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-div438" type="section" level="1" n="134">
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            <s xml:id="echoid-s4702" xml:space="preserve">
              <pb o="119" file="0157" n="157" rhead="Conicor. Lib. V."/>
            ſemierecto, aut æqualis, aut minor illo; </s>
            <s xml:id="echoid-s4703" xml:space="preserve">ſed ſi eſſet æqualis, aut maior eſ-
              <lb/>
            ſet quoque E C maximus ramorum (16. </s>
            <s xml:id="echoid-s4704" xml:space="preserve">17. </s>
            <s xml:id="echoid-s4705" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4706" xml:space="preserve">19. </s>
            <s xml:id="echoid-s4707" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4708" xml:space="preserve">ergo C E mi-
              <lb/>
            nor eſt dimidio erecti, & </s>
            <s xml:id="echoid-s4709" xml:space="preserve">ideo aliqua minor, quàm D C ad reſiduam vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s4710" xml:space="preserve">
              <note position="left" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">c</note>
            ad E eandem proportionẽ habebit, quàm D C ad ſemiſſim erecti; </s>
            <s xml:id="echoid-s4711" xml:space="preserve">& </s>
            <s xml:id="echoid-s4712" xml:space="preserve">ſit D G
              <lb/>
            ad G E, & </s>
            <s xml:id="echoid-s4713" xml:space="preserve">ex G ad axim ducamus perpendicularem: </s>
            <s xml:id="echoid-s4714" xml:space="preserve">hanc, dico, occur-
              <lb/>
            rere ſectioni in F; </s>
            <s xml:id="echoid-s4715" xml:space="preserve">alioquin occurrat ei in H, & </s>
            <s xml:id="echoid-s4716" xml:space="preserve">iungamus E H; </s>
            <s xml:id="echoid-s4717" xml:space="preserve">igitur E
              <lb/>
            H eſt maximus ramus (20. </s>
            <s xml:id="echoid-s4718" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4719" xml:space="preserve">& </s>
            <s xml:id="echoid-s4720" xml:space="preserve">propterea maior, quàm E F, qui
              <lb/>
            maximus ſuppoſitus fuit, & </s>
            <s xml:id="echoid-s4721" xml:space="preserve">hoc eſt abſurdum; </s>
            <s xml:id="echoid-s4722" xml:space="preserve">igitur occurrit ſectioni in
              <lb/>
            F; </s>
            <s xml:id="echoid-s4723" xml:space="preserve">& </s>
            <s xml:id="echoid-s4724" xml:space="preserve">quia G eſt rectus angulus, erit F E G acutus. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">Siverò ramus maxi-
              <lb/>
              <note position="left" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">d</note>
            mus educatur ex cẽtro, vt D B erit perpendicularis ſuper A C; </s>
            <s xml:id="echoid-s4726" xml:space="preserve">alioquin
              <lb/>
            educatur D I perpẽdicularis ad axim; </s>
            <s xml:id="echoid-s4727" xml:space="preserve">igitur D I eſt ſemiſsis axis tranſuer-
              <lb/>
            ſi (11. </s>
            <s xml:id="echoid-s4728" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4729" xml:space="preserve">& </s>
            <s xml:id="echoid-s4730" xml:space="preserve">propterea eſt ramus omnium maximus, ſed D B ſuppo-
              <lb/>
            ſitus fuit maximus, quod eſt abſurdum, vti dictum eſt; </s>
            <s xml:id="echoid-s4731" xml:space="preserve">quare patet pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s4732" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div441" type="section" level="1" n="135">
          <head xml:id="echoid-head181" xml:space="preserve">PROPOSITIO XXV.</head>
          <p>
            <s xml:id="echoid-s4733" xml:space="preserve">SI in ellipſi ramus
              <lb/>
              <note position="left" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a" number="149">
                <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0157-01"/>
              </figure>
            maximus E B mẽ-
              <lb/>
            ſuram ſecans vltra ori-
              <lb/>
            ginem E, in axe eius
              <lb/>
            minori exiſtentem, pro-
              <lb/>
            ducatur ad F, fiet F B
              <lb/>
            maximus omniũ ramo-
              <lb/>
            rum F G, F H, FI, ab
              <lb/>
            eodem puncto, ad ſe-
              <lb/>
            ctionem A B C caden-
              <lb/>
            tium, & </s>
            <s xml:id="echoid-s4734" xml:space="preserve">propinquior
              <lb/>
            maximo maior eſt remotiore.</s>
            <s xml:id="echoid-s4735" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4736" xml:space="preserve">Educamus B G, B H, H I, I A, E G, E H, E I; </s>
            <s xml:id="echoid-s4737" xml:space="preserve">& </s>
            <s xml:id="echoid-s4738" xml:space="preserve">quia E B maior
              <lb/>
              <note position="left" xlink:label="note-0157-04" xlink:href="note-0157-04a" xml:space="preserve">b</note>
            eſt, quàm E H, erit angulus B H E maior, quàm E B H; </s>
            <s xml:id="echoid-s4739" xml:space="preserve">igitur angulus
              <lb/>
            B H F multo maior erit, quàm H B F, & </s>
            <s xml:id="echoid-s4740" xml:space="preserve">propterea B F maior, eſt quàm
              <lb/>
            F H; </s>
            <s xml:id="echoid-s4741" xml:space="preserve">atque ſic demonſtrabitur, quod H F maior ſit, quàm F I, & </s>
            <s xml:id="echoid-s4742" xml:space="preserve">F I,
              <lb/>
            quàm F A; </s>
            <s xml:id="echoid-s4743" xml:space="preserve">& </s>
            <s xml:id="echoid-s4744" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s4745" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div444" type="section" level="1" n="136">
          <head xml:id="echoid-head182" xml:space="preserve">Notæ in Propoſit. XIX.</head>
          <p style="it">
            <s xml:id="echoid-s4746" xml:space="preserve">SI vero fuerit menſura E C ex recto duorum axium ellipſis A B C,
              <lb/>
              <note position="left" xlink:label="note-0157-05" xlink:href="note-0157-05a" xml:space="preserve">a</note>
            fed ſit maior comparata, &</s>
            <s xml:id="echoid-s4747" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">Similiter bic declarari debet, quod axis
              <lb/>
            rectus ſit minor; </s>
            <s xml:id="echoid-s4749" xml:space="preserve">& </s>
            <s xml:id="echoid-s4750" xml:space="preserve">propterea lego: </s>
            <s xml:id="echoid-s4751" xml:space="preserve">Si menſura E C ſumatur in axe minori
              <lb/>
            ellipſis, &</s>
            <s xml:id="echoid-s4752" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4753" xml:space="preserve"/>
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