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-div711" type="section" level="1" n="234">
          <p style="it">
            <s xml:id="echoid-s7871" xml:space="preserve">
              <pb o="211" file="0249" n="249" rhead="Conicor. Lib. VI."/>
            inter E, & </s>
            <s xml:id="echoid-s7872" xml:space="preserve">I exiſtit; </s>
            <s xml:id="echoid-s7873" xml:space="preserve">ergo recta linea I K poſita intra conicũ ſegmentum E K I
              <lb/>
            ſupra eius baſim E I cadit; </s>
            <s xml:id="echoid-s7874" xml:space="preserve">& </s>
            <s xml:id="echoid-s7875" xml:space="preserve">ideo ei parallela E O cadit infra eandem ſeg-
              <lb/>
            menti conici baſim E I, & </s>
            <s xml:id="echoid-s7876" xml:space="preserve">propterea occurret ipſi H L intra coniſectionem, & </s>
            <s xml:id="echoid-s7877" xml:space="preserve">
              <lb/>
            infra punctum L in ſectione poſitum, vt in O; </s>
            <s xml:id="echoid-s7878" xml:space="preserve">& </s>
            <s xml:id="echoid-s7879" xml:space="preserve">ideo O S maior erit, quàm,
              <lb/>
            S L. </s>
            <s xml:id="echoid-s7880" xml:space="preserve">Et quoniam S E, & </s>
            <s xml:id="echoid-s7881" xml:space="preserve">R K ſunt inter ſe parallelæ ( quia eidem A C æqui-
              <lb/>
            diſtant) pariterque E O, & </s>
            <s xml:id="echoid-s7882" xml:space="preserve">K I factæ ſunt parallelæ, atque S O, & </s>
            <s xml:id="echoid-s7883" xml:space="preserve">R I (ex
              <lb/>
            hypotheſi) æquidiſtantes erant; </s>
            <s xml:id="echoid-s7884" xml:space="preserve">igitur duo triangula E S O, & </s>
            <s xml:id="echoid-s7885" xml:space="preserve">K R I ſimilia
              <lb/>
            ſunt inter ſe, & </s>
            <s xml:id="echoid-s7886" xml:space="preserve">eorũ latera homologa E S, & </s>
            <s xml:id="echoid-s7887" xml:space="preserve">K R æqualia ſunt inter ſe (quiæ
              <lb/>
            in parallelogrãmis C S, & </s>
            <s xml:id="echoid-s7888" xml:space="preserve">G R latera E S, R K æqualia ſunt oppoſitis C H, G
              <lb/>
            F inter ſe æqualibus, ex hypotheſi) igitur reliqua latera homologa S O, & </s>
            <s xml:id="echoid-s7889" xml:space="preserve">R I
              <lb/>
            æqualia ſunt inter ſe; </s>
            <s xml:id="echoid-s7890" xml:space="preserve">& </s>
            <s xml:id="echoid-s7891" xml:space="preserve">propterea R I differentia æquidiſtantium F I, G K ad
              <lb/>
            partes centri A, & </s>
            <s xml:id="echoid-s7892" xml:space="preserve">asymptoti A B vlterius tendentium, maior erit, quàm S L,
              <lb/>
            quæ portio eſt ipſius S O, & </s>
            <s xml:id="echoid-s7893" xml:space="preserve">eſt differentia æquidiſtantium H L, & </s>
            <s xml:id="echoid-s7894" xml:space="preserve">C E alte-
              <lb/>
            rius ſegmenti H C. </s>
            <s xml:id="echoid-s7895" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7896" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7897" xml:space="preserve">Ex conſtructione, & </s>
            <s xml:id="echoid-s7898" xml:space="preserve">demonſtratione huius propoſitionis colligitur, quod ſi à
              <lb/>
              <note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">COROL
                <lb/>
              LAR.</note>
            duobus punctis eiuſdem asymptoti A C ad hyperbolen ducantur duæ rectæ lineæ
              <lb/>
            inter ſe parallelæ; </s>
            <s xml:id="echoid-s7899" xml:space="preserve">illa, quæ ad partes centri A, & </s>
            <s xml:id="echoid-s7900" xml:space="preserve">asymptoti A B vlterius ten-
              <lb/>
            dit, maior eſt reliqua. </s>
            <s xml:id="echoid-s7901" xml:space="preserve">Nam recta linea K R, asymptoto A C parallela cadit ex-
