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-div418" type="section" level="1" n="129">
          <pb o="112" file="0150" n="150" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s4511" xml:space="preserve">Lineæ vero breuiſſimæ, quæ ca-
              <lb/>
              <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a" number="136">
                <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0150-01"/>
              </figure>
              <note position="right" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">d</note>
            dunt ad peripheriam ſectionis B
              <lb/>
            A, continent angulos minores,
              <lb/>
            quàm B C D, vtique non occur-
              <lb/>
            runt D F, &</s>
            <s xml:id="echoid-s4512" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s4514" xml:space="preserve">quia quælibet
              <lb/>
            breuiſsima ex puncto peripheriæ A B
              <lb/>
            ad axim ducta efſicit angulum propin-
              <lb/>
              <note position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">26. 27.
                <lb/>
              huius.</note>
            quiorem vertici, minorem ipſo angulo
              <lb/>
            C; </s>
            <s xml:id="echoid-s4515" xml:space="preserve">& </s>
            <s xml:id="echoid-s4516" xml:space="preserve">propterea quælibet breuiſsima,
              <lb/>
            ad peripheriam A B extenſa ſecabit ne-
              <lb/>
              <note position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">28. huius.</note>
            ceſſario ipſam B C vlterius productam
              <lb/>
            ad partes C: </s>
            <s xml:id="echoid-s4517" xml:space="preserve">ſed prius oſtenſa fuit B
              <lb/>
            C parallela asymptoto D F; </s>
            <s xml:id="echoid-s4518" xml:space="preserve">igitur quæ-
              <lb/>
            libet breuiſsima ad peripheriam A B
              <lb/>
            educta ideſt inter parallelas poſita non
              <lb/>
            occurret alteri æquidiſtantium D F ad partes F, ſed ad partes oppoſitas verſus
              <lb/>
            D; </s>
            <s xml:id="echoid-s4519" xml:space="preserve">eo quod quælibet recta linea intra hyperbolam ducta non ſecat peripheriam ſe-
              <lb/>
              <note position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">Conuerſ.
                <lb/>
              8. lib. 2.
                <lb/>
              26. 27.
                <lb/>
              huius.
                <lb/>
              28. huius.</note>
            ctionis in ea parte, in qua continentem D F nõ ſecat; </s>
            <s xml:id="echoid-s4520" xml:space="preserve">At quælibet alia breuiſsima
              <lb/>
            infra C B ducta, neceſſario efſiciet ad axim angulum maiorem, quàm C; </s>
            <s xml:id="echoid-s4521" xml:space="preserve">& </s>
            <s xml:id="echoid-s4522" xml:space="preserve">pro-
              <lb/>
            pterea vlterius producta ſecabit ipſam B C ad partes C; </s>
            <s xml:id="echoid-s4523" xml:space="preserve">ſed quælibet breuiſsima
              <lb/>
            extra parallelas poſita quæ ſecat vnam æquidiſtantium B C, ſecabit quoq; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">reli-
              <lb/>
            quam ad eaſdem partes F C; </s>
            <s xml:id="echoid-s4525" xml:space="preserve">quare prius ſectioni occurret, vt dictum eſt.</s>
            <s xml:id="echoid-s4526" xml:space="preserve"/>
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        <div xml:id="echoid-div423" type="section" level="1" n="130">
          <head xml:id="echoid-head174" xml:space="preserve">SECTIO DECIMASEXTA</head>
          <head xml:id="echoid-head175" xml:space="preserve">Continens XVI. XVII. XVIII. Propoſ.
            <lb/>
          Apollonij.</head>
          <p>
            <s xml:id="echoid-s4527" xml:space="preserve">SI menſura comparata ſumpta fuerit in axe recto minore elli-
              <lb/>
              <note position="right" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">a</note>
            pſis, erit maximus ramorum ab eius origine egredientium,
              <lb/>
            & </s>
            <s xml:id="echoid-s4528" xml:space="preserve">illi propinquior maior eſt remotiore: </s>
            <s xml:id="echoid-s4529" xml:space="preserve">minimus vero ramorũ
              <lb/>
            eſt differentia recti, & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">comparatæ, & </s>
            <s xml:id="echoid-s4531" xml:space="preserve">illi propinquior, minor
              <lb/>
            eſt remotiore, atque exceſſus quadrati comparatæ ſupra qua-
              <lb/>
            dratum cuiuſcunque rami aſſignati æqualis eſt exemplari appli-
              <lb/>
            cato ad abſciſſam illius rami, ſiue comparata ſit minor, aut
              <lb/>
            æqualis, aut maior recto.</s>
            <s xml:id="echoid-s4532" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4533" xml:space="preserve">Sit D C rectus a-
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              <figure xlink:label="fig-0150-02" xlink:href="fig-0150-02a" number="137">
                <image file="0150-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0150-02"/>
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            xis minor ſectionis
              <lb/>
            ellipticæ A B C ſit-
              <lb/>
            que C I comparata,
              <lb/>
            & </s>
            <s xml:id="echoid-s4534" xml:space="preserve">rami I H, I K, I
              <lb/>
            B, I L, I A, I D, & </s>
            <s xml:id="echoid-s4535" xml:space="preserve">
              <lb/>
            ſemiſſis erecti ſit C
              <lb/>
            F, & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">centrum E, &</s>
            <s xml:id="echoid-s4537" xml:space="preserve"/>
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