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-div862" type="section" level="1" n="263">
          <p>
            <s xml:id="echoid-s10274" xml:space="preserve">
              <pb o="277" file="0315" n="315" rhead="Conicor. Lib. VII."/>
            A F ad A C, & </s>
            <s xml:id="echoid-s10275" xml:space="preserve">vt A G ad G C; </s>
            <s xml:id="echoid-s10276" xml:space="preserve">ergo H E ad E C eſt vt A G ad G
              <lb/>
            C; </s>
            <s xml:id="echoid-s10277" xml:space="preserve">& </s>
            <s xml:id="echoid-s10278" xml:space="preserve">componendo in hyperbolis, & </s>
            <s xml:id="echoid-s10279" xml:space="preserve">diuidendo in ellipſibus, deinde
              <lb/>
              <note position="left" xlink:label="note-0315-01" xlink:href="note-0315-01a" xml:space="preserve">b</note>
            comparando homologorum differentias in duabus figuris prioribus, & </s>
            <s xml:id="echoid-s10280" xml:space="preserve">
              <lb/>
            ſummas homologorum in reliquis, fiet A H ad G E, vt C A ad C G;
              <lb/>
            </s>
            <s xml:id="echoid-s10281" xml:space="preserve">ergo A H in A E; </s>
            <s xml:id="echoid-s10282" xml:space="preserve">nempe quadratum A B ad G E in A E eſt vt C A
              <lb/>
            inclinatus, ſiue tranſuerſus ad C G præſectam. </s>
            <s xml:id="echoid-s10283" xml:space="preserve">Quod fuerat propoſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s10284" xml:space="preserve"/>
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        <div xml:id="echoid-div865" type="section" level="1" n="264">
          <head xml:id="echoid-head332" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s10285" xml:space="preserve">SI hyperbolen, aut ellipſin A B tangat recta linea I M in I,
              <lb/>
              <note position="left" xlink:label="note-0315-02" xlink:href="note-0315-02a" xml:space="preserve">a</note>
            & </s>
            <s xml:id="echoid-s10286" xml:space="preserve">occurrat axi A C in M; </s>
            <s xml:id="echoid-s10287" xml:space="preserve">vtique ipſius I M quadratum
              <lb/>
            ad quadratum ſemidiametri ND coniugatæ ipſi I L habebit eã-
              <lb/>
            dem proportionem, quàm axis contenta M S ad eius inuerſam
              <lb/>
            S D.</s>
            <s xml:id="echoid-s10288" xml:space="preserve"/>
          </p>
          <figure number="364">
            <image file="0315-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0315-01"/>
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          <p>
            <s xml:id="echoid-s10289" xml:space="preserve">Educantur A Q, M R perpendiculares ad axim vſque ad I L, ponatur-
              <lb/>
            que linea P, quæ ad I M eandem proportionem habeat, quàm K I ad
              <lb/>
            Q I, ſeu eandem, quàm habet M I ad I R; </s>
            <s xml:id="echoid-s10290" xml:space="preserve">Ergo P eſt ſemiſſis erecti
              <lb/>
              <note position="right" xlink:label="note-0315-03" xlink:href="note-0315-03a" xml:space="preserve">50. lib. 1.</note>
            diametri I L (52. </s>
            <s xml:id="echoid-s10291" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s10292" xml:space="preserve">atque D N dimidium coniugatæ diametri N O
              <lb/>
            poterit P in I D, atque I M poterit P in I R; </s>
            <s xml:id="echoid-s10293" xml:space="preserve">& </s>
            <s xml:id="echoid-s10294" xml:space="preserve">ideo I R ad I D,
              <lb/>
            nempe M S contenta ad S D inuerſam eandem proportionem habet, quã
              <lb/>
            quadratum tangentis I M ad quadratum N D ſemiſſis coniugatæ ipſius I
              <lb/>
            L. </s>
            <s xml:id="echoid-s10295" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s10296" xml:space="preserve"/>
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