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-div749" type="section" level="1" n="235">
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            <s xml:id="echoid-s8874" xml:space="preserve">
              <pb o="237" file="0275" n="275" rhead="Conicor. Lib. VI."/>
            ter poſita in eodem plano; </s>
            <s xml:id="echoid-s8875" xml:space="preserve">ſuntquè etiam duo circuli baſium in vno plano extenſi;
              <lb/>
            </s>
            <s xml:id="echoid-s8876" xml:space="preserve">igitur coni A B C, & </s>
            <s xml:id="echoid-s8877" xml:space="preserve">N L Q ſimiles ſunt inter ſe; </s>
            <s xml:id="echoid-s8878" xml:space="preserve">& </s>
            <s xml:id="echoid-s8879" xml:space="preserve">quoniam, vt latus
              <lb/>
              <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">Lem. 9.
                <lb/>
              huius.</note>
            tranſuerſum ad rectum ſectionis datæ X, ita eſt quadratum A d ad quadratum
              <lb/>
            radij G d, & </s>
            <s xml:id="echoid-s8880" xml:space="preserve">ita eſt latus tranſuerſum ad rectum ſectionis H I K; </s>
            <s xml:id="echoid-s8881" xml:space="preserve">pariterque
              <lb/>
            vt quadratum N b ad quadratum radij L b ita eſt latus tranſuerſum ad rectũ
              <lb/>
            hyperbolæ T V c; </s>
            <s xml:id="echoid-s8882" xml:space="preserve">Et quadrata axium ad quadrata radiorum baſeos eandem
              <lb/>
            proportionem habet ideo latus tranſuerſum ad rectum ſectionis H I K eandem
              <lb/>
            proportionem habebit, quàm latus tranſuerſum ad rectum alterius ſectionis T
              <lb/>
            V c, ſeu eandem, quàm babet latus tranſuerſum ad rectum datæ ſectionis X;
              <lb/>
            </s>
            <s xml:id="echoid-s8883" xml:space="preserve">atque diametri I V D, & </s>
            <s xml:id="echoid-s8884" xml:space="preserve">diameter ſectionis X æquè inclinantur ad baſes, vt
              <lb/>
            dictum eſt; </s>
            <s xml:id="echoid-s8885" xml:space="preserve">igitur duæ ſectiones H I K, & </s>
            <s xml:id="echoid-s8886" xml:space="preserve">T V c, nedum datæ hyperbolæ X; </s>
            <s xml:id="echoid-s8887" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0275-02" xlink:href="note-0275-02a" xml:space="preserve">Prop. 12.
                <lb/>
              huius.</note>
            ſed etiam inter ſe ſimiles ſunt. </s>
            <s xml:id="echoid-s8888" xml:space="preserve">Secundò quoniam duæ peripheriæ circulorum
              <lb/>
            baſium circa communem diametrum B C Q ſe ſe mutuo ſecant in duobus pun-
              <lb/>
            ctis R, & </s>
            <s xml:id="echoid-s8889" xml:space="preserve">a, quæ neceſſario cadunt inter duas circulorum diametros G O, S P
              <lb/>
            perpendiculares ad communem diametrum B C Q; </s>
            <s xml:id="echoid-s8890" xml:space="preserve">igitur ſuperficies conorum
              <lb/>
            viciſſim ſe ſecant ſemper inter duo triangula, per conorum axes A G O, & </s>
            <s xml:id="echoid-s8891" xml:space="preserve">N
              <lb/>
            S P, in reliquis autem locis ſeparatæ ſunt; </s>
            <s xml:id="echoid-s8892" xml:space="preserve">planum verò efficiens ſectiones H I
              <lb/>
            K, T V c cadit nõ inter axes A d, & </s>
            <s xml:id="echoid-s8893" xml:space="preserve">N b; </s>
            <s xml:id="echoid-s8894" xml:space="preserve">igitur duæ ſectiones H I K, & </s>
            <s xml:id="echoid-s8895" xml:space="preserve">T
              <lb/>
            V c exiſtentes in duabus conicis ſuperficiebus, non ſe ſecantibus, nunquàm con-
              <lb/>
            uenient, & </s>
            <s xml:id="echoid-s8896" xml:space="preserve">asymptoticæ erunt. </s>
            <s xml:id="echoid-s8897" xml:space="preserve">Tertiò quoniam recta linea N A M per verti-
              <lb/>
            ces conorum ducta parallela eſt communi baſi B Q triangulorum per axes, & </s>
            <s xml:id="echoid-s8898" xml:space="preserve">
              <lb/>
            ſecat diametrum communem D V I in M: </s>
            <s xml:id="echoid-s8899" xml:space="preserve">ergo (ſicuti oſtenſum eſt in prop. </s>
            <s xml:id="echoid-s8900" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s8901" xml:space="preserve">addit. </s>
            <s xml:id="echoid-s8902" xml:space="preserve">huius) erit punctum M centrum ſectionis H I K, atq; </s>
            <s xml:id="echoid-s8903" xml:space="preserve">centrum alterius
              <lb/>
            ſectionis T V c; </s>
            <s xml:id="echoid-s8904" xml:space="preserve">ergo duæ ſectiones H I K, & </s>
            <s xml:id="echoid-s8905" xml:space="preserve">T V c ſimiles ſunt inter ſe,
              <lb/>
            concentricæ, & </s>
            <s xml:id="echoid-s8906" xml:space="preserve">ſimiliter poſitæ circa communem diametrum D V I; </s>
            <s xml:id="echoid-s8907" xml:space="preserve">igitur ſe-
              <lb/>
              <note position="right" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">Propoſ. 9.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ctionum interualla ſemper magis, ac magis in infinitum minuuntur, & </s>
            <s xml:id="echoid-s8908" xml:space="preserve">repe-
              <lb/>
            riri poßunt minora quolibet interuallo dato. </s>
            <s xml:id="echoid-s8909" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s8910" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div759" type="section" level="1" n="236">
          <head xml:id="echoid-head297" xml:space="preserve">SECTIO DECIMA
            <lb/>
          Continens Propoſit. XXVI. XXVII.
            <lb/>
          & XXVIII.
            <lb/>
          PROPOSITIO XXVI.</head>
          <p>
            <s xml:id="echoid-s8911" xml:space="preserve">IN cono recto, cuius triangulum per axim ſit A B C reperi-
              <lb/>
            re ſectionem datæ parabolæ D E æqualem, cuius axis E F,
              <lb/>
            & </s>
            <s xml:id="echoid-s8912" xml:space="preserve">erectum E G.</s>
            <s xml:id="echoid-s8913" xml:space="preserve"/>
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