Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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        <div xml:id="echoid-div423" type="section" level="1" n="130">
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              <pb o="114" file="0152" n="152" rhead="Apollonij Pergæi"/>
            I D minus eſt, quàm quadratũ I C duplo trianguli N F M, quod æqua-
              <lb/>
            le eſt exemplari applicato ad D C, & </s>
            <s xml:id="echoid-s4563" xml:space="preserve">quadratum I R æquale eſt duplo
              <lb/>
            trianguli I X R, & </s>
            <s xml:id="echoid-s4564" xml:space="preserve">quadratum A R æquale eſt duplo trapezij R M (3. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">ex
              <lb/>
            5.) </s>
            <s xml:id="echoid-s4566" xml:space="preserve">ergo quadratũ I A minus eſt, quàm quadratum I C duplo trianguli
              <lb/>
            F Z X, quod æquale ex exemplari applicato ad C R (6. </s>
            <s xml:id="echoid-s4567" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4568" xml:space="preserve">ſimiliter
              <lb/>
            quadratum I L minus eſt, quàm quadratum I C exemplari applicato ad
              <lb/>
            C Q; </s>
            <s xml:id="echoid-s4569" xml:space="preserve">eſtque C D maior, quàm C R, & </s>
            <s xml:id="echoid-s4570" xml:space="preserve">C R quàm C Q; </s>
            <s xml:id="echoid-s4571" xml:space="preserve">ergo I A ma-
              <lb/>
            ior eſt, quàm I D, & </s>
            <s xml:id="echoid-s4572" xml:space="preserve">I L, quàm I A; </s>
            <s xml:id="echoid-s4573" xml:space="preserve">quod erat propoſitum.</s>
            <s xml:id="echoid-s4574" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div426" type="section" level="1" n="131">
          <head xml:id="echoid-head176" xml:space="preserve">Notæ in Propoſit. XVI. XVII. XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s4575" xml:space="preserve">COmparata ſi fuerit ex recto duorum axium ellipſis crit maximus ra-
              <lb/>
              <note position="right" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">a</note>
            morum, &</s>
            <s xml:id="echoid-s4576" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4577" xml:space="preserve">Addidi particulam illam axis minoris, quæ in textu defi-
              <lb/>
            ciebat, nunquam enim C F ſemiſsis lateris recti, eſſe poteſt maior C E ſemiſſe
              <lb/>
            lateris tranſuerſi, niſi C D fuerit axis minor ellipſis.</s>
            <s xml:id="echoid-s4578" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4579" xml:space="preserve">Conſtat, quemadmodum demonſtrauimus in propoſitione 6. </s>
            <s xml:id="echoid-s4580" xml:space="preserve">&</s>
            <s xml:id="echoid-s4581" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4582" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">b</note>
            niã menſura I C ſupponitur cõparata, ideſt æqualis ipſi C F ſemiſsi lateris recti;
              <lb/>
            </s>
            <s xml:id="echoid-s4583" xml:space="preserve">propterea triangulum I C F iſoſceleum erit, & </s>
            <s xml:id="echoid-s4584" xml:space="preserve">rectangulum in C; </s>
            <s xml:id="echoid-s4585" xml:space="preserve">& </s>
            <s xml:id="echoid-s4586" xml:space="preserve">ideo qua-
              <lb/>
            dratum I C æquale erit duplo trianguli I C F: </s>
            <s xml:id="echoid-s4587" xml:space="preserve">eadem ratione propter parallelas
              <lb/>
            S O, & </s>
            <s xml:id="echoid-s4588" xml:space="preserve">C F, erit triangulum I O S ſimile triangulo I C F, & </s>
            <s xml:id="echoid-s4589" xml:space="preserve">propterea illud
              <lb/>
            quoque iſoſceleum erit, & </s>
            <s xml:id="echoid-s4590" xml:space="preserve">rectangulum in O, & </s>
            <s xml:id="echoid-s4591" xml:space="preserve">ideo quadratum I O æquale,
              <lb/>
            erit duplo trianguli I O S: </s>
            <s xml:id="echoid-s4592" xml:space="preserve">eſt verò quadratum O H æquale duplo trapezij F T
              <lb/>
              <note position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">1. huius.</note>
            O C; </s>
            <s xml:id="echoid-s4593" xml:space="preserve">igitur quadratum I H ( quod eſt æquale duobus quadratis I O, O H circa
              <lb/>
            angulum rectum O) æquale erit duplo trianguli I O S cum duplo trapezij F T
              <lb/>
            O C, ſed hæc duo ſpatia minora ſunt duplo integri trianguli I C F, eſtque de-
              <lb/>
            fectus duplum trianguli F T S, ſiue rectangulum S T b a; </s>
            <s xml:id="echoid-s4594" xml:space="preserve">igitur duplum trian-
              <lb/>
            guli I C F, ſiue quadratum I C maius eſt quadrato I H, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">exceſſus eſt rectan-
              <lb/>
            gulum T a: </s>
            <s xml:id="echoid-s4596" xml:space="preserve">quod vero rectangulum T a ſit exemplar demonſtrabitur modo, vt
              <lb/>
            in ſexta propoſitione huius.</s>
            <s xml:id="echoid-s4597" xml:space="preserve"/>
          </p>
          <figure number="140">
            <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0152-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4598" xml:space="preserve">Et conſtat, vt dictum eſt, quod ſit exemplar applicatum ad O C, &</s>
            <s xml:id="echoid-s4599" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4600" xml:space="preserve">
              <note position="right" xlink:label="note-0152-04" xlink:href="note-0152-04a" xml:space="preserve">c</note>
            Quoniam rectæ S a, T b, I C ſunt parallelæ, erunt triangula I C F, & </s>
            <s xml:id="echoid-s4601" xml:space="preserve">S a </s>
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