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-div652" type="section" level="1" n="217">
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        </div>
        <div xml:id="echoid-div654" type="section" level="1" n="218">
          <head xml:id="echoid-head275" xml:space="preserve">LEMMA VIII.</head>
          <p style="it">
            <s xml:id="echoid-s7044" xml:space="preserve">SI duo hyperbolica, aut elliptica ſegmenta A B C, D E F fuerint
              <lb/>
            ſimilia, quorum baſes A C, D F efficiant cum diametrorum ab-
              <lb/>
            ſciſsis B M, E O angulos æquales M, & </s>
            <s xml:id="echoid-s7045" xml:space="preserve">O; </s>
            <s xml:id="echoid-s7046" xml:space="preserve">ſintque eorum tranſ-
              <lb/>
            uerſa latera T B, Z E, recta vero B L, E Q. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">Dico figuras eorum;
              <lb/>
            </s>
            <s xml:id="echoid-s7048" xml:space="preserve">ſiue rectangula T B L, & </s>
            <s xml:id="echoid-s7049" xml:space="preserve">Z E Q ſimilia eße.</s>
            <s xml:id="echoid-s7050" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7051" xml:space="preserve">Secentur ſegmentorum abſciſſæ M B, O E proportionaliter in N, P, & </s>
            <s xml:id="echoid-s7052" xml:space="preserve">per
              <lb/>
            ea puncta ducantur ordinatim ad diametros applicatæ G N, I P æquidiſtantes
              <lb/>
            baſibus, efficientes abſciſſas B N, E P, coniunganturq; </s>
            <s xml:id="echoid-s7053" xml:space="preserve">duæ rectæ lineæ T L, Z
              <lb/>
            Q ſecantes rectas lineas N H, M V, P K, O S æquidiſtantes lateribus rectis B
              <lb/>
            L, E Q in punctis H, V,
              <lb/>
              <figure xlink:label="fig-0224-01" xlink:href="fig-0224-01a" number="251">
                <image file="0224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-01"/>
              </figure>
            K, S, atque à punctis H, & </s>
            <s xml:id="echoid-s7054" xml:space="preserve">
              <lb/>
            K ducantur rectæ lineæ H X,
              <lb/>
            K R parallelæ diametris occur-
              <lb/>
            rentes ipſis M V, O S in X,
              <lb/>
              <note position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s7055" xml:space="preserve">R. </s>
            <s xml:id="echoid-s7056" xml:space="preserve">Quoniam ſegmenta ſup-
              <lb/>
            ponuntur ſimilia erit A M ad
              <lb/>
            M B, vt D O ad O E, & </s>
            <s xml:id="echoid-s7057" xml:space="preserve">G
              <lb/>
            N ad N B erit vt I P ad P
              <lb/>
            E, atque quadratum A M, ſeu
              <lb/>
            ei æquale rectangulum B M V,
              <lb/>
              <note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">12. 13.
                <lb/>
              lib. 1.</note>
            ad quadratum M B eandem
              <lb/>
            proportionem habebit, quàm,
              <lb/>
              <note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve">Ibidem.</note>
            quadratum D O, ſeu ei æquale
              <lb/>
            rectangulum E O S ad quadratum O E; </s>
            <s xml:id="echoid-s7058" xml:space="preserve">ſed vt rectangulum B M V ad quadra-
              <lb/>
            tum M B ita eſt M V ad M B (cum M B ſit eorum altitudo communis) pari-
              <lb/>
            terque vt rectangulum E O S ad quadratum O E, ita eſt O S ad O E; </s>
            <s xml:id="echoid-s7059" xml:space="preserve">quare
              <lb/>
            M V ad M B eandem proportionem habebit, quàm O S ad O E; </s>
            <s xml:id="echoid-s7060" xml:space="preserve">non aliter oſten-
              <lb/>
            detur N H ad N B eandem proportionem
              <lb/>
              <figure xlink:label="fig-0224-02" xlink:href="fig-0224-02a" number="252">
                <image file="0224-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-02"/>
              </figure>
            habere, quàm P K ad P E: </s>
            <s xml:id="echoid-s7061" xml:space="preserve">erat autem
              <lb/>
              <note position="left" xlink:label="note-0224-04" xlink:href="note-0224-04a" xml:space="preserve">Lem. 1.
                <lb/>
              lib. 5.</note>
            M B ad B N vt O E ad E P; </s>
            <s xml:id="echoid-s7062" xml:space="preserve">ergo compa-
              <lb/>
            rando antecedentes, & </s>
            <s xml:id="echoid-s7063" xml:space="preserve">poſtea conſequentes
              <lb/>
            ad differentias terminorum erit B M ad M
              <lb/>
            N vt E O ad O P; </s>
            <s xml:id="echoid-s7064" xml:space="preserve">atque B N ad N M eã-
              <lb/>
            dem proportionem habebit, quàm E P ad P
              <lb/>
            O. </s>
            <s xml:id="echoid-s7065" xml:space="preserve">Quare ex æquali V M ad M N erit vt
              <lb/>
            S O ad O P, atque H N ad N M erit vt K
              <lb/>
            P ad P O; </s>
            <s xml:id="echoid-s7066" xml:space="preserve">& </s>
            <s xml:id="echoid-s7067" xml:space="preserve">differentia ipſarum V M & </s>
            <s xml:id="echoid-s7068" xml:space="preserve">
              <lb/>
            H N ideſt X V ad M N, ſeu ad X H ean-
              <lb/>
            dem proportionem habebit, quàm differentia ipſarum S O, & </s>
            <s xml:id="echoid-s7069" xml:space="preserve">K P, ideſt S R
              <lb/>
            ad O P, ſeu ad R K; </s>
            <s xml:id="echoid-s7070" xml:space="preserve">quapropter V X ad X H erit vt S R ad R K; </s>
            <s xml:id="echoid-s7071" xml:space="preserve">ſed quia
              <lb/>
            X V, L B inter ſe, nec non X H, & </s>
            <s xml:id="echoid-s7072" xml:space="preserve">B T ſunt parallelæ, atq; </s>
            <s xml:id="echoid-s7073" xml:space="preserve">etiam S R, Q E
              <lb/>
            inter ſe, nec nõ R K, & </s>
            <s xml:id="echoid-s7074" xml:space="preserve">E Z ſunt æquidiſtantes; </s>
            <s xml:id="echoid-s7075" xml:space="preserve">erunt triangula V X H, & </s>
            <s xml:id="echoid-s7076" xml:space="preserve">L </s>
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