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-div395" type="section" level="1" n="123">
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            <s xml:id="echoid-s4371" xml:space="preserve">
              <pb o="109" file="0147" n="147" rhead="Conicor. Lib. V."/>
            educuntur, tunc quidem circulus, cuius centrum eſt concurſus, radius vero mi-
              <lb/>
            nor maximo breuiſecantium, & </s>
            <s xml:id="echoid-s4372" xml:space="preserve">maior duobus reliquis neceßariò ellipſin duobus
              <lb/>
            in locis ſecabit; </s>
            <s xml:id="echoid-s4373" xml:space="preserve">& </s>
            <s xml:id="echoid-s4374" xml:space="preserve">ideo duo tantummodo rami inter ſe æquales erunt.</s>
            <s xml:id="echoid-s4375" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div405" type="section" level="1" n="124">
          <head xml:id="echoid-head167" xml:space="preserve">SECTIO DECIMAQVINTA</head>
          <head xml:id="echoid-head168" xml:space="preserve">Continens Propoſ. XXXXI. XXXXII.
            <lb/>
          XXXXIII. Apollonij.
            <lb/>
          PROPOSITIO XXXXI.</head>
          <p>
            <s xml:id="echoid-s4376" xml:space="preserve">IN hyperhola angulus contentus à linea breuiſſima, & </s>
            <s xml:id="echoid-s4377" xml:space="preserve">à men-
              <lb/>
              <note position="left" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">a</note>
            ſura minor eſt angulo compræhenſo à linea diſtante cum cõ-
              <lb/>
            tinente.</s>
            <s xml:id="echoid-s4378" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4379" xml:space="preserve">Sit hyberbole A B, eius axis D
              <lb/>
              <figure xlink:label="fig-0147-01" xlink:href="fig-0147-01a" number="134">
                <image file="0147-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0147-01"/>
              </figure>
              <note position="left" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">b</note>
            C, linea breuiſſima B C, duo con-
              <lb/>
            tinentes D E, D F, & </s>
            <s xml:id="echoid-s4380" xml:space="preserve">diſtantia ſit
              <lb/>
            A E, & </s>
            <s xml:id="echoid-s4381" xml:space="preserve">dimidium erecti A G: </s>
            <s xml:id="echoid-s4382" xml:space="preserve">Di-
              <lb/>
            co, angulum B C D minorem eſſe
              <lb/>
            angulo D E A. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">Educamus itaque
              <lb/>
            perdendicularem B H, & </s>
            <s xml:id="echoid-s4384" xml:space="preserve">iungamus
              <lb/>
            B D, quæ ſecet A E in I. </s>
            <s xml:id="echoid-s4385" xml:space="preserve">Quia.
              <lb/>
            </s>
            <s xml:id="echoid-s4386" xml:space="preserve">D A ad A G eſt, vt D H ad H C
              <lb/>
            (14. </s>
            <s xml:id="echoid-s4387" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4388" xml:space="preserve">& </s>
            <s xml:id="echoid-s4389" xml:space="preserve">I A ad A D eſt, vt
              <lb/>
              <note position="right" xlink:label="note-0147-03" xlink:href="note-0147-03a" xml:space="preserve">9. huius.</note>
            B H ad H D; </s>
            <s xml:id="echoid-s4390" xml:space="preserve">ergo ex æqualitate,
              <lb/>
            I A ad A G, eandem proportionẽ
              <lb/>
            habebit, quàm B H ad H C, & </s>
            <s xml:id="echoid-s4391" xml:space="preserve">
              <lb/>
            propterea E A ad A G, nempe D
              <lb/>
            A ad diſtantiam A E maiorẽ pro-
              <lb/>
            portionem habebit, quàm B H ad H C igitur angulus B C H minor eſt,
              <lb/>
            quàm D E A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4392" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div408" type="section" level="1" n="125">
          <head xml:id="echoid-head169" xml:space="preserve">PROPOSITO XXXXII.</head>
          <p>
            <s xml:id="echoid-s4393" xml:space="preserve">IN parabola lineæ breuiſſimæ productæ occurrunt ſectioni ex
              <lb/>
              <note position="left" xlink:label="note-0147-04" xlink:href="note-0147-04a" xml:space="preserve">a</note>
            vtraque parte.</s>
            <s xml:id="echoid-s4394" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4395" xml:space="preserve">Quoniam breuiſſima eſt linea recta ſecans diametrum paraboles intra
              <lb/>
            ſectionem; </s>
            <s xml:id="echoid-s4396" xml:space="preserve">& </s>
            <s xml:id="echoid-s4397" xml:space="preserve">propterea ſectioni occurret ex vtraque parte (28. </s>
            <s xml:id="echoid-s4398" xml:space="preserve">ex pr.)
              <lb/>
            </s>
            <s xml:id="echoid-s4399" xml:space="preserve">
              <note position="right" xlink:label="note-0147-05" xlink:href="note-0147-05a" xml:space="preserve">27 lib. 1.</note>
            & </s>
            <s xml:id="echoid-s4400" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s4401" xml:space="preserve"/>
          </p>
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