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="289" file="0327" n="327" rhead="Conicor. Lib. VII."/>
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        <div xml:id="echoid-div894" type="section" level="1" n="276">
          <head xml:id="echoid-head345" xml:space="preserve">Notæ in Propoſit. XVI.</head>
          <p style="it">
            <s xml:id="echoid-s10573" xml:space="preserve">SIue ad quadratum ex recta linea æquali ſummæ duarum I L, & </s>
            <s xml:id="echoid-s10574" xml:space="preserve">I P
              <lb/>
              <note position="left" xlink:label="note-0327-01" xlink:href="note-0327-01a" xml:space="preserve">h</note>
            erit, vt C G in H E ad quadratum ex recta linea compoſita ex H E,
              <lb/>
            E G, &</s>
            <s xml:id="echoid-s10575" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10576" xml:space="preserve">Quia I L ad I P erat vt H E ad E G comparando, antecedentes ad
              <lb/>
            ſummas terminorum, erit I L ad I L, & </s>
            <s xml:id="echoid-s10577" xml:space="preserve">I P ſimul ſumptas, vt H E ad H E,
              <lb/>
            & </s>
            <s xml:id="echoid-s10578" xml:space="preserve">E G ſimul ſumptas, & </s>
            <s xml:id="echoid-s10579" xml:space="preserve">quadratum I L ad quadratum ex ſumma ipſarum
              <lb/>
            I L, & </s>
            <s xml:id="echoid-s10580" xml:space="preserve">I P deſcriptum, erit vt quadratum H E ad quadratum ex ſumma
              <lb/>
            duarum H E, & </s>
            <s xml:id="echoid-s10581" xml:space="preserve">E G deſcriptum; </s>
            <s xml:id="echoid-s10582" xml:space="preserve">& </s>
            <s xml:id="echoid-s10583" xml:space="preserve">erat prius quadratum A C ad quadra-
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            tum I L, vt rectangulum A H E ad quadratum H E; </s>
            <s xml:id="echoid-s10584" xml:space="preserve">igitur ex æqualitate
              <lb/>
            quadratum A C ad quadratum ex ſumma ipſarum I L, & </s>
            <s xml:id="echoid-s10585" xml:space="preserve">I P deſcriptum eã-
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            dem proportionem habebit, quàm rectangulum A H E ad quadratum ex ſumma
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            ipſarum H E, & </s>
            <s xml:id="echoid-s10586" xml:space="preserve">E G deſcriptum.</s>
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          <figure number="379">
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        <div xml:id="echoid-div896" type="section" level="1" n="277">
          <head xml:id="echoid-head346" xml:space="preserve">Notæ in Propoſit. XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s10588" xml:space="preserve">SIue ad I L in I P erit, vt C G in G E, &</s>
            <s xml:id="echoid-s10589" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10590" xml:space="preserve">Quia I L ad I P eſt vt H
              <lb/>
              <note position="left" xlink:label="note-0327-02" xlink:href="note-0327-02a" xml:space="preserve">i</note>
            E ad G E poſitis communibus altitudinibus I L, H E habebit quadratum
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            I L ad rectangulum ſub I L, & </s>
            <s xml:id="echoid-s10591" xml:space="preserve">I P eandem proportionem, quàm quadratum
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            H E ad rectangulum H E G: </s>
            <s xml:id="echoid-s10592" xml:space="preserve">ſed quadratum A C ad quadratum I L eandem
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            proportionem habebat, quàm rectangulum A H E ad quadratum H E; </s>
            <s xml:id="echoid-s10593" xml:space="preserve">ergo ex
              <lb/>
            æqualitate quadratum A C ad rectangulum L I P eandem proportionem habebit
              <lb/>
            quàm rectangulum A H E ad rectangulum H E G, ſeu vt A H, vel C G ad
              <lb/>
            G E.</s>
            <s xml:id="echoid-s10594" xml:space="preserve"/>
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