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-div1098" type="section" level="1" n="344">
          <head xml:id="echoid-head427" xml:space="preserve">Notæ in Propoſit. XXXI. & XXXII.</head>
          <p style="it">
            <s xml:id="echoid-s12678" xml:space="preserve">PLanum axium coniugatarum in ellipſi, &</s>
            <s xml:id="echoid-s12679" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12680" xml:space="preserve">Ideſt in ſectionibus coniu-
              <lb/>
              <note position="right" xlink:label="note-0410-01" xlink:href="note-0410-01a" xml:space="preserve">a</note>
            gatis, & </s>
            <s xml:id="echoid-s12681" xml:space="preserve">in ellipſi rectangulum ſub axibus coniugatis contentum æquale
              <lb/>
            eſt parallelogrammo ſub diametris coniugatis in angulo æquali, ei qui ad cen-
              <lb/>
            trum à diametris continetur. </s>
            <s xml:id="echoid-s12682" xml:space="preserve">In textu arabico reperitur numerus 9. </s>
            <s xml:id="echoid-s12683" xml:space="preserve">in illa
              <lb/>
            propoſitione, quæ ellipſim conſiderat, ſed mendoſe, vt arbitror debet potius
              <lb/>
            cenſeri propoſit. </s>
            <s xml:id="echoid-s12684" xml:space="preserve">32.</s>
            <s xml:id="echoid-s12685" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12686" xml:space="preserve">Et quia quadratum A E ad qua-
              <lb/>
              <note position="right" xlink:label="note-0410-02" xlink:href="note-0410-02a" xml:space="preserve">b</note>
              <figure xlink:label="fig-0410-01" xlink:href="fig-0410-01a" number="484">
                <image file="0410-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0410-01"/>
              </figure>
            dratum E C eſt, vt O R in R E,
              <lb/>
            nempe quadratum S R ad quadra-
              <lb/>
            tum F R, &</s>
            <s xml:id="echoid-s12687" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12688" xml:space="preserve">Quoniam axis rectus
              <lb/>
            D C medius proportionalis eſt inter a-
              <lb/>
            xim tranſuerſum A B, eiuſque latus
              <lb/>
            rectum, quadratum A B ad quadra-
              <lb/>
            tum D C, vel eorundem quadrantes,
              <lb/>
            ſcilicet quadratum ſemiaxis A E ad
              <lb/>
            quadratum ſemiaxis E C eandem pro-
              <lb/>
            portionem habebit, quàm axis tran-
              <lb/>
            ſuerſus A B ad eius latus rectum, ſed
              <lb/>
            rectangulum E R O ad quadratum F R
              <lb/>
              <note position="left" xlink:label="note-0410-03" xlink:href="note-0410-03a" xml:space="preserve">Prop. 37.
                <lb/>
              lib. I.</note>
            eandem proportionem habet, quàm axis
              <lb/>
            tranſuerſus A B ad eius latus rectum,
              <lb/>
            atque quadratum S R æquale eſt rectan-
              <lb/>
            gulo E R O (eo quod S R facta fuit me-
              <lb/>
            dia proportionalis inter E R, & </s>
            <s xml:id="echoid-s12689" xml:space="preserve">R O)
              <lb/>
            erit quadratum S R ad quadratum F
              <lb/>
            R, vt latus tranſuerſum A B ad eius
              <lb/>
            latus rectum: </s>
            <s xml:id="echoid-s12690" xml:space="preserve">quare quadratum A E
              <lb/>
            ad quadratum E C eandem proportio-
              <lb/>
            nem habebit, quàm quadratum S R ad
              <lb/>
            quadratum F R: </s>
            <s xml:id="echoid-s12691" xml:space="preserve">& </s>
            <s xml:id="echoid-s12692" xml:space="preserve">A E ad E C ean-
              <lb/>
            dem proportionem habebit, quàm S R ad F R: </s>
            <s xml:id="echoid-s12693" xml:space="preserve">& </s>
            <s xml:id="echoid-s12694" xml:space="preserve">ſumptis altitudinibus A E,
              <lb/>
            & </s>
            <s xml:id="echoid-s12695" xml:space="preserve">O E erit quadratum A E, ſeu ei æquale rectangulum R E O ad rectangu-
              <lb/>
              <note position="left" xlink:label="note-0410-04" xlink:href="note-0410-04a" xml:space="preserve">Ibidem.</note>
            lum A E C, vt rectangulum ſub S R, & </s>
            <s xml:id="echoid-s12696" xml:space="preserve">ſub O E ad rectangulum ſub F R,
              <lb/>
            & </s>
            <s xml:id="echoid-s12697" xml:space="preserve">ſub O E, & </s>
            <s xml:id="echoid-s12698" xml:space="preserve">permutando rectangulum R E O ad rectangulum ſub S R, & </s>
            <s xml:id="echoid-s12699" xml:space="preserve">
              <lb/>
            ſub O E, ſeu vt R E ad S R eandem proportionem habebit, quàm rectangu-
              <lb/>
            lum A E C ad rectangulum ſub F R, & </s>
            <s xml:id="echoid-s12700" xml:space="preserve">ſub O E: </s>
            <s xml:id="echoid-s12701" xml:space="preserve">& </s>
            <s xml:id="echoid-s12702" xml:space="preserve">inuertendo rectangulum
              <lb/>
            ſub F R, & </s>
            <s xml:id="echoid-s12703" xml:space="preserve">ſub O E ad rectangulum A E C eandem proportionem habet quàm
              <lb/>
            S R ad R E.</s>
            <s xml:id="echoid-s12704" xml:space="preserve"/>
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