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-div489" type="section" level="1" n="152">
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            <s xml:id="echoid-s5151" xml:space="preserve">
              <pb o="131" file="0169" n="169" rhead="Conicor. Lib. V."/>
            breuiſsimæ B D, GI, quarum B D per centrũ
              <lb/>
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            tranſit, quæ productæ concurrunt in puncto E
              <lb/>
            axis minoris, & </s>
            <s xml:id="echoid-s5152" xml:space="preserve">concluditur, quodrami E F,
              <lb/>
            portio F H, nedũ breuiſsima non eſt, ſed ſupra
              <lb/>
            ipſam breuiſsimã ex puncto F eductam cadit.</s>
            <s xml:id="echoid-s5153" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s5154" xml:space="preserve">Sed duo hic notanda ſunt. </s>
            <s xml:id="echoid-s5155" xml:space="preserve">Primo, quod hæc
              <lb/>
            prop. </s>
            <s xml:id="echoid-s5156" xml:space="preserve">35. </s>
            <s xml:id="echoid-s5157" xml:space="preserve">non poterat poſtponi, nã vſum habet
              <lb/>
            in 57. </s>
            <s xml:id="echoid-s5158" xml:space="preserve">huius vbi malè citatur prop. </s>
            <s xml:id="echoid-s5159" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5160" xml:space="preserve">loco hu-
              <lb/>
            ius 35.</s>
            <s xml:id="echoid-s5161" xml:space="preserve">, vt ibidem inſinuatum eſt. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">Secundo,
              <lb/>
            quod hæc demonſtratio non videtur omnino
              <lb/>
            perſecta nam pendet ex prop. </s>
            <s xml:id="echoid-s5163" xml:space="preserve">34.</s>
            <s xml:id="echoid-s5164" xml:space="preserve">, & </s>
            <s xml:id="echoid-s5165" xml:space="preserve">ex eius
              <lb/>
            conuerſa, quæ demonſtrata non reperitur qua-
              <lb/>
            re ſuperuacanea non fuit noua demonſtratio in
              <lb/>
            Lemmat. </s>
            <s xml:id="echoid-s5166" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5167" xml:space="preserve">appoſita.</s>
            <s xml:id="echoid-s5168" xml:space="preserve"/>
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        <div xml:id="echoid-div491" type="section" level="1" n="153">
          <head xml:id="echoid-head202" xml:space="preserve">Notæ in Prop. XXXVI.</head>
          <p style="it">
            <s xml:id="echoid-s5169" xml:space="preserve">SI verò nulla earum tranſit per centrũ,
              <lb/>
              <note position="left" xlink:label="note-0169-01" xlink:href="note-0169-01a" xml:space="preserve">a</note>
            educamus D O, &</s>
            <s xml:id="echoid-s5170" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5171" xml:space="preserve">Si enim fuerint
              <lb/>
            quatuor lineæ breuiſſimæ G K, F I, H L, M
              <lb/>
            N, quarum nulla per centrum D tranſit, ſi-
              <lb/>
            militer oſtendetur, quod non conueniunt in
              <lb/>
            vno puncto E; </s>
            <s xml:id="echoid-s5172" xml:space="preserve">nam ducto ſemiaxe minori
              <lb/>
            D O neceſſe eſt, vt punctum E concurſus duorũ
              <lb/>
            breuiſecantiũ E G, E F cadat intra angulũ A
              <lb/>
            D O; </s>
            <s xml:id="echoid-s5173" xml:space="preserve">pariterque idem punctum E concurſus
              <lb/>
              <note position="right" xlink:label="note-0169-02" xlink:href="note-0169-02a" xml:space="preserve">34. huius.
                <lb/>
              Ibidem.</note>
            duorum breuiſec antium E H, E M, cadet ne-
              <lb/>
            ceſſario intra angulum C D O, ſed idem pun-
              <lb/>
            ctum E nequit duobus in locis reperiri, ni-
              <lb/>
            mirũ intra angulum A D O, & </s>
            <s xml:id="echoid-s5174" xml:space="preserve">intra angu-
              <lb/>
            lum C D O, igitur non poſſunt ab eodẽ puncto
              <lb/>
            educi ad ellipſim quatuor rami breuiſecantes.</s>
            <s xml:id="echoid-s5175" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div493" type="section" level="1" n="154">
          <head xml:id="echoid-head203" xml:space="preserve">Notæ in Prop. XXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s5176" xml:space="preserve">NAm ſi educamus B G tangentem erit
              <lb/>
              <note position="left" xlink:label="note-0169-03" xlink:href="note-0169-03a" xml:space="preserve">a</note>
              <note position="right" xlink:label="note-0169-04" xlink:href="note-0169-04a" xml:space="preserve">32. huius.</note>
            B D minor quàm D H, &</s>
            <s xml:id="echoid-s5177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5178" xml:space="preserve">Quo-
              <lb/>
            niam C B eſt linea breuiſſima, aut ſi maxima
              <lb/>
              <note position="right" xlink:label="note-0169-05" xlink:href="note-0169-05a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            eſt, eius portio erit breuiſſima, & </s>
            <s xml:id="echoid-s5179" xml:space="preserve">G B cõtin-
              <lb/>
            gens ſectionem in eius termino B perpendicu-
              <lb/>
            laris ad B C; </s>
            <s xml:id="echoid-s5180" xml:space="preserve">propterea in triangulo B D H
              <lb/>
            latus H D, ſubtendens angulum rectum B,
              <lb/>
            maius erit latere D B; </s>
            <s xml:id="echoid-s5181" xml:space="preserve">eſt verò D E maior,
              <lb/>
            quàm D H, eo quod punctum H contingentis
              <lb/>
            B G cadit extra ſectionem; </s>
            <s xml:id="echoid-s5182" xml:space="preserve">igitur linea B D
              <lb/>
            minor eſt, quàm D E, & </s>
            <s xml:id="echoid-s5183" xml:space="preserve">propterea angulus
              <lb/>
            D E B acutus erit, quare eſt minor </s>
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