ſecat, cui prima æquidiſtat,
              <lb/>
            rectæ data puncta iungenti æquidiſtabit.</s>
            <s xml:id="echoid-s5578" xml:space="preserve"/>
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          <figure number="159">
            <image file="0199-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0199-01"/>
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          <p>
            <s xml:id="echoid-s5579" xml:space="preserve">SInt in Hyperbola A B, cuius aſymptoti C D, C E, ſumpta duo
              <lb/>
            quæcunque puncta A, B, è quorum altero A ducta ſit A E I alteri
              <lb/>
            aſymptoto C D æquidiſtans, ex B verò quælibet B G F vtranque ſecans
              <lb/>
            in G, & </s>
            <s xml:id="echoid-s5580" xml:space="preserve">F; </s>
            <s xml:id="echoid-s5581" xml:space="preserve">ſectaque G H in directum, & </s>
            <s xml:id="echoid-s5582" xml:space="preserve">æquali ipſi B F, ducatur ex H
              <lb/>
            recta H I parallela ad C E occurrens cum productis D C, A E in L, & </s>
            <s xml:id="echoid-s5583" xml:space="preserve">
              <lb/>
            I. </s>
            <s xml:id="echoid-s5584" xml:space="preserve">Dico iunctas A B, F I eſſe inter ſe parallelas.</s>
            <s xml:id="echoid-s5585" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5586" xml:space="preserve">Ducta enim B D parallela ad C E, iunctaque D E, cum ſit B F æqua-
              <lb/>
            lis G H, erit quoque D F æqualis C L, ob parallelas D B, G E, HI, ſed
              <lb/>
            eſt C L æqualis ipſi E I, quare D F, & </s>
            <s xml:id="echoid-s5587" xml:space="preserve">E I æquales erunt, ſuntque etiam
              <lb/>
            parallelæ, ergo F I æquidiſtat ipſi D E, ſed eſt A B æquidiſtans
              <note symbol="a" position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">13. h.</note>
            D E, quare F I, & </s>
            <s xml:id="echoid-s5588" xml:space="preserve">A B ſunt quoque inter ſe parallelæ. </s>
            <s xml:id="echoid-s5589" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s5590" xml:space="preserve">c.</s>
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