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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          <pb o="373" file="0411" n="412" rhead="Conicor. Lib. VII."/>
          <p style="it">
            <s xml:id="echoid-s12705" xml:space="preserve">Et quadratum F O ad quadratum E H, nempe triangulum E F O ad
              <lb/>
              <note position="left" xlink:label="note-0411-01" xlink:href="note-0411-01a" xml:space="preserve">c</note>
            triangulum E H P, &</s>
            <s xml:id="echoid-s12706" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12707" xml:space="preserve">Quia G F, I H ſunt diametri coniugatæ, quibus
              <lb/>
            æquidiſtant contingentes F O, & </s>
            <s xml:id="echoid-s12708" xml:space="preserve">L H erunt triangula E O F, & </s>
            <s xml:id="echoid-s12709" xml:space="preserve">E H P ſimi-
              <lb/>
            lia, quorum latera homologa O F, & </s>
            <s xml:id="echoid-s12710" xml:space="preserve">E H; </s>
            <s xml:id="echoid-s12711" xml:space="preserve">& </s>
            <s xml:id="echoid-s12712" xml:space="preserve">ideo triangulum E O F ad
              <lb/>
              <figure xlink:label="fig-0411-01" xlink:href="fig-0411-01a" number="485">
                <image file="0411-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0411-01"/>
              </figure>
              <note position="right" xlink:label="note-0411-02" xlink:href="note-0411-02a" xml:space="preserve">Prop. 4.
                <lb/>
              huius.</note>
            triangulum E H P eandem proportionem habebit, quàm quadratum O F ad
              <lb/>
            quadratum E H: </s>
            <s xml:id="echoid-s12713" xml:space="preserve">eſtque O R ad R E, vt quadratum O F ad quadratum E H,
              <lb/>
            igitur triangulum E O F ad triangulum E H P eandem proportionem habebit,
              <lb/>
            quàm O R ad R E. </s>
            <s xml:id="echoid-s12714" xml:space="preserve">Ducatur poſtea recta linea E K, erit triangulum E F K
              <lb/>
            medium proportionale inter duo ſimilia triangula E O F, & </s>
            <s xml:id="echoid-s12715" xml:space="preserve">E H P (eo quod
              <lb/>
            triangulum E O F ad triangulum E F K æquè altum eandem proportionem ha-
              <lb/>
            bet quàm O F ad F K, ſeu ad latus E H ei homologum) poſita autem fuit S
              <lb/>
            R media proportionalis inter O R, & </s>
            <s xml:id="echoid-s12716" xml:space="preserve">R E; </s>
            <s xml:id="echoid-s12717" xml:space="preserve">ergo triangulum E O F ad trian-
              <lb/>
            gulum E F K eſt vt S R ad R E: </s>
            <s xml:id="echoid-s12718" xml:space="preserve">eſtquè parallelogrammum E K æquale duplo
              <lb/>
            trianguli E F K; </s>
            <s xml:id="echoid-s12719" xml:space="preserve">ergo duplum trianguli E O F ad parallelogrammum E K ean-
              <lb/>
            dem proportionem habet, quàm S R ad R E; </s>
            <s xml:id="echoid-s12720" xml:space="preserve">Et quia rectangulum ſub O E,
              <lb/>
            & </s>
            <s xml:id="echoid-s12721" xml:space="preserve">ſub perpendiculari R F æquale eſt duplo trianguli E O F (cum habeant baſim
              <lb/>
            O E communem, & </s>
            <s xml:id="echoid-s12722" xml:space="preserve">eandem altitudinem perpendicularis R F); </s>
            <s xml:id="echoid-s12723" xml:space="preserve">igitur rectan-
              <lb/>
            gulum ſub O E, & </s>
            <s xml:id="echoid-s12724" xml:space="preserve">ſub R F ad parallelogrammum E K eandem proportionem
              <lb/>
            habebit, quàm S R ad R E: </s>
            <s xml:id="echoid-s12725" xml:space="preserve">ſed prius rectangulum ſub O E, & </s>
            <s xml:id="echoid-s12726" xml:space="preserve">ſub R F ad
              <lb/>
            rectangulum A E C eandem proportionem habebat, quàm S R ad R E: </s>
            <s xml:id="echoid-s12727" xml:space="preserve">ergo
              <lb/>
            idem rectangulum ſub O E, & </s>
            <s xml:id="echoid-s12728" xml:space="preserve">ſub R F ad parallelogrammum E K eandem
              <lb/>
            proportionem habet, quàm ad rectangulum A E C; </s>
            <s xml:id="echoid-s12729" xml:space="preserve">& </s>
            <s xml:id="echoid-s12730" xml:space="preserve">propterea </s>
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