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-div339" type="section" level="1" n="111">
          <head xml:id="echoid-head152" xml:space="preserve">Notæ in Propoſit. LXXII.</head>
          <p style="it">
            <s xml:id="echoid-s3550" xml:space="preserve">ET minimus eorum D C, &</s>
            <s xml:id="echoid-s3551" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3552" xml:space="preserve">
              <figure xlink:label="fig-0123-01" xlink:href="fig-0123-01a" number="105">
                <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01"/>
              </figure>
            Textus videtur mendoſus; </s>
            <s xml:id="echoid-s3553" xml:space="preserve">nam
              <lb/>
              <note position="left" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">a</note>
            vt inferius oſtendetur, ramus breuiſe-
              <lb/>
            cans D C à vertice remotior, non ſem-
              <lb/>
            per minimus eſt omnium ramorum ca-
              <lb/>
            dentium ex concurſu D ad ſectionem
              <lb/>
            A B C; </s>
            <s xml:id="echoid-s3554" xml:space="preserve">itaque legendum puto; </s>
            <s xml:id="echoid-s3555" xml:space="preserve">D C
              <lb/>
            eſt minimus ramorum cadentium ad
              <lb/>
            peripheriam ſectionis B C N; </s>
            <s xml:id="echoid-s3556" xml:space="preserve">quod
              <lb/>
            manifeſtè indicatur ex determinatione
              <lb/>
            in fine propoſitionis appoſita; </s>
            <s xml:id="echoid-s3557" xml:space="preserve">inquit
              <lb/>
            enim: </s>
            <s xml:id="echoid-s3558" xml:space="preserve">propinquiores D C (ex ramis
              <lb/>
            egredientibus ad ſectionem in ea par-
              <lb/>
            te) minores ſunt remotioribus, vbi
              <lb/>
            conijcitur, Apollonium noluiſſe pronũ-
              <lb/>
            ciare, ramum D C minimum eße omnium, qui in ſectione A C N duci poſſunt,
              <lb/>
            neque propinquiores D C minores eſſe quolibet remotiori ad partes verticis A
              <lb/>
            conſtituto, ſed tantummodo eorum, qui in ſectione C B, & </s>
            <s xml:id="echoid-s3559" xml:space="preserve">in inferiori C N
              <lb/>
            ducuntur minimum eſſe D C, & </s>
            <s xml:id="echoid-s3560" xml:space="preserve">ei propinquiores minores eſſe remotioribus.</s>
            <s xml:id="echoid-s3561" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3562" xml:space="preserve">Atque ſic patet, quod D H maior ſit, quàm D I, &</s>
            <s xml:id="echoid-s3563" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">Ex vndecimo
              <lb/>
              <note position="left" xlink:label="note-0123-02" xlink:href="note-0123-02a" xml:space="preserve">b</note>
            enim Lemmate angulus D H M eſt acutus, & </s>
            <s xml:id="echoid-s3565" xml:space="preserve">D I M obtuſus, & </s>
            <s xml:id="echoid-s3566" xml:space="preserve">coniuncta
              <lb/>
            D M erunt duo quadrata D H, H M maiora quadrato D M, quæ ſubtendit
              <lb/>
            angulum acutum; </s>
            <s xml:id="echoid-s3567" xml:space="preserve">quadratum verò D M maius eſt duobus quadratis D I, I M,
              <lb/>
            ergo multo magis duo quadrata D H, H M ſimul ſumpta maiora ſunt duobus
              <lb/>
            quadratis D I, I M ſimul ſumptis, & </s>
            <s xml:id="echoid-s3568" xml:space="preserve">auferatur ex aggregato maiori quadra-
              <lb/>
            tum minus H M, & </s>
            <s xml:id="echoid-s3569" xml:space="preserve">ex minori tollatur quadratum maius I M (cum contin-
              <lb/>
            gens H M propinquior vertici A minor ſit remotiore M I) remanet quadratũ
              <lb/>
              <note position="right" xlink:label="note-0123-03" xlink:href="note-0123-03a" xml:space="preserve">68. 69.
                <lb/>
              huius.</note>
            D H maius quadrato D I, & </s>
            <s xml:id="echoid-s3570" xml:space="preserve">propterea ramus D H maior erit ramo D I, & </s>
            <s xml:id="echoid-s3571" xml:space="preserve">
              <lb/>
            ſimili modo ramus D I maior oſtendetur ramo D C.</s>
            <s xml:id="echoid-s3572" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3573" xml:space="preserve">Et iam demonſtratũ eſt, &</s>
            <s xml:id="echoid-s3574" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3575" xml:space="preserve">Scilicet: </s>
            <s xml:id="echoid-s3576" xml:space="preserve">quia omnesrami ex D ad peripheriã
              <lb/>
              <note position="left" xlink:label="note-0123-04" xlink:href="note-0123-04a" xml:space="preserve">c</note>
              <note position="right" xlink:label="note-0123-05" xlink:href="note-0123-05a" xml:space="preserve">Lem. 11.
                <lb/>
              Coroll.
                <lb/>
              64. 65.
                <lb/>
              huius.</note>
            A B ducti efficiunt cum ſuis tangentibus angulos verticem reſpicientes acutos;
              <lb/>
            </s>
            <s xml:id="echoid-s3577" xml:space="preserve">& </s>
            <s xml:id="echoid-s3578" xml:space="preserve">propterea ramus D B maior erit quolibet alio ramo inter B, & </s>
            <s xml:id="echoid-s3579" xml:space="preserve">A ducto; </s>
            <s xml:id="echoid-s3580" xml:space="preserve">
              <lb/>
            ideoque D B erit maximus cadentium in peripheria A B.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3582" xml:space="preserve">Poſtea oſtendetur, quemadmodum hìc dictum eſt, &</s>
            <s xml:id="echoid-s3583" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3584" xml:space="preserve">Textus eſt val-
              <lb/>
              <note position="left" xlink:label="note-0123-06" xlink:href="note-0123-06a" xml:space="preserve">d</note>
            de corruptus, ſic reſtituendum puto; </s>
            <s xml:id="echoid-s3585" xml:space="preserve">Oſtendetur, quemadmodum ſupra dictum
              <lb/>
            eſt, (scilicet in ſecunda parte propoſ. </s>
            <s xml:id="echoid-s3586" xml:space="preserve">67.) </s>
            <s xml:id="echoid-s3587" xml:space="preserve">quod D C minimus ſit omnium ra-
              <lb/>
            morum ad ſectionem infimam C N cadentium, & </s>
            <s xml:id="echoid-s3588" xml:space="preserve">vt hic oſtenſum eſt, ſit mi-
              <lb/>
            nimus ramorum egredientium ad ſectionem B C; </s>
            <s xml:id="echoid-s3589" xml:space="preserve">quare patet, quod D B ſit
              <lb/>
            maximus ramorum cadentium ad ſectionem A C, & </s>
            <s xml:id="echoid-s3590" xml:space="preserve">D C ſit minimus caden-
              <lb/>
            tium ad ſectionem B C N, & </s>
            <s xml:id="echoid-s3591" xml:space="preserve">quod propinquiores maioribus, ſunt maiores re-
              <lb/>
            motioribus in peripheria ſectionis A C, & </s>
            <s xml:id="echoid-s3592" xml:space="preserve">propinquiores minoribus, ſunt mi-
              <lb/>
            nores remotioribus in peripheria ſectionis B C N, & </s>
            <s xml:id="echoid-s3593" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s3594" xml:space="preserve"/>
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