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-div45" type="section" level="1" n="38">
          <p>
            <s xml:id="echoid-s938" xml:space="preserve">
              <pb o="9" file="0047" n="47" rhead="Conicor. Lib. V."/>
            tum I L duplum eſt trianguli I C H vnà cum duplo trianguli Q H O, nem-
              <lb/>
            pe cum plano rectanguli QZ; </s>
            <s xml:id="echoid-s939" xml:space="preserve">ſed quadratum I C eſt duplum trianguli I
              <lb/>
            H C (eò quod C H æqualis eſt C I) ergo quadratum C I minus eſt qua-
              <lb/>
            drato L I plano rectanguli Q Z.</s>
            <s xml:id="echoid-s940" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s941" xml:space="preserve">Deindè ponamus in ellipſi Y F æqualem differentiæ, & </s>
            <s xml:id="echoid-s942" xml:space="preserve">in hyperbola
              <lb/>
              <note position="left" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">c</note>
            æqualem aggregato D C, C F; </s>
            <s xml:id="echoid-s943" xml:space="preserve">ergo propter ſimilitudinem duorum trian-
              <lb/>
              <note position="left" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve">d</note>
            gulorum G M Q, H V Q, & </s>
            <s xml:id="echoid-s944" xml:space="preserve">H V O, M I O, erit H V æqualis V O, & </s>
            <s xml:id="echoid-s945" xml:space="preserve">H
              <lb/>
            V, vel ei æqualis O V ad V Q eſt, vt M G ad M Q, nempe vt G C ad
              <lb/>
              <note position="left" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve">e</note>
              <figure xlink:label="fig-0047-01" xlink:href="fig-0047-01a" number="14">
                <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0047-01"/>
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            H C, ſeù vt D C ad C F, igi-
              <lb/>
            tur V O ad V Q eſt vt D C
              <lb/>
              <note position="left" xlink:label="note-0047-04" xlink:href="note-0047-04a" xml:space="preserve">f</note>
            ad CF, & </s>
            <s xml:id="echoid-s946" xml:space="preserve">comparando ſum-
              <lb/>
            mas terminorum ad antece-
              <lb/>
            dentes in hyperbola, & </s>
            <s xml:id="echoid-s947" xml:space="preserve">dif-
              <lb/>
            ferentias eorundem ad ante-
              <lb/>
            cedentes in ellipſi fiet O Q
              <lb/>
            ad V O (quæ æqualis eſt O
              <lb/>
            Z, nempè M C) vt Y F ad
              <lb/>
              <note position="left" xlink:label="note-0047-05" xlink:href="note-0047-05a" xml:space="preserve">g</note>
            Y C, & </s>
            <s xml:id="echoid-s948" xml:space="preserve">eſt Y C, æqualis D
              <lb/>
            C, & </s>
            <s xml:id="echoid-s949" xml:space="preserve">Y F æqualis ſummæ
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s950" xml:space="preserve">differentiæ
              <lb/>
            in ellipſi ipſarum D C, & </s>
            <s xml:id="echoid-s951" xml:space="preserve">C
              <lb/>
            F; </s>
            <s xml:id="echoid-s952" xml:space="preserve">quadratum igitur I C mi-
              <lb/>
              <note position="left" xlink:label="note-0047-06" xlink:href="note-0047-06a" xml:space="preserve">h</note>
              <note position="right" xlink:label="note-0047-07" xlink:href="note-0047-07a" xml:space="preserve">Def. 8. 9.
                <lb/>
              huius.</note>
            nus eſt quadrato I L rectangulo Q Z, quod eſt exemplar ſimile
              <lb/>
            plano rectanguli C D in Y F, quæ eſt figura comparata. </s>
            <s xml:id="echoid-s953" xml:space="preserve">Atque ſic de-
              <lb/>
            monſtrabitur, quod quadratum I C minus ſit quadrato I K exemplari ap-
              <lb/>
            plicato ad N C, & </s>
            <s xml:id="echoid-s954" xml:space="preserve">minus eſt quadrato B I exemplari applicato ad I C,
              <lb/>
            & </s>
            <s xml:id="echoid-s955" xml:space="preserve">minus quadrato A I exemplari applicato ad E C: </s>
            <s xml:id="echoid-s956" xml:space="preserve">Eſtque M C minor,
              <lb/>
            quàm N C, & </s>
            <s xml:id="echoid-s957" xml:space="preserve">N C, quam C I, & </s>
            <s xml:id="echoid-s958" xml:space="preserve">C I, quàm C E; </s>
            <s xml:id="echoid-s959" xml:space="preserve">igitur L I maior eſt,
              <lb/>
            quàm I C, & </s>
            <s xml:id="echoid-s960" xml:space="preserve">I K maior, quàm L I, & </s>
            <s xml:id="echoid-s961" xml:space="preserve">I B maior, quàm I K, & </s>
            <s xml:id="echoid-s962" xml:space="preserve">I A, quàm
              <lb/>
            I B. </s>
            <s xml:id="echoid-s963" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s964" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div48" type="section" level="1" n="39">
          <head xml:id="echoid-head64" xml:space="preserve">Notæ in pro poſitionem quartam.</head>
          <p style="it">
            <s xml:id="echoid-s965" xml:space="preserve">QVoniam in parabola L M poteſt
              <lb/>
              <note position="left" xlink:label="note-0047-08" xlink:href="note-0047-08a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0047-02" xlink:href="fig-0047-02a" number="15">
                <image file="0047-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0047-02"/>
              </figure>
            duplum M C, &</s>
            <s xml:id="echoid-s966" xml:space="preserve">c. </s>
            <s xml:id="echoid-s967" xml:space="preserve">Quadratum
              <lb/>
            enim L M æquale eſt rectangu-
              <lb/>
            lo ſub abſciſſa M C, & </s>
            <s xml:id="echoid-s968" xml:space="preserve">latere recto C F,
              <lb/>
            eſtque C H ſemiſsis erecti C F; </s>
            <s xml:id="echoid-s969" xml:space="preserve">ergo L M
              <lb/>
            poteſt duplum rectanguli M C H.</s>
            <s xml:id="echoid-s970" xml:space="preserve"/>
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