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-div992" type="section" level="1" n="314">
          <pb o="328" file="0366" n="367" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s11571" xml:space="preserve">Fiat H M æqualis maiori H D, erit E A differentia minimæ H A, & </s>
            <s xml:id="echoid-s11572" xml:space="preserve">in-
              <lb/>
            termediæ H E minor, quàm M A, quæ eſt differentia maximæ M H, & </s>
            <s xml:id="echoid-s11573" xml:space="preserve">mi-
              <lb/>
            nimæ H A, & </s>
            <s xml:id="echoid-s11574" xml:space="preserve">A D maior eſt quàm A H, ergo E A ad M A minorem pro-
              <lb/>
            portionem habet, quàm D A ad A H, & </s>
            <s xml:id="echoid-s11575" xml:space="preserve">permutando E A ad A D habebit mi-
              <lb/>
            norem proportionem, quàm M A ad A H, & </s>
            <s xml:id="echoid-s11576" xml:space="preserve">componendo E D ad D A mino-
              <lb/>
            proportionem habebit, quàm M H, ſiue D H ad A H, & </s>
            <s xml:id="echoid-s11577" xml:space="preserve">iterum componendo
              <lb/>
            E D A ad D A minorem proportionem habebit, quàm eadem D A ad A H, & </s>
            <s xml:id="echoid-s11578" xml:space="preserve">
              <lb/>
            propterea rectangulum ſub E D A in A H minus erit quadrato D A.</s>
            <s xml:id="echoid-s11579" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div994" type="section" level="1" n="315">
          <head xml:id="echoid-head390" xml:space="preserve">LEMMA VIII.</head>
          <p style="it">
            <s xml:id="echoid-s11580" xml:space="preserve">I Iſdem poſitis ſi D H maior fuerit, quàm A H ſed minor quàm E
              <lb/>
            H, fueritque proportio E A ad A D eadem proportioni M A ad A
              <lb/>
            H, dico rectangulum ſub E D A in A H æquale eſſe quadrato D A:
              <lb/>
            </s>
            <s xml:id="echoid-s11581" xml:space="preserve">ſi verò proportio illa maior fuerit, vel minor rectangulum ſimiliter qua-
              <lb/>
            drato maius, vel minus erit.</s>
            <s xml:id="echoid-s11582" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11583" xml:space="preserve">Quia E A ad A D po-
              <lb/>
              <figure xlink:label="fig-0366-01" xlink:href="fig-0366-01a" number="435">
                <image file="0366-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0366-01"/>
              </figure>
            nitur vt M A ad A H,
              <lb/>
            componendo E D ad D A,
              <lb/>
            erit vt M H, ſeu D H ad
              <lb/>
            H A, & </s>
            <s xml:id="echoid-s11584" xml:space="preserve">iterum componen-
              <lb/>
            do E D A ad D A, erit vt
              <lb/>
            D A ad A H, & </s>
            <s xml:id="echoid-s11585" xml:space="preserve">propterea rectangulum ſub E D A in A H æquale erit qua-
              <lb/>
            drato D A.</s>
            <s xml:id="echoid-s11586" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11587" xml:space="preserve">Quando verò E A ad A D maiorem proportionem habet, quàm M A ad A
              <lb/>
            H, t@nc bis componendo E D A ad D A maiorem proportionem habebit, quàm
              <lb/>
            D A ad A H, & </s>
            <s xml:id="echoid-s11588" xml:space="preserve">propterea rectangulum ſub extremis; </s>
            <s xml:id="echoid-s11589" xml:space="preserve">ſcilicet ſub E D A in
              <lb/>
            A H maius erit quadrato intermediæ D A: </s>
            <s xml:id="echoid-s11590" xml:space="preserve">non ſecus quando E A ad A D
              <lb/>
            minorem peoportionem habet, quàm M A ad A H, oſtendetur rectangulum ſub
              <lb/>
            E D A in A H minus quadrato ex D A.</s>
            <s xml:id="echoid-s11591" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div996" type="section" level="1" n="316">
          <head xml:id="echoid-head391" xml:space="preserve">LEMMA IX.</head>
          <p style="it">
            <s xml:id="echoid-s11592" xml:space="preserve">I N hyperbola, cuius axis A C, erectus A F, præſecta H A, in-
              <lb/>
            tercepta G A, centrum D, diameter I L, eiuſque erectus I K,
              <lb/>
            @ C E ſit latus eiuſdem, ſitque diameter Q P, cuius erectus P R,
              <lb/>
            @ latus L O: </s>
            <s xml:id="echoid-s11593" xml:space="preserve">dico quod rectangulum ſub O D E in E H ab ipſo qua-
              <lb/>
            drato D E, atque Q P R ſumma laterum figuræ Diametri P Q ab L
              <lb/>
            I K ſumma laterum figuræ I L, vel ab ipſa C A F ſumma laterum
              <lb/>
            figuræ axis, vna deficiunt, vel vna æqualia ſunt, aut vna excedunt.</s>
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