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-div355" type="section" level="1" n="115">
          <pb o="92" file="0130" n="130" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s3760" xml:space="preserve">Si vero ex illo educatur alius bre-
              <lb/>
              <figure xlink:label="fig-0130-01" xlink:href="fig-0130-01a" number="114">
                <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0130-01"/>
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            uiſecans erit æqualis vni breuiſecan-
              <lb/>
            ti ex altera parte recti poſito, & </s>
            <s xml:id="echoid-s3761" xml:space="preserve">
              <lb/>
            omnium reliquorum erit maximus.</s>
            <s xml:id="echoid-s3762" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">b</note>
          <p>
            <s xml:id="echoid-s3763" xml:space="preserve">Quia breuiſſimæ egredientes ab ex-
              <lb/>
            tremitatibus reliquorum ramorum ab-
              <lb/>
            ſcindunt cum C, vel A lineas maiores,
              <lb/>
            quàm ſecent rami (illi 44. </s>
            <s xml:id="echoid-s3764" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3765" xml:space="preserve">de-
              <lb/>
            monſtrabitur ductis tangentibus, per
              <lb/>
            extremitates illorum (quemadmodum,
              <lb/>
            antea oſtenſum eſt) quod E B ſit maximus ramorum egredientium ad
              <lb/>
            duos quadrantes C B, B A, & </s>
            <s xml:id="echoid-s3766" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s3767" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div358" type="section" level="1" n="116">
          <head xml:id="echoid-head159" xml:space="preserve">PROPOSITIO LXXVII.</head>
          <p>
            <s xml:id="echoid-s3768" xml:space="preserve">POſtea educatur alius breuiſe-
              <lb/>
              <figure xlink:label="fig-0130-02" xlink:href="fig-0130-02a" number="115">
                <image file="0130-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0130-02"/>
              </figure>
              <note position="right" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">a</note>
            cans E F; </s>
            <s xml:id="echoid-s3769" xml:space="preserve">Dico, quod eſt æ-
              <lb/>
            qualis vni breuiſecanti E G æque
              <lb/>
            remoto à recto D B, & </s>
            <s xml:id="echoid-s3770" xml:space="preserve">eſt maxi-
              <lb/>
            mus reliquorum omnium.</s>
            <s xml:id="echoid-s3771" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3772" xml:space="preserve">Quia B D, F H ſunt duæ breuiſſimæ,
              <lb/>
              <note position="right" xlink:label="note-0130-03" xlink:href="note-0130-03a" xml:space="preserve">b</note>
            ergo rami egredientes ad ſectionem B
              <lb/>
            F abſcindunt cum A maiores lineas,
              <lb/>
            quàm ſecent breuiſſimæ, egredientes ab
              <lb/>
            eorum extremitatibus: </s>
            <s xml:id="echoid-s3773" xml:space="preserve">idem dicendum eſt de ramis educti ad ſectionis
              <lb/>
            peripheriam B G, & </s>
            <s xml:id="echoid-s3774" xml:space="preserve">rami educti ad peripherias C G, A F abſcindunt
              <lb/>
            cum C, vel A lineas minores (45. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3776" xml:space="preserve">conſtat itaque adhibitis li-
              <lb/>
              <note position="right" xlink:label="note-0130-04" xlink:href="note-0130-04a" xml:space="preserve">c</note>
            neis tangentibus, vt dictum eſt, quod E F ſit maximus ramorum ſecan-
              <lb/>
            tium ex E ad C B A egredientium, excepto vno E G, cui eſt æqualis,
              <lb/>
            quod erat oſtendendum.</s>
            <s xml:id="echoid-s3777" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div361" type="section" level="1" n="117">
          <head xml:id="echoid-head160" xml:space="preserve">Notæ in Propoſit. LXXIII.</head>
          <p>
            <s xml:id="echoid-s3778" xml:space="preserve">PR O clariori intelligentia propoſitionum huius ſectionis hæc præmitto.</s>
            <s xml:id="echoid-s3779" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div362" type="section" level="1" n="118">
          <head xml:id="echoid-head161" xml:space="preserve">LEMMA XII.</head>
          <p style="it">
            <s xml:id="echoid-s3780" xml:space="preserve">Si in ellipſi A B C à concurſu E ductus fuerit ramus E G ſecans
              <lb/>
            vtrumque axim in H, & </s>
            <s xml:id="echoid-s3781" xml:space="preserve">1, cuius portio G 1, inter axim maiorem
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s3782" xml:space="preserve">ſectionem intercepta, ſit linea breuiſsima; </s>
            <s xml:id="echoid-s3783" xml:space="preserve">dico, quod quili-
              <lb/>
            bet alius ramus E K inter breuiſecantem G E, & </s>
            <s xml:id="echoid-s3784" xml:space="preserve">axim minorem in-
              <lb/>
            terceptus, efficit cum ſectionem tangente K P angulum E K P </s>
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