              <lb/>
            tra ſectionem, & </s>
            <s xml:id="echoid-s7902" xml:space="preserve">ideo ſecat interceptam parallelam F I, quæ erit maior, quàm
              <lb/>
            F R, ſeu G K; </s>
            <s xml:id="echoid-s7903" xml:space="preserve">igitur F I ad partes centri A vlterius tendens maior eſt quali-
              <lb/>
            bet alia parallela G K ad partes oppoſitas tendente. </s>
            <s xml:id="echoid-s7904" xml:space="preserve">Eadem ratione F I maior
              <lb/>
            erit quàm H L, & </s>
            <s xml:id="echoid-s7905" xml:space="preserve">H L maior, quàm C E. </s>
            <s xml:id="echoid-s7906" xml:space="preserve">Vnde patet propoſitum.</s>
            <s xml:id="echoid-s7907" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7908" xml:space="preserve">Si fuerint duæ hyperbolæ A B, & </s>
            <s xml:id="echoid-s7909" xml:space="preserve">D E æquales, & </s>
            <s xml:id="echoid-s7910" xml:space="preserve">ſimiles ad eaſ-
              <lb/>
              <note position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">PROP.3.
                <lb/>
              Addit.</note>
            dem partes cauæ, quarum centra H, & </s>
            <s xml:id="echoid-s7911" xml:space="preserve">L, & </s>
            <s xml:id="echoid-s7912" xml:space="preserve">aſymptoti G H I, & </s>
            <s xml:id="echoid-s7913" xml:space="preserve">
              <lb/>
            K L M, nec non axes A H, & </s>
            <s xml:id="echoid-s7914" xml:space="preserve">D L ſint parallelæ inter ſe, & </s>
            <s xml:id="echoid-s7915" xml:space="preserve">rectæ
              <lb/>
            lineæ B E, & </s>
            <s xml:id="echoid-s7916" xml:space="preserve">C F ab hyperbolis interceptæ parallelæ fuerint rectæ H
              <lb/>
            L centra coniungenti; </s>
            <s xml:id="echoid-s7917" xml:space="preserve">erunt B E, & </s>
            <s xml:id="echoid-s7918" xml:space="preserve">C F æquales ipſi H L, & </s>
            <s xml:id="echoid-s7919" xml:space="preserve">in-
              <lb/>
            ter ſe.</s>
            <s xml:id="echoid-s7920" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7921" xml:space="preserve">Si autem parallelæ ſint alicui rectæ lineæ L f diuidenti angulum K L
              <lb/>
              <figure xlink:label="fig-0249-01" xlink:href="fig-0249-01a" number="287">
                <image file="0249-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0249-01"/>
                <caption xml:id="echoid-caption2" xml:space="preserve">Dd 2</caption>
              </figure>
            H contentum à recta linea L H cen- tra coniungente, & </s>
            <s xml:id="echoid-s7922" xml:space="preserve">interiore aſympto- to L K, in qua B E, & </s>
            <s xml:id="echoid-s7923" xml:space="preserve">C F poſitæ ſunt: </s>
            <s xml:id="echoid-s7924" xml:space="preserve">Dico B E vlterius tendentem.</s>
            <s xml:id="echoid-s7925" xml:space="preserve"> ad partes reliquæ aſymptoti L M ma- iorem eſſe, quàm C F.</s>
            <s xml:id="echoid-s7926" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7927" xml:space="preserve">Si vero B E, & </s>
            <s xml:id="echoid-s7928" xml:space="preserve">C F parallelæ
              <lb/>
            ſint alicui rectæ lineæ H g diuidenti
              <lb/>
            angulum L H G à recta linea L H
              <lb/>
            centra coniungente, & </s>
            <s xml:id="echoid-s7929" xml:space="preserve">eadem aſym-
              <lb/>
            ptoto H G contentum: </s>
            <s xml:id="echoid-s7930" xml:space="preserve">Dico B E vl-
              <lb/>
            terius tendentẽ ad partes reliquæ aſym-
              <lb/>
            ptoti H I minorem eſſe, quàm C F.</s>
            <s xml:id="echoid-s7931" xml:space="preserve"/>
          </p>
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    </echo>
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