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-div426" type="section" level="1" n="131">
          <pb o="116" file="0154" n="154" rhead="Apollonij Pergæi"/>
          <figure number="143">
            <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0154-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4633" xml:space="preserve">Ergo quadratum I C æquale eſt duplo trianguli N F M cum duplo
              <lb/>
              <note position="right" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">e</note>
            trianguli D I N, &</s>
            <s xml:id="echoid-s4634" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4635" xml:space="preserve">Quoniam quadratum I C æquale eſt duplo trianguli I
              <lb/>
            C F, ſeu duplo trianguli I F E vna cum duplo trianguli E F C; </s>
            <s xml:id="echoid-s4636" xml:space="preserve">eſtque duplum
              <lb/>
            trianguli E D M æquale duplo trianguli E C F; </s>
            <s xml:id="echoid-s4637" xml:space="preserve">igitur quadratum I C æquale
              <lb/>
            eſt duplo trianguli I F E vna cum duplo trianguli E M D: </s>
            <s xml:id="echoid-s4638" xml:space="preserve">ijs vero triangulis
              <lb/>
            æquatur duplum trianguli N F M vna cum duplo trianguli D I N; </s>
            <s xml:id="echoid-s4639" xml:space="preserve">igitur qua-
              <lb/>
            dratum I C æquale eſt duplo trianguli N F M vna cum duplo trianguli D I N:
              <lb/>
            </s>
            <s xml:id="echoid-s4640" xml:space="preserve">eſt vero quadratum I D æquale duplo trianguli D I N; </s>
            <s xml:id="echoid-s4641" xml:space="preserve">igitur exceſſus quadrati
              <lb/>
            I C ſupra quadratum I D eſt triangulum N F M bis ſumptum; </s>
            <s xml:id="echoid-s4642" xml:space="preserve">ſcilicet exem-
              <lb/>
            plar applicatum ad latus tranſuerſum D C.</s>
            <s xml:id="echoid-s4643" xml:space="preserve"/>
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        <div xml:id="echoid-div432" type="section" level="1" n="132">
          <head xml:id="echoid-head177" xml:space="preserve">SECTIO DECIMASEPTIMA
            <lb/>
          Continens XIX. XX. XXI. XXII. XXIII.
            <lb/>
          XXIV. & XXV. Propoſ. Apollonij.</head>
          <head xml:id="echoid-head178" xml:space="preserve">PROPOSITIO XIX.</head>
          <p>
            <s xml:id="echoid-s4644" xml:space="preserve">SI menſura E C ſumatur in axe minori ellipſis A B C, ſitque
              <lb/>
              <note position="right" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">a</note>
            maior comparata; </s>
            <s xml:id="echoid-s4645" xml:space="preserve">erit maximus omniũ ramorũ egredientiũ
              <lb/>
            ex ſua origine, vt E F, E B, E G; </s>
            <s xml:id="echoid-s4646" xml:space="preserve">& </s>
            <s xml:id="echoid-s4647" xml:space="preserve">maximo propinquior,
              <lb/>
            maior erit remotiore, nempe E F, quàm E B, & </s>
            <s xml:id="echoid-s4648" xml:space="preserve">E B, quàm E G.</s>
            <s xml:id="echoid-s4649" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4650" xml:space="preserve">Coniungamus rectas A G, G B, B F,
              <lb/>
              <figure xlink:label="fig-0154-02" xlink:href="fig-0154-02a" number="144">
                <image file="0154-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0154-02"/>
              </figure>
              <note position="right" xlink:label="note-0154-03" xlink:href="note-0154-03a" xml:space="preserve">b</note>
            F C; </s>
            <s xml:id="echoid-s4651" xml:space="preserve">& </s>
            <s xml:id="echoid-s4652" xml:space="preserve">ſecetur C H æqualis compara-
              <lb/>
            tæ: </s>
            <s xml:id="echoid-s4653" xml:space="preserve">iungãturque F H, H B, H G.</s>
            <s xml:id="echoid-s4654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4655" xml:space="preserve">Et quoniam H C maior eſt, quàm H
              <lb/>
            F, (16. </s>
            <s xml:id="echoid-s4656" xml:space="preserve">17. </s>
            <s xml:id="echoid-s4657" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4658" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4659" xml:space="preserve">erit angulus H C
              <lb/>
            F minor, quàm H F C; </s>
            <s xml:id="echoid-s4660" xml:space="preserve">& </s>
            <s xml:id="echoid-s4661" xml:space="preserve">ideo multo
              <lb/>
            minor erit, quàm E F C, quare E C
              <lb/>
            maior eſt, quàm E F: </s>
            <s xml:id="echoid-s4662" xml:space="preserve">& </s>
            <s xml:id="echoid-s4663" xml:space="preserve">ſic conſtat, quod
              <lb/>
            E F maior ſit, quàm E B, & </s>
            <s xml:id="echoid-s4664" xml:space="preserve">E B, quàm
              <lb/>
            E G, & </s>
            <s xml:id="echoid-s4665" xml:space="preserve">E G, quàm A E; </s>
            <s xml:id="echoid-s4666" xml:space="preserve">quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s4667" xml:space="preserve"/>
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