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-div435" type="section" level="1" n="133">
          <pb o="118" file="0156" n="156" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s4672" xml:space="preserve">Quoniam proportio E G ad G I facta eſt, vt E C ad C F, nempè E
              <lb/>
              <note position="right" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">b</note>
            G ad G V, erit G V æqualis G I; </s>
            <s xml:id="echoid-s4673" xml:space="preserve">& </s>
            <s xml:id="echoid-s4674" xml:space="preserve">propterea quadratum G I æquale.
              <lb/>
            </s>
            <s xml:id="echoid-s4675" xml:space="preserve">eſt duplo trianguli G I V, & </s>
            <s xml:id="echoid-s4676" xml:space="preserve">quadratum G B æquale eſt duplo trapezij
              <lb/>
            G F (1. </s>
            <s xml:id="echoid-s4677" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4678" xml:space="preserve">ergo quadratum I B æquale eſt duplo trianguli I C S cum
              <lb/>
              <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a" number="147">
                <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-01"/>
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            duplo trianguli F S V; </s>
            <s xml:id="echoid-s4679" xml:space="preserve">& </s>
            <s xml:id="echoid-s4680" xml:space="preserve">ſic conſtat, quod quadratum I K æquale eſt du-
              <lb/>
            plo trianguli I C S cum duplo trapezij S L; </s>
            <s xml:id="echoid-s4681" xml:space="preserve">& </s>
            <s xml:id="echoid-s4682" xml:space="preserve">propterea quadrati I B ex-
              <lb/>
            ceſſus ſupra quadratũ I K æqualis erit duplo trianguli L T V, quæ æqua-
              <lb/>
            lia ſunt exemplari applicato ad G P (6. </s>
            <s xml:id="echoid-s4683" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4684" xml:space="preserve">atque ſic oſtendetur, quod
              <lb/>
            I B potentia ſuperat I H; </s>
            <s xml:id="echoid-s4685" xml:space="preserve">eſtque exceſſus exemplar applicatum ad G O,
              <lb/>
            & </s>
            <s xml:id="echoid-s4686" xml:space="preserve">ſuperat quoque I A poteſtate, eſtque exceſſus æqualis exemplari ap-
              <lb/>
            plicato ad G Q; </s>
            <s xml:id="echoid-s4687" xml:space="preserve">eſt vero G O maior, quàm G P; </s>
            <s xml:id="echoid-s4688" xml:space="preserve">ergo I B maior eſt quã
              <lb/>
            I K, & </s>
            <s xml:id="echoid-s4689" xml:space="preserve">quàm I H; </s>
            <s xml:id="echoid-s4690" xml:space="preserve">& </s>
            <s xml:id="echoid-s4691" xml:space="preserve">ſic oſtendetur, quod I B maior ſit, quàm I A; </s>
            <s xml:id="echoid-s4692" xml:space="preserve">& </s>
            <s xml:id="echoid-s4693" xml:space="preserve">
              <lb/>
            hoc erat oſtendendum.</s>
            <s xml:id="echoid-s4694" xml:space="preserve"/>
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        <div xml:id="echoid-div438" type="section" level="1" n="134">
          <head xml:id="echoid-head180" xml:space="preserve">PROPOSITIO XXIII. & XXIV.</head>
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            <s xml:id="echoid-s4695" xml:space="preserve">EContra, ſi maximi rami origo
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              <figure xlink:label="fig-0156-02" xlink:href="fig-0156-02a" number="148">
                <image file="0156-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-02"/>
              </figure>
              <note position="right" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">a</note>
            ponatur in axi minore, at non in
              <lb/>
            cẽtro ellipſis, nec ſit menſura continet
              <lb/>
            cum ipſa menſura angulum acutum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4696" xml:space="preserve">eius inuerſa ad abſciſſam à poten-
              <lb/>
            tiali cum origine habet eandem pro-
              <lb/>
            portionem figuræ axis recti minoris:
              <lb/>
            </s>
            <s xml:id="echoid-s4697" xml:space="preserve">ſi vero educatur ex centro, erit per-
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            pendicularis ſuper rectum.</s>
            <s xml:id="echoid-s4698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4699" xml:space="preserve">Sit ſectio elliptica A B C centrum D, & </s>
            <s xml:id="echoid-s4700" xml:space="preserve">E origo, quæ ſit in axi mino-
              <lb/>
              <note position="right" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">b</note>
            ri C A, & </s>
            <s xml:id="echoid-s4701" xml:space="preserve">E F ramus omnium maximus; </s>
            <s xml:id="echoid-s4702" xml:space="preserve">erit vtique E C, vel </s>
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