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-div123" type="section" level="1" n="55">
          <pb o="29" file="0067" n="67" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div126" type="section" level="1" n="56">
          <head xml:id="echoid-head85" xml:space="preserve">SECTIO SEPTIMA</head>
          <head xml:id="echoid-head86" xml:space="preserve">Continens XXVI. XXVII. XXVIII. Propoſ.
            <lb/>
          Apollonij.</head>
          <head xml:id="echoid-head87" xml:space="preserve">PROPOSITIO XXVI. & XXVII.</head>
          <p>
            <s xml:id="echoid-s1641" xml:space="preserve">ANgulorum ab axi ſectionis A H, & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">à lineis breuiſſimis F
              <lb/>
            B, H G contentorum proximiores vertici ſectionis mi-
              <lb/>
            nores ſunt remotioribus, nempe angulus AFB minor eſt AHG.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <figure number="44">
            <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/>
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          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">SIt itaque centrum D, & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">ſemi inclinatus axis A D, ſiue ſemitranſuer-
              <lb/>
            ſus, & </s>
            <s xml:id="echoid-s1646" xml:space="preserve">dimidium erecti A C: </s>
            <s xml:id="echoid-s1647" xml:space="preserve">educamus itaque duas perpendiculares
              <lb/>
              <note position="left" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">a</note>
            GL, BI, & </s>
            <s xml:id="echoid-s1648" xml:space="preserve">ſi ſectio fuerit parabole, erit FI æqualis LH, quia quælibet
              <lb/>
            earum æqualis eſt A C (13. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1650" xml:space="preserve">L G maior eſt, quàm BI; </s>
            <s xml:id="echoid-s1651" xml:space="preserve">an-
              <lb/>
              <note position="left" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">b</note>
            gulus igitur F minor quàm H; </s>
            <s xml:id="echoid-s1652" xml:space="preserve">ſi verò ſectio fuerit hyperbole, aut ellipſis,
              <lb/>
            erit FI ad ID, vt HL ad LD, quia quælibet earum eſt, vt AC ad AD
              <lb/>
              <note position="left" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">c</note>
            (14. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1655" xml:space="preserve">permutando, erit I D ad L D nempe B I ad M L,
              <lb/>
              <note position="left" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">d</note>
            vt I F ad L H, & </s>
            <s xml:id="echoid-s1656" xml:space="preserve">anguli I, & </s>
            <s xml:id="echoid-s1657" xml:space="preserve">L ſunt recti; </s>
            <s xml:id="echoid-s1658" xml:space="preserve">igitur duo triangula BIF, M
              <lb/>
            L H ſunt ſimilia, ideoque angulus A H G maior eſt, quàm angulus A F
              <lb/>
            B, & </s>
            <s xml:id="echoid-s1659" xml:space="preserve">hoc erat propoſitum.</s>
            <s xml:id="echoid-s1660" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div128" type="section" level="1" n="57">
          <head xml:id="echoid-head88" xml:space="preserve">PROPOSITIO XXVIII.</head>
          <p>
            <s xml:id="echoid-s1661" xml:space="preserve">Hinc patet, lineas breuiſſimas ſibi occurrere ad partes axis
              <lb/>
            ſectionis.</s>
            <s xml:id="echoid-s1662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1663" xml:space="preserve">QVia angulus AFB minor eſt, quàm angulus AHG; </s>
            <s xml:id="echoid-s1664" xml:space="preserve">quare ſibi oc-
              <lb/>
              <note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">26. 27. h.</note>
              <note position="left" xlink:label="note-0067-06" xlink:href="note-0067-06a" xml:space="preserve">e</note>
            currunt ad partes F, H, & </s>
            <s xml:id="echoid-s1665" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s1666" xml:space="preserve"/>
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