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="191" file="0229" n="229" rhead="Conicor. Lib. VI."/>
            ad A M eandem
              <lb/>
              <figure xlink:label="fig-0229-01" xlink:href="fig-0229-01a" number="257">
                <image file="0229-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0229-01"/>
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            proportionem ha-
              <lb/>
            bebit, quàm X O
              <lb/>
            C ad quadratum
              <lb/>
            O C, ſeu eandẽ,
              <lb/>
            quàm habet X O
              <lb/>
            ad C O, & </s>
            <s xml:id="echoid-s7253" xml:space="preserve">com-
              <lb/>
            parando conſequẽ
              <lb/>
            tes ad differẽtias
              <lb/>
            terminorum M A
              <lb/>
            ad A T eandem
              <lb/>
            proportionem ha-
              <lb/>
            bebit, quàm O C
              <lb/>
            ad C X: </s>
            <s xml:id="echoid-s7254" xml:space="preserve">erat autẽ
              <lb/>
            prius T A ad A
              <lb/>
            E, vt X C ad C F; </s>
            <s xml:id="echoid-s7255" xml:space="preserve">igitur ex æquali M A ad A E erit, vt O C ad C F, & </s>
            <s xml:id="echoid-s7256" xml:space="preserve">fue-
              <lb/>
            runt oſtenſi anguli E, & </s>
            <s xml:id="echoid-s7257" xml:space="preserve">F æquales. </s>
            <s xml:id="echoid-s7258" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7259" xml:space="preserve"/>
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        <div xml:id="echoid-div665" type="section" level="1" n="221">
          <head xml:id="echoid-head278" xml:space="preserve">SECTIO SEPTIMA</head>
          <head xml:id="echoid-head279" xml:space="preserve">Continens Propoſit. XVIII. & XIX.</head>
          <p>
            <s xml:id="echoid-s7260" xml:space="preserve">CViuslibet ſectionis A B C duo ſegmenta C F, A E ca-
              <lb/>
            dentia inter duas ordinationes A C, E F ad vtraſque par-
              <lb/>
            tes axis B V ſunt inter ſe ſimilia, & </s>
            <s xml:id="echoid-s7261" xml:space="preserve">ſimiliter poſita, nec ſunt
              <lb/>
            ſimilia alteri ſegmento (niſi
              <lb/>
              <figure xlink:label="fig-0229-02" xlink:href="fig-0229-02a" number="258">
                <image file="0229-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0229-02"/>
              </figure>
            in ellipſi, in qua quatuor ſeg
              <lb/>
            menta memorata in propo-
              <lb/>
            ſitione 8. </s>
            <s xml:id="echoid-s7262" xml:space="preserve">ſunt æqualia, ſimi-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s7263" xml:space="preserve">ſimiliter poſita, quæ al-
              <lb/>
            teri ſegmẽto ſimilia nõ ſunt.</s>
            <s xml:id="echoid-s7264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7265" xml:space="preserve">Quoniam vnumquodque eo-
              <lb/>
              <note position="left" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">a</note>
            rum alteri congruit, nec non cõ-
              <lb/>
            gruunt duo ſegmenta GI, K H
              <lb/>
            in ellipſi (7. </s>
            <s xml:id="echoid-s7266" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7267" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7268" xml:space="preserve">at non ſunt
              <lb/>
            ſimilia alteri ſegmento: </s>
            <s xml:id="echoid-s7269" xml:space="preserve">ſi enim
              <lb/>
            hoc fieri poteſt, ſit ſegmentum
              <lb/>
            L M ſimile ſegmento F C. </s>
            <s xml:id="echoid-s7270" xml:space="preserve">Et
              <lb/>
            quia F C congruit A E. </s>
            <s xml:id="echoid-s7271" xml:space="preserve">Ergo
              <lb/>
            duo ſegmenta L M, A E ſunt
              <lb/>
            ſimilia, producamus A E, L M
              <lb/>
            quouſque occurrant axi in N,
              <lb/>
              <note position="left" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">b</note>
            O, erit angulus N æqualis O (vti
              <lb/>
            demonſtrauimus in 16. </s>
            <s xml:id="echoid-s7272" xml:space="preserve">& </s>
            <s xml:id="echoid-s7273" xml:space="preserve">17.</s>
            <s xml:id="echoid-s7274" xml:space="preserve"/>
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