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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          <p>
            <s xml:id="echoid-s10426" xml:space="preserve">Iiſdem figuris manentibus ſit H V potens comparata, & </s>
            <s xml:id="echoid-s10427" xml:space="preserve">I P ſit erectũ
              <lb/>
              <note position="right" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">a</note>
            ipſius I L. </s>
            <s xml:id="echoid-s10428" xml:space="preserve">Dico quod quadratum A C ad quadratum ſummæ I L, & </s>
            <s xml:id="echoid-s10429" xml:space="preserve">N
              <lb/>
            O eſt vt C G in E H ad quadratum E H V. </s>
            <s xml:id="echoid-s10430" xml:space="preserve">Quia quadratũ A D æquale
              <lb/>
              <figure xlink:label="fig-0322-01" xlink:href="fig-0322-01a" number="374">
                <image file="0322-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0322-01"/>
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            eſt S D in D M (39. </s>
            <s xml:id="echoid-s10431" xml:space="preserve">ex I.) </s>
            <s xml:id="echoid-s10432" xml:space="preserve">ergo S D in D M ad quadratum I D, nem-
              <lb/>
              <note position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">37. lib. I.</note>
              <note position="right" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">b</note>
            pe E C in C A ad quadratum C B (propter ſimilitudinem triangulorũ)
              <lb/>
            eſt vt quadratum A D ad quadratum I D, nempe vt quadratum A C ad
              <lb/>
            quadratum I L: </s>
            <s xml:id="echoid-s10433" xml:space="preserve">eſtque quadratum C B ad C E in E H, vt C A ad A
              <lb/>
            H, ſeu ad C G (2. </s>
            <s xml:id="echoid-s10434" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10435" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10436" xml:space="preserve">ideſt vt A C in C E ad C G in C E, & </s>
            <s xml:id="echoid-s10437" xml:space="preserve">
              <lb/>
            permutando; </s>
            <s xml:id="echoid-s10438" xml:space="preserve">igitur A C in C E ad quadratum C B, quod habebat
              <lb/>
            (vt oſtenſum eſt) eandem proportionem, quàm quadratum A C ad
              <lb/>
            quadratum I L, erit vt G C in C E ad C E in E H, nempe vt C
              <lb/>
            G ad E H, ſeu C G in E H ad quadratum E H; </s>
            <s xml:id="echoid-s10439" xml:space="preserve">igitur quadratum.
              <lb/>
            </s>
            <s xml:id="echoid-s10440" xml:space="preserve">A C ad quadratum I L eandem proportionem habet, quàm C G in. </s>
            <s xml:id="echoid-s10441" xml:space="preserve">
              <lb/>
            E H ad quadratum E H. </s>
            <s xml:id="echoid-s10442" xml:space="preserve">Et quadratum I L ad quadratum N O, ſeu L I
              <lb/>
            ad I P eſt vt H E ad E G (6. </s>
            <s xml:id="echoid-s10443" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10444" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10445" xml:space="preserve">ſcilicet vt quadratum E H ad
              <lb/>
            H E in E G, quod æquale ſuppoſitum fuit quadrato H V; </s>
            <s xml:id="echoid-s10446" xml:space="preserve">Ideoque
              <lb/>
            I I. </s>
            <s xml:id="echoid-s10447" xml:space="preserve">ad N O eandem proportionem habebit, quàm E H ad H V; </s>
            <s xml:id="echoid-s10448" xml:space="preserve">qua-
              <lb/>
            propter quadratum I L, ſiue ad quadratum ſummæ ipſarum I L, N O eſt
              <lb/>
            vt quadratum H E ad quadratum E H V; </s>
            <s xml:id="echoid-s10449" xml:space="preserve">ſiue ad quadratum differentiæ
              <lb/>
            I L, & </s>
            <s xml:id="echoid-s10450" xml:space="preserve">N O erit vt quadratum E H ad quadratum differentiæ E H, & </s>
            <s xml:id="echoid-s10451" xml:space="preserve">
              <lb/>
            H V, ſiue ad I L in N O habebit eandem proportionem, quàm E H ad
              <lb/>
            H V; </s>
            <s xml:id="echoid-s10452" xml:space="preserve">ſiue ad duo quadrata I L, N O eandem proportionem habebit,
              <lb/>
            quàm E H ad ſummam E H, E G; </s>
            <s xml:id="echoid-s10453" xml:space="preserve">eo quod quadratum I L ad quadra-
              <lb/>
            tum N O eſt vt E H ad E G; </s>
            <s xml:id="echoid-s10454" xml:space="preserve">ſiue inſuper ad quadratum I P eandem
              <lb/>
            proportionem habebit, quàm quadratum E H ad quadratum E G; </s>
            <s xml:id="echoid-s10455" xml:space="preserve">vel
              <lb/>
            potius ad quadratum differentiæ I L, & </s>
            <s xml:id="echoid-s10456" xml:space="preserve">I P erit vt quadratum E H ad
              <lb/>
            quadratum differentiæ E H, & </s>
            <s xml:id="echoid-s10457" xml:space="preserve">E G, vel rurſus ad quadratum rectæ li-
              <lb/>
            neæ ex L I, & </s>
            <s xml:id="echoid-s10458" xml:space="preserve">I P compoſitæ, erit vt quadratum H E ad quadratum
              <lb/>
            ſummæ duarum H E, E G, atque ad L I in I P eandem proportionem
              <lb/>
            habebit, quàm H E ad E G; </s>
            <s xml:id="echoid-s10459" xml:space="preserve">vel ad quadratum ipſius L I cum quadrato
              <lb/>
            I P habebit eandem proportionem, quàm quadratum H E ad duo </s>
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