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-div581" type="section" level="1" n="190">
          <pb o="155" file="0193" n="193" rhead="Conicor. Lib. VI."/>
          <figure number="208">
            <image file="0193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0193-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s6080" xml:space="preserve">Ponamus itaque C B ad B D, vt H F ad F I, & </s>
            <s xml:id="echoid-s6081" xml:space="preserve">diuidantur tam B C,
              <lb/>
            quàm F H in punctis K, L, M, N in eiſdem rationibus, & </s>
            <s xml:id="echoid-s6082" xml:space="preserve">educamus ſu-
              <lb/>
            per eas ordinationes O P, Q R, A S, T V, X Y , E Z. </s>
            <s xml:id="echoid-s6083" xml:space="preserve">Quia B C ad
              <lb/>
            B D eſt vt H F ad F I, & </s>
            <s xml:id="echoid-s6084" xml:space="preserve">A C eſt media proportionalis inter C B, B D
              <lb/>
              <note position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve">Ex 11.
                <lb/>
              Lib. 1.</note>
            (12. </s>
            <s xml:id="echoid-s6085" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6086" xml:space="preserve">pariterque E H inter H F, F I (12. </s>
            <s xml:id="echoid-s6087" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6088" xml:space="preserve">igitur A C ad C
              <lb/>
            B eſt, vt E H ad H F , & </s>
            <s xml:id="echoid-s6089" xml:space="preserve">A S dupla ipſius A C ad C B eſt, vt E Z ad
              <lb/>
            H F; </s>
            <s xml:id="echoid-s6090" xml:space="preserve">cumque B C ad B L poſita ſit, vt H F ad F N, erit B D ad B L, vt
              <lb/>
              <note position="left" xlink:label="note-0193-02" xlink:href="note-0193-02a" xml:space="preserve">a</note>
            I F ad F N; </s>
            <s xml:id="echoid-s6091" xml:space="preserve">igitur Q R ad L B eſt vt X Y ad N F; </s>
            <s xml:id="echoid-s6092" xml:space="preserve">atque ſic oſtendetur,
              <lb/>
            quod O P ad K B eſt, vt T V ad M F, quare proportio ordinationum
              <lb/>
            axis vnius ſectionum ad ſua abſciſſa eſt, vt proportio ordinationum alte-
              <lb/>
            rius ad ſua abſciſſa, & </s>
            <s xml:id="echoid-s6093" xml:space="preserve">proportiones abſciſſarum vnius ſectionis ad abſciſ-
              <lb/>
            ſa alterius ſectionis eædem ſunt. </s>
            <s xml:id="echoid-s6094" xml:space="preserve">Quare ſectio A B ſimilis eſt ſectioni E
              <lb/>
              <note position="right" xlink:label="note-0193-03" xlink:href="note-0193-03a" xml:space="preserve">Defin. 2. huius.</note>
            F. </s>
            <s xml:id="echoid-s6095" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s6096" xml:space="preserve"/>
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        <div xml:id="echoid-div583" type="section" level="1" n="191">
          <head xml:id="echoid-head245" xml:space="preserve">PROPOSITIO XII.</head>
          <p>
            <s xml:id="echoid-s6097" xml:space="preserve">SI duarum hyperbolarum, aut ellipſium duæ axium figuræ
              <lb/>
            fuerint ſimiles, vtique ſectiones ſimiles erunt: </s>
            <s xml:id="echoid-s6098" xml:space="preserve">Si verò fue-
              <lb/>
            rint ſectiones ſimiles, figuræ etiam ſimiles erunt.</s>
            <s xml:id="echoid-s6099" xml:space="preserve"/>
          </p>
          <figure number="209">
            <image file="0193-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0193-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s6100" xml:space="preserve">Sint ſectiones A B, E F, earum axes inclinati, vel tranſuerſi B a, F b,
              <lb/>
            & </s>
            <s xml:id="echoid-s6101" xml:space="preserve">erecti earum B D, F I, & </s>
            <s xml:id="echoid-s6102" xml:space="preserve">maneant ſigna, ordinationes, & </s>
            <s xml:id="echoid-s6103" xml:space="preserve">proportio-
              <lb/>
              <note position="left" xlink:label="note-0193-04" xlink:href="note-0193-04a" xml:space="preserve">a</note>
            nes eædem, quæ in præcedenti propoſitione. </s>
            <s xml:id="echoid-s6104" xml:space="preserve">Quoniam figura ſectionis
              <lb/>
              <note position="left" xlink:label="note-0193-05" xlink:href="note-0193-05a" xml:space="preserve">b</note>
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