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-div868" type="section" level="1" n="265">
          <head xml:id="echoid-head333" xml:space="preserve">PROPOSITIO VI. & VII.</head>
          <p>
            <s xml:id="echoid-s10297" xml:space="preserve">SI in hyperbole, aut ellipſi addantur axi tranſuerſo, vel au-
              <lb/>
              <note position="right" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">a</note>
            ferantur ab inclinato duæ interceptæ A G, C H ab eius
              <lb/>
            terminis A, C, atque à vertice ſectionis A educatur recta linea
              <lb/>
            A B ad terminum alicuius potentialis B E, & </s>
            <s xml:id="echoid-s10298" xml:space="preserve">per centrum D
              <lb/>
              <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="365">
                <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0316-01"/>
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            ducãtur diametri coniugatæ I L, N O, ita vt rectus N O æqui-
              <lb/>
            diſtet ipſi lineæ A B: </s>
            <s xml:id="echoid-s10299" xml:space="preserve">vtiquè proportio figuræ inclinatæ, vel
              <lb/>
            tranſuerſæ coniugatarum, quæ eſt eadem proportioni quadrati
              <lb/>
            I L ad quadratum N O, erit quoquè eadem, quàm habent li-
              <lb/>
            neæ inter incidentiam illius ordinatim applicatæ ad axim, & </s>
            <s xml:id="echoid-s10300" xml:space="preserve">ter-
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            minos diuidentes duarum interceptarũ, ſcilicet vt H E ad E G.</s>
            <s xml:id="echoid-s10301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10302" xml:space="preserve">Educamus I M tangentem, & </s>
            <s xml:id="echoid-s10303" xml:space="preserve">I S perpendicularem. </s>
            <s xml:id="echoid-s10304" xml:space="preserve">Et quia A D eſt
              <lb/>
              <note position="right" xlink:label="note-0316-02" xlink:href="note-0316-02a" xml:space="preserve">b</note>
            æqualis D C, & </s>
            <s xml:id="echoid-s10305" xml:space="preserve">A K æqualis K B (eo quod I L cum ſit coniugata N O
              <lb/>
            bifariam diuidit A B) erit C B parallela ipſi I D, & </s>
            <s xml:id="echoid-s10306" xml:space="preserve">propterea M S ad
              <lb/>
            S D, nempè A E ad E C (propter ſimilitudinem triangulorum) eſt vt
              <lb/>
            quadratum I M ad quadratum N D (4. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10308" xml:space="preserve">& </s>
            <s xml:id="echoid-s10309" xml:space="preserve">quadratum I D ad qua-
              <lb/>
            dratum I M eſt vt quadratum C B ad quadratum B A (propter ſimilitu-
              <lb/>
            dinem triangulorum); </s>
            <s xml:id="echoid-s10310" xml:space="preserve">ergo proportio quadrati I D ad quadratum N D
              <lb/>
            eſt compoſita ex ratione A E ad E C, & </s>
            <s xml:id="echoid-s10311" xml:space="preserve">ex ratione quadrati C B ad qua-
              <lb/>
            dratum B A; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">ſed proportio quadrati C B ad quadratum B A eſt compo-
              <lb/>
            ſita ex ratione quadrati C B ad C E in E H, & </s>
            <s xml:id="echoid-s10313" xml:space="preserve">ex ratione C E in E H
              <lb/>
            ad A E in E G, & </s>
            <s xml:id="echoid-s10314" xml:space="preserve">ex ratione A E in E G ad quadratum A B; </s>
            <s xml:id="echoid-s10315" xml:space="preserve">eſt vero
              <lb/>
            quadratum C B ad C E in E H, vt C A ad A H (3. </s>
            <s xml:id="echoid-s10316" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10317" xml:space="preserve">atquè A E
              <lb/>
            in E G ad quadratum A B eſt vt G C ad C A (2. </s>
            <s xml:id="echoid-s10318" xml:space="preserve">ex 7.)</s>
            <s xml:id="echoid-s10319" xml:space="preserve">, & </s>
            <s xml:id="echoid-s10320" xml:space="preserve">proportio
              <lb/>
            C E in E H ad A E in E G, componitur ex ratione C E ad A E, & </s>
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