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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              <pb o="275" file="0313" n="313" rhead="Conicor. Lib. VII."/>
            A F; </s>
            <s xml:id="echoid-s10232" xml:space="preserve">igitur rectangulum F D A æquale eſt
              <lb/>
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            rectangulo D A E vna cum quadrato D A;
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            <s xml:id="echoid-s10233" xml:space="preserve">ſed quadratum ordinatim ad axim applicatæ
              <lb/>
              <note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">2 1. lib. 1.</note>
            B D æquale eſt rectangulo D A E ſub abſciſ-
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            ſa & </s>
            <s xml:id="echoid-s10234" xml:space="preserve">latere recto contento; </s>
            <s xml:id="echoid-s10235" xml:space="preserve">igitur rectangu-
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            lum F D A æquale eſt duobus quadratis B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s10236" xml:space="preserve">D A: </s>
            <s xml:id="echoid-s10237" xml:space="preserve">eſtquè quadratum A B ſubtenden-
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            tis rectum angulum D æquale duobus quadra-
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            tis B D, & </s>
            <s xml:id="echoid-s10238" xml:space="preserve">D A; </s>
            <s xml:id="echoid-s10239" xml:space="preserve">igitur quadratum ſubten-
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            ſæ A B æquale eſt rectangulo A D E ſub ab-
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            ſciſſa D A, & </s>
            <s xml:id="echoid-s10240" xml:space="preserve">ſub D F, quæ æqualis eſt ei-
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            dem abſciſſæ cum latere recto.</s>
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        <div xml:id="echoid-div858" type="section" level="1" n="262">
          <head xml:id="echoid-head328" xml:space="preserve">Notæ in Propoſit. V. & XXIII.</head>
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            <s xml:id="echoid-s10242" xml:space="preserve">ET diametri G C remotioris ab axe erectus C I maior eſt erecto B H
              <lb/>
              <note position="left" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">a</note>
            diametri propinquioris B F, &</s>
            <s xml:id="echoid-s10243" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">Videtur hæc 23. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">propoſitio deficiens;
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            </s>
            <s xml:id="echoid-s10246" xml:space="preserve">cum omnino inueriſimile ſit Apollonium non animaduertiſſe rem adeo facilem; </s>
            <s xml:id="echoid-s10247" xml:space="preserve">
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            quod nimirum diametri G C remotioris ab axe erectus C I maior ſit erecto B
              <lb/>
            H diametri B F proximioris quadruplo differentiæ axis abſciſſarum potentium
              <lb/>
            à terminis diametrorum ad axim ductorum.</s>
            <s xml:id="echoid-s10248" xml:space="preserve"/>
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            <s xml:id="echoid-s10249" xml:space="preserve">Quare A E cum duplo K D, nempe cum quadruplo A D eſt æqualis
              <lb/>
              <note position="left" xlink:label="note-0313-03" xlink:href="note-0313-03a" xml:space="preserve">b</note>
            duplo K N, nempe dimidio B H, &</s>
            <s xml:id="echoid-s10250" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10251" xml:space="preserve">Zuoniam B H latus rectum diame-
              <lb/>
              <note position="right" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">49. lib. 1.</note>
            tri B F ad duplum contingentis B K eſt vt M B ad B L, ſed (propter æqui-
              <lb/>
            diſtantes, & </s>
            <s xml:id="echoid-s10252" xml:space="preserve">ſimilitudinem triangulorum L B M, & </s>
            <s xml:id="echoid-s10253" xml:space="preserve">K N B) vt M B ad B
              <lb/>
            L, ita eſt duplum N K ad duplum R B; </s>
            <s xml:id="echoid-s10254" xml:space="preserve">ergo latus rectum B H æquale eſt du-
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            plo K N; </s>
            <s xml:id="echoid-s10255" xml:space="preserve">ſed prius oſtenſum eſt quod D A æqualis eſt medietati ipſius D K, & </s>
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              <lb/>
              <note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">35. .lib. 1.</note>
            D N æqualis medietati ipſius A E; </s>
            <s xml:id="echoid-s10257" xml:space="preserve">igitur duplum K N æquale eſt duplo K D,
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            ſeu quadruplo A D cum duplo D N, ſeu cum A E.</s>
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            <s xml:id="echoid-s10259" xml:space="preserve">Et A O maior eſt, quàm A D; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">ergo erectus diametri C G remotioris
              <lb/>
              <note position="left" xlink:label="note-0313-06" xlink:href="note-0313-06a" xml:space="preserve">c</note>
            maior eſt quàm erectus B F proximioris, &</s>
            <s xml:id="echoid-s10261" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10262" xml:space="preserve">Addidi in bac concluſione
              <lb/>
            verba bæc (quadruplo D O differētiæ abſciſſarum) quæ videntur deficere. </s>
            <s xml:id="echoid-s10263" xml:space="preserve">Ma-
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            nifeſtum enim eſt, quod C I latus rectum diametri C G ab axe remotioris ſu-
              <lb/>
            perat latus rectum B H diametri F B axi propinguioris quadruplo D O diffe-
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            rentiæ abſeiſſarum axis ab ordinatis à verticibus earũdem diametrorum ductis;
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            </s>
            <s xml:id="echoid-s10264" xml:space="preserve">nam B H æqualis oſtenſa eſt E A vna cum quadruplo A D, eademque ratione
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            C I æqualis eſt eidem axis lateri recto E A cum quadruplo A O; </s>
            <s xml:id="echoid-s10265" xml:space="preserve">ergo exceſſus
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            C I ſupra B H erit æqualis quadruplo differentiæ D O.</s>
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