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="187" file="0225" n="225" rhead="Conicor. Lib. VI."/>
            T ſimilia, pariterque triangula S R K, & </s>
            <s xml:id="echoid-s7077" xml:space="preserve">Q E Z inter ſe ſimilia; </s>
            <s xml:id="echoid-s7078" xml:space="preserve">ideoque erit
              <lb/>
            L B ad B T vt V X ad X H, pariterque Q E ad E Z erit vt S R ad R K;
              <lb/>
            </s>
            <s xml:id="echoid-s7079" xml:space="preserve">erat autem prius V X ad X H, vt S R ad R K; </s>
            <s xml:id="echoid-s7080" xml:space="preserve">igitur L B ad B T eandem
              <lb/>
            proportionem habebit, quàm Q E ad E Z; </s>
            <s xml:id="echoid-s7081" xml:space="preserve">& </s>
            <s xml:id="echoid-s7082" xml:space="preserve">propterea circa roctos angulos B,
              <lb/>
            E, figuræ ſectionum ſimiles erunt inter ſe. </s>
            <s xml:id="echoid-s7083" xml:space="preserve">Quod erat oſtendendum.</s>
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        <div xml:id="echoid-div656" type="section" level="1" n="219">
          <head xml:id="echoid-head276" xml:space="preserve">Notæ in Propoſit. XVI.</head>
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            <s xml:id="echoid-s7085" xml:space="preserve">ERgo M A ad A P eſt vt O C ad C Q, & </s>
            <s xml:id="echoid-s7086" xml:space="preserve">angulus O æqualis eſt M,
              <lb/>
              <note position="left" xlink:label="note-0225-01" xlink:href="note-0225-01a" xml:space="preserve">a</note>
            oſtendetur (vt diximus in 11. </s>
            <s xml:id="echoid-s7087" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7088" xml:space="preserve">quod, &</s>
            <s xml:id="echoid-s7089" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7090" xml:space="preserve">Sequitur enim ex
              <lb/>
            æqualitate ordinata, quod M A ad A P eandem proportionem habet, quàm O C
              <lb/>
            ad C Q, cumque ſint duo ſegmenta parabolica H A G, & </s>
            <s xml:id="echoid-s7091" xml:space="preserve">K C I, quorũ diame-
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            tri A M, & </s>
            <s xml:id="echoid-s7092" xml:space="preserve">C O efficiunt cum baſibus G H, & </s>
            <s xml:id="echoid-s7093" xml:space="preserve">K I angulos M, & </s>
            <s xml:id="echoid-s7094" xml:space="preserve">O æquales
              <lb/>
            inter ſe (cum ſint æquales angulis R A L, & </s>
            <s xml:id="echoid-s7095" xml:space="preserve">S C N æqualibus à contingentibus
              <lb/>
              <figure xlink:label="fig-0225-01" xlink:href="fig-0225-01a" number="253">
                <image file="0225-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0225-01"/>
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            verticalibus parallelis baſibus, & </s>
            <s xml:id="echoid-s7096" xml:space="preserve">à diametris contentis) atque abſcißa M A ad
              <lb/>
            latus rectum A P eandem proportionem habet, quàm altera abſcißa O C ad C Q
              <lb/>
            latus rectum alterius ſectionis; </s>
            <s xml:id="echoid-s7097" xml:space="preserve">igitur duo ſegmenta H A G, & </s>
            <s xml:id="echoid-s7098" xml:space="preserve">K C I ſimilia
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              <note position="right" xlink:label="note-0225-02" xlink:href="note-0225-02a" xml:space="preserve">Lem. 6.
                <lb/>
              huius.</note>
            ſunt inter ſe.</s>
            <s xml:id="echoid-s7099" xml:space="preserve"/>
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            <s xml:id="echoid-s7100" xml:space="preserve">Et quia G M poteſt A P in A M, & </s>
            <s xml:id="echoid-s7101" xml:space="preserve">ſimiliter I O poteſt C Q in C
              <lb/>
              <note position="left" xlink:label="note-0225-03" xlink:href="note-0225-03a" xml:space="preserve">b</note>
            O; </s>
            <s xml:id="echoid-s7102" xml:space="preserve">ergo P A ad G M eſt, vt C Q ad I O, & </s>
            <s xml:id="echoid-s7103" xml:space="preserve">G M ad M A eſt, vt I O
              <lb/>
            ad O C; </s>
            <s xml:id="echoid-s7104" xml:space="preserve">quia duo ſegmenta ſunt ſimilia, & </s>
            <s xml:id="echoid-s7105" xml:space="preserve">E A ad A M, eſt vt F C ad
              <lb/>
            C O; </s>
            <s xml:id="echoid-s7106" xml:space="preserve">&</s>
            <s xml:id="echoid-s7107" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7108" xml:space="preserve">Senſus huius textus confuſi, talis eſt. </s>
            <s xml:id="echoid-s7109" xml:space="preserve">Quia ſegmenta H A G, & </s>
            <s xml:id="echoid-s7110" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0225-04" xlink:href="note-0225-04a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            K C I ſimilia ſupponuntur erit A M ad M G, vt C O ad O I, & </s>
            <s xml:id="echoid-s7111" xml:space="preserve">quadratum
              <lb/>
            A M ad quadratum M G erit vt quadratum C O ad quadratum O I; </s>
            <s xml:id="echoid-s7112" xml:space="preserve">eſt verò
              <lb/>
              <note position="right" xlink:label="note-0225-05" xlink:href="note-0225-05a" xml:space="preserve">11. lib. 1.</note>
            rectangulum P A M æquale quadrato G M; </s>
            <s xml:id="echoid-s7113" xml:space="preserve">pariterque rectangulum Q C O eſt
              <lb/>
            æquale quadrato I O; </s>
            <s xml:id="echoid-s7114" xml:space="preserve">igitur quadratum A M ad rectangulum P A M eandem
              <lb/>
            proportionem habet, quàm quadratum C O ad rectangulum Q C O; </s>
            <s xml