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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          <pb o="202" file="0240" n="240" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s7576" xml:space="preserve">Sed tangens in V perueniens ad L O, &</s>
            <s xml:id="echoid-s7577" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7578" xml:space="preserve">Si enim ex punctis γ, V du-
              <lb/>
              <note position="right" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">f</note>
            cantur V e, & </s>
            <s xml:id="echoid-s7579" xml:space="preserve">γ f tangentes parabolas, & </s>
            <s xml:id="echoid-s7580" xml:space="preserve">producantur quouſque ſecent axes
              <lb/>
            in e, & </s>
            <s xml:id="echoid-s7581" xml:space="preserve">f eſſicientur duo parallelogramma V e O R, & </s>
            <s xml:id="echoid-s7582" xml:space="preserve">γ f Q S, in quibus tã-
              <lb/>
            gentes V e, & </s>
            <s xml:id="echoid-s7583" xml:space="preserve">γ f efficientur æquales ipſis O R, & </s>
            <s xml:id="echoid-s7584" xml:space="preserve">Q S: </s>
            <s xml:id="echoid-s7585" xml:space="preserve">& </s>
            <s xml:id="echoid-s7586" xml:space="preserve">propterea inuer-
              <lb/>
            tendo R V abſciſſa ad contingentem V e æqualem ipſi R O eandem proportionem
              <lb/>
            habebit, quàm abſcißa S γ ad contingentem γ f æqualem ipſi S Q, atque effi-
              <lb/>
            ciunt prædictæ contingentes cum axibus angulos e, f æquales ipſis O, & </s>
            <s xml:id="echoid-s7587" xml:space="preserve">Q æ-
              <lb/>
            qualibus propter parallelas; </s>
            <s xml:id="echoid-s7588" xml:space="preserve">igitur ſegmenta N V A, & </s>
            <s xml:id="echoid-s7589" xml:space="preserve">P γ D ſimilia ſunt in-
              <lb/>
              <note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">Prop. 16.
                <lb/>
              huius.</note>
            ter ſe.</s>
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          <figure number="273">
            <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0240-01"/>
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            <s xml:id="echoid-s7591" xml:space="preserve">Et pariter duo ſegmenta A B C, D E F, atque duo ſegmenta N B, P
              <lb/>
              <note position="right" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">g</note>
            E ſunt ſimilia inter ſe, & </s>
            <s xml:id="echoid-s7592" xml:space="preserve">ſimiliter poſita, &</s>
            <s xml:id="echoid-s7593" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7594" xml:space="preserve">Hoc manifeſtum eſt, ſi enim
              <lb/>
            coniungantur rectæ lineæ N C, & </s>
            <s xml:id="echoid-s7595" xml:space="preserve">P F, & </s>
            <s xml:id="echoid-s7596" xml:space="preserve">bifariam diuidantur, atque ducan-
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            tur diametri, &</s>
            <s xml:id="echoid-s7597" xml:space="preserve">c, vti fecimus in ſectione N A, oſtendetur ſimiliter (ex ea-
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            dem 16. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">propoſitione) ſegmenta N C, P F ſimilia eſſe inter ſe. </s>
            <s xml:id="echoid-s7599" xml:space="preserve">Non ſecus ſi
              <lb/>
            coniungantur rectæ lineæ N B, & </s>
            <s xml:id="echoid-s7600" xml:space="preserve">P E, & </s>
            <s xml:id="echoid-s7601" xml:space="preserve">bifariam diuidantur, atque ducan-
              <lb/>
            tur diametri, & </s>
            <s xml:id="echoid-s7602" xml:space="preserve">reliqua perficiantur, vt prius, oſtendentur codem modo, ſegmẽ-
              <lb/>
            ta N B, & </s>
            <s xml:id="echoid-s7603" xml:space="preserve">P E ſimilia inter ſe.</s>
            <s xml:id="echoid-s7604" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s7605" xml:space="preserve">Deinde ponamus ſegmentũ P d; </s>
            <s xml:id="echoid-s7606" xml:space="preserve">quia non abſcindunt illa duæ ordina-
              <lb/>
              <note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">h</note>
            tiones vnius axis (18. </s>
            <s xml:id="echoid-s7607" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s7608" xml:space="preserve">, & </s>
            <s xml:id="echoid-s7609" xml:space="preserve">hoc erat, &</s>
            <s xml:id="echoid-s7610" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7611" xml:space="preserve">Sed legendum puto vt in
              <lb/>
            textu apparet. </s>
            <s xml:id="echoid-s7612" xml:space="preserve">& </s>
            <s xml:id="echoid-s7613" xml:space="preserve">horum verborũ ſenſus erit; </s>
            <s xml:id="echoid-s7614" xml:space="preserve">fieri non poteſt, vt ſegmentũ p d ſit
              <lb/>
            ſimile ipſi N A, vel N B, propterea quod in ſectione P F ſegmenta P d vni tan-
              <lb/>
            tummodo portioni ſimile eſt (præter quàm in ellipſi), & </s>
            <s xml:id="echoid-s7615" xml:space="preserve">ambo intercipi debent à
              <lb/>
            duabus ordinatim applicatis ad axim E Q: </s>
            <s xml:id="echoid-s7616" xml:space="preserve">& </s>
            <s xml:id="echoid-s7617" xml:space="preserve">propterea ſegmenta P D, vel P E
              <lb/>
            non erunt ſimilia ipſi P d, & </s>
            <s xml:id="echoid-s7618" xml:space="preserve">quia N A oſtenſum eſt ſimile P D, pariterque N
              <lb/>
            B oſtenſum eſt ſimile P E; </s>
            <s xml:id="echoid-s7619" xml:space="preserve">igitur ſegmentum P d ſimile non eſt, neque N A,
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            neque ſegmento N B; </s>
            <s xml:id="echoid-s7620" xml:space="preserve">quod erat oſtendundum.</s>
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