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-div917" type="section" level="1" n="287">
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            <s xml:id="echoid-s10814" xml:space="preserve">
              <pb o="299" file="0337" n="338" rhead="Conicor. Lib. VII."/>
            differentia duorum laterum figuræ ſui homologi; </s>
            <s xml:id="echoid-s10815" xml:space="preserve">pariterque pro-
              <lb/>
            ximioris axi homologi differentia duorum laterum figuræ eius
              <lb/>
            maior eſt, quàm differentia duorum laterum figuræ remotioris.</s>
            <s xml:id="echoid-s10816" xml:space="preserve"/>
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        <div xml:id="echoid-div919" type="section" level="1" n="288">
          <head xml:id="echoid-head359" xml:space="preserve">PROPOSITIO XXI. & XXVIII.</head>
          <p>
            <s xml:id="echoid-s10817" xml:space="preserve">SIt itaque ſectio A B P, & </s>
            <s xml:id="echoid-s10818" xml:space="preserve">duo axes coniugati eius A C, Q
              <lb/>
            R, centrum D; </s>
            <s xml:id="echoid-s10819" xml:space="preserve">ſintque I L, N O duæ aliæ diametri con-
              <lb/>
            iugatæ; </s>
            <s xml:id="echoid-s10820" xml:space="preserve">pariterque S T, V X, & </s>
            <s xml:id="echoid-s10821" xml:space="preserve">educamus ad axim C A M
              <lb/>
            perpendiculares B E, P M. </s>
            <s xml:id="echoid-s10822" xml:space="preserve">Dico quod ſi fuerit A C æqualis
              <lb/>
            Q R; </s>
            <s xml:id="echoid-s10823" xml:space="preserve">erit quoque I L æqualis ipſi N O, & </s>
            <s xml:id="echoid-s10824" xml:space="preserve">S T ipſi V X. </s>
            <s xml:id="echoid-s10825" xml:space="preserve">Si
              <lb/>
            verò fuerit eorum aliquis reliquo major, vtique eius homologa
              <lb/>
            diameter maior quoque erit ſua coniugata, & </s>
            <s xml:id="echoid-s10826" xml:space="preserve">ſimiliter in reli-
              <lb/>
            quis propoſitionibus.</s>
            <s xml:id="echoid-s10827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10828" xml:space="preserve">Sit prius alter axis A C maior in prima figura, ſed Q R in ſecunda;
              <lb/>
            </s>
            <s xml:id="echoid-s10829" xml:space="preserve">ſintque A G, C H duæ interceptæ diametri A C. </s>
            <s xml:id="echoid-s10830" xml:space="preserve">Et quia quadratum
              <lb/>
            A C ad quadratum Q R, nempe A C ad eius erectum eſt vt A H ad H
              <lb/>
            C, ſeu ad A G; </s>
            <s xml:id="echoid-s10831" xml:space="preserve">& </s>
            <s xml:id="echoid-s10832" xml:space="preserve">habet H A ad A G maiorem proportionem in prima
              <lb/>
              <note position="right" xlink:label="note-0337-01" xlink:href="note-0337-01a" xml:space="preserve">ex Def. I.
                <lb/>
              huius.</note>
            figura, & </s>
            <s xml:id="echoid-s10833" xml:space="preserve">minorem in ſecunda, quàm H E ad E G, quæ oſtenſa eſt
              <lb/>
            ( 6. </s>
            <s xml:id="echoid-s10834" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10835" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10836" xml:space="preserve">) vt quadratum I L ad
              <lb/>
              <figure xlink:label="fig-0337-01" xlink:href="fig-0337-01a" number="391">
                <image file="0337-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0337-01"/>
              </figure>
            quadratum N O, nempe I L ad eius
              <lb/>
            erectum. </s>
            <s xml:id="echoid-s10837" xml:space="preserve">Et ſimiliter proportio illa
              <lb/>
            maior, aut minor eſt, quam H M ad
              <lb/>
            M G, quæ eſt vt quadratum S T ad
              <lb/>
            quadratum V X; </s>
            <s xml:id="echoid-s10838" xml:space="preserve">igitur A C ad Q R,
              <lb/>
            ſiue ad erectum ipſius A C in prima
              <lb/>
            maiorem proportionem habet, & </s>
            <s xml:id="echoid-s10839" xml:space="preserve">in
              <lb/>
            ſecunda minorem, quàm I L ad N O,
              <lb/>
            ſiue ad erectum ipſius I L, ſiue quàm
              <lb/>
            S T ad V X, vel ad erectum ipſius
              <lb/>
            S T; </s>
            <s xml:id="echoid-s10840" xml:space="preserve">ſed quia H E ad E G in prima
              <lb/>
            figura maiorem proportionem, & </s>
            <s xml:id="echoid-s10841" xml:space="preserve">in
              <lb/>
            ſecunda minorem, quàm H M ad M
              <lb/>
            G habebit I L ad N O maiorem pro-
              <lb/>
            portionem in prima, & </s>
            <s xml:id="echoid-s10842" xml:space="preserve">minorem in
              <lb/>
            ſecunda, quàm S T ad V X, cum-
              <lb/>
            que H E in prima figura ſit maior, & </s>
            <s xml:id="echoid-s10843" xml:space="preserve">
              <lb/>
            in ſecunda minor, quàm E G, pari-
              <lb/>
            terque H M, quàm M G, erit I L in
              <lb/>
            prima maior, & </s>
            <s xml:id="echoid-s10844" xml:space="preserve">in ſecunda minor,
              <lb/>
            quàm N O, ſimiliterque S T, quàm
              <lb/>
            V X.</s>
            <s xml:id="echoid-s10845" xml:space="preserve"/>
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