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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            <s xml:id="echoid-s10204" xml:space="preserve">
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            cum quadrato D B, quod eſt æquale ipſi A D in A F; </s>
            <s xml:id="echoid-s10205" xml:space="preserve">igitur eſt æqua-
              <lb/>
            le ipſi F D in D A. </s>
            <s xml:id="echoid-s10206" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s10207" xml:space="preserve"/>
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        <div xml:id="echoid-div853" type="section" level="1" n="260">
          <head xml:id="echoid-head326" xml:space="preserve">PROPOSITIO V. & XXIII.</head>
          <p>
            <s xml:id="echoid-s10208" xml:space="preserve">IN parabola A B C cuiuſcumque diametri B F erectus B H ex-
              <lb/>
            cedit axis A D erectum A E quadruplo abciſſæ A D potentis
              <lb/>
            à termino illius diametri ad axim ductæ 23. </s>
            <s xml:id="echoid-s10209" xml:space="preserve">& </s>
            <s xml:id="echoid-s10210" xml:space="preserve">diametri C G, re-
              <lb/>
              <note position="right" xlink:label="note-0312-01" xlink:href="note-0312-01a" xml:space="preserve">a</note>
            motioris ab axe, erectus C I maior eſt erecto B H diametri propin-
              <lb/>
            quioris B F quadruplo differentiæ axis abſciſſarum potentium à
              <lb/>
            terminis diametrorum ad axim ductorum.</s>
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            <s xml:id="echoid-s10212" xml:space="preserve">Educamus A L, B K tangentes in A, B, & </s>
            <s xml:id="echoid-s10213" xml:space="preserve">B N perpendicularem ad
              <lb/>
            B K, erit K D in D N æquale quadrato D B, quod eſt æquale ipſi A E
              <lb/>
              <note position="left" xlink:label="note-0312-02" xlink:href="note-0312-02a" xml:space="preserve">11. lib. 1.</note>
            in A D; </s>
            <s xml:id="echoid-s10214" xml:space="preserve">ergo K D ad D A eandem proportionem habet, quàm A E ad
              <lb/>
            D N: </s>
            <s xml:id="echoid-s10215" xml:space="preserve">eſtque D K dupla ipſius A D (37. </s>
            <s xml:id="echoid-s10216" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s10217" xml:space="preserve">igitur A E eſt dupla
              <lb/>
              <note position="left" xlink:label="note-0312-03" xlink:href="note-0312-03a" xml:space="preserve">35. lib. 1.</note>
            ipſius D N; </s>
            <s xml:id="echoid-s10218" xml:space="preserve">quarè A E cum duplo D K, nempe cum quadruplo A D eſt
              <lb/>
              <note position="right" xlink:label="note-0312-04" xlink:href="note-0312-04a" xml:space="preserve">b</note>
            æqualis duplo K N, nempe B H (eo quod N K ad B K tangentem ean-
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            dem proportionem habet, quàm aſſumpta M B ad B L coniugatam (57.
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            </s>
            <s xml:id="echoid-s10219" xml:space="preserve">
              <note position="left" xlink:label="note-0312-05" xlink:href="note-0312-05a" xml:space="preserve">44. lib. 1.</note>
            ex 1.) </s>
            <s xml:id="echoid-s10220" xml:space="preserve">(propter ſimilitudinem duorum triangulorum); </s>
            <s xml:id="echoid-s10221" xml:space="preserve">ergo B H æqualis
              <lb/>
            eſt quadruplo A D cum A E; </s>
            <s xml:id="echoid-s10222" xml:space="preserve">quarè erectus diametri B F excedit A E
              <lb/>
            quadruplo A D. </s>
            <s xml:id="echoid-s10223" xml:space="preserve">& </s>
            <s xml:id="echoid-s10224" xml:space="preserve">A O maior eſt, quàm A D; </s>
            <s xml:id="echoid-s10225" xml:space="preserve">ergo erectus diametri
              <lb/>
              <note position="right" xlink:label="note-0312-06" xlink:href="note-0312-06a" xml:space="preserve">c</note>
            C G remotioris maior eſt, quàm erectus B F proximioris quadruplo D
              <lb/>
            O differentiæ abſciſſarum. </s>
            <s xml:id="echoid-s10226" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s10227" xml:space="preserve"/>
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        <div xml:id="echoid-div856" type="section" level="1" n="261">
          <head xml:id="echoid-head327" xml:space="preserve">Notæ in Propoſit. I.</head>
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            <s xml:id="echoid-s10228" xml:space="preserve">QVia quadratum A B eſt æquale quadrato D A, &</s>
            <s xml:id="echoid-s10229" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10230" xml:space="preserve">Quoniam re-
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              <note position="right" xlink:label="note-0312-07" xlink:href="note-0312-07a" xml:space="preserve">a</note>
            ctangulum F D A æquale eſt rectangulo F A D ſubſegmentis vna cum
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            quadrato reliqui ſegmenti D A; </s>
            <s xml:id="echoid-s10231" xml:space="preserve">eſtque latus rectum A E </s>
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