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

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            F G recta G H ęqualis dimidio re-
              <lb/>
              <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a" number="167">
                <image file="0206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0206-01"/>
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            cti B E, & </s>
            <s xml:id="echoid-s5746" xml:space="preserve">ex H agatur H I paral-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">4. ſec.
                <lb/>
              conic.</note>
            lela ad G F, & </s>
            <s xml:id="echoid-s5747" xml:space="preserve">in angulo I H D per
              <lb/>
            punctum F deſcribatur Hyperbo- le F A, quæ Parabolæ periphe-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">12. h.</note>
            riam in vno tantùm puncto A ſe-
              <lb/>
            cabit, & </s>
            <s xml:id="echoid-s5748" xml:space="preserve">iungatur F A. </s>
            <s xml:id="echoid-s5749" xml:space="preserve">Dico hãc eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s5750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5751" xml:space="preserve">Applicetur A L, & </s>
            <s xml:id="echoid-s5752" xml:space="preserve">ex A duca-
              <lb/>
            tur contingens A M, axi occur-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">8. ſecũ-
                <lb/>
              di conic.</note>
            rens in M, producaturque F A ad
              <lb/>
            vtranque partem, quæ cum aſym-
              <lb/>
            ptotis conueniet in I, D, eruntq;</s>
            <s xml:id="echoid-s5753" xml:space="preserve"> in vtraque figura, interceptę A I,
              <lb/>
            F D inter ſe ęquales, ac ideo H L,
              <lb/>
            G D ęquales erunt, ob ęquidiſtan-
              <lb/>
            tes lineas I H, A L, F G, in trian-
              <lb/>
            gulo I H D; </s>
            <s xml:id="echoid-s5754" xml:space="preserve">ſi ergo, in tertia figu-
              <lb/>
            ra, dematur communis L G, & </s>
            <s xml:id="echoid-s5755" xml:space="preserve">
              <lb/>
            in quarta, addatur, fient H G,
              <lb/>
            L D inter ſe æquales; </s>
            <s xml:id="echoid-s5756" xml:space="preserve">ſed eſt G
              <lb/>
            H dimidia B E, quare, & </s>
            <s xml:id="echoid-s5757" xml:space="preserve">L D
              <lb/>
            ipſius B E dimidia erit. </s>
            <s xml:id="echoid-s5758" xml:space="preserve">Et quo-
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            niam quadratum A L æquatur re-
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              <note symbol="d" position="left" xlink:label="note-0206-04" xlink:href="note-0206-04a" xml:space="preserve">Coroll.
                <lb/>
              primæ 1.
                <lb/>
              huius.</note>
            ctangulo L B E, & </s>
            <s xml:id="echoid-s5759" xml:space="preserve">rectangulum L B E, æquale eſt rectangulo ſub
              <lb/>
              <note symbol="e" position="left" xlink:label="note-0206-05" xlink:href="note-0206-05a" xml:space="preserve">35. pri-
                <lb/>
              mi conic.</note>
            dupla L B, ſiue ſub M L, & </s>
            <s xml:id="echoid-s5760" xml:space="preserve">ſub dimidia B E, hoc eſt ſub L D, ergo qua- dratum A L æquale erit rectangulo M L D, ac ideo angulus M A D re-
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              <note symbol="f" position="left" xlink:label="note-0206-06" xlink:href="note-0206-06a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            ctus erit, ſiue F A erit ex contactu A contingenti A M
              <note symbol="g" position="left" xlink:label="note-0206-07" xlink:href="note-0206-07a" xml:space="preserve">10. h. &
                <lb/>
              11. h. ad
                <lb/>
              num. 1.</note>
            laris: </s>
            <s xml:id="echoid-s5761" xml:space="preserve">quare F A, in vtraque figura, erit _MINIMA_ quæſita. </s>
            <s xml:id="echoid-s5762" xml:space="preserve">Quod fa- ciendum erat.</s>
            <s xml:id="echoid-s5763" xml:space="preserve"/>
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        <div xml:id="echoid-div597" type="section" level="1" n="241">
          <head xml:id="echoid-head249" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s5764" xml:space="preserve">NOn te pigeat hoc loco, Lector humaniſsime, à ſuſcepta MA-
              <lb/>
            XIMARVM, MINIMARV MQVE linearum inueſti-
              <lb/>
            gatione circa reliquas coni- ſectiones, aliquantisper recedere,
              <lb/>
            dum elegantiſsimam quandam, ac vere admirabilem affe-
              <lb/>
            ctionem exhibere tibi decernimus, circa MINIMAS lineas, ad peri-
              <lb/>
            pherias infinitarum Parabolarum, per eundem verticem ſimul adſcripta-
              <lb/>
            rum, ex eodem communis axis puncto ducibiles, quarum veſtigia, dum
              <lb/>
            hoc ipſam
              <unsure/>
            propoſitio prælo ſubijcitur, neſcio qua parùm morata cura inſe-
              <lb/>
            qui voluimus. </s>
            <s xml:id="echoid-s5765" xml:space="preserve">Huius itaque itineris delineatio, eſt quæ conſequitur.</s>
            <s xml:id="echoid-s5766" xml:space="preserve"/>
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