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-div668" type="section" level="1" n="222">
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            <s xml:id="echoid-s7313" xml:space="preserve">
              <pb o="193" file="0231" n="231" rhead="Conicor. Lib. VI."/>
            gulos æquales; </s>
            <s xml:id="echoid-s7314" xml:space="preserve">ij verò anguli æquales ſunt angulis O, & </s>
            <s xml:id="echoid-s7315" xml:space="preserve">N, cum baſes L M, & </s>
            <s xml:id="echoid-s7316" xml:space="preserve">
              <lb/>
            A E parallelæ ſint contingentibus verticalibus eorundem ſegmentorum; </s>
            <s xml:id="echoid-s7317" xml:space="preserve">igitur an-
              <lb/>
            guli L O B, & </s>
            <s xml:id="echoid-s7318" xml:space="preserve">A N B æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s7319" xml:space="preserve">& </s>
            <s xml:id="echoid-s7320" xml:space="preserve">propterea duorum ſegmentorũ
              <lb/>
            baſes L M, & </s>
            <s xml:id="echoid-s7321" xml:space="preserve">A E parallelæ ſunt inter ſe.</s>
            <s xml:id="echoid-s7322" xml:space="preserve"/>
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        <div xml:id="echoid-div671" type="section" level="1" n="223">
          <head xml:id="echoid-head281" xml:space="preserve">SECTIO OCTAVA</head>
          <head xml:id="echoid-head282" xml:space="preserve">Continens Propoſit. XX. & XXI.
            <lb/>
          Apollonij.</head>
          <head xml:id="echoid-head283" xml:space="preserve">PROPOSITIO XX.</head>
          <p>
            <s xml:id="echoid-s7323" xml:space="preserve">SI in quibuslibet ſimilibus coniſectionibus A B C, & </s>
            <s xml:id="echoid-s7324" xml:space="preserve">D E F
              <lb/>
              <note position="left" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">a</note>
            ductæ fuerint ad axes B O, E Q ordinatim applicatæ A C,
              <lb/>
            D F, N L, P M, quarum illæ, quæ ad eaſdem partes verticum
              <lb/>
            B, & </s>
            <s xml:id="echoid-s7325" xml:space="preserve">E ducuntur efficiant abſciſſas erectis proportionales, ſci-
              <lb/>
            licet I B ad B G ſit, vt K E ad E H, nec non L B ad B G, vt
              <lb/>
            M E ad E H: </s>
            <s xml:id="echoid-s7326" xml:space="preserve">Dico ſegmenta facta ab ordinatis ſimiliter poſi-
              <lb/>
            tis eſſe inter ſe ſimilia, ac ſimiliter poſita, ſcilicet N A ipſi P D,
              <lb/>
            atque A B ipſi D E, nec non N B ipſi P E.</s>
            <s xml:id="echoid-s7327" xml:space="preserve"/>
          </p>
          <figure number="261">
            <image file="0231-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0231-01"/>
          </figure>
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            <s xml:id="echoid-s7328" xml:space="preserve">Sintque primò ſectiones parabolæ; </s>
            <s xml:id="echoid-s7329" xml:space="preserve">& </s>
            <s xml:id="echoid-s7330" xml:space="preserve">educamus N A ad B L in O, & </s>
            <s xml:id="echoid-s7331" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">b</note>
            P D ad M E in Q. </s>
            <s xml:id="echoid-s7332" xml:space="preserve">Et quia G B ad B I eſt, vt H E ad E K, & </s>
            <s xml:id="echoid-s7333" xml:space="preserve">B L ad
              <lb/>
            B G eſt vt M E ad E H; </s>
            <s xml:id="echoid-s7334" xml:space="preserve">ergo L B ad B I, nempe L N ad I A potentia
              <lb/>
            (19. </s>
            <s xml:id="echoid-s7335" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7336" xml:space="preserve">nempe L N ad O I eandem proportionem habet, quàm M E
              <lb/>
              <note position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">20. lib. 1.</note>
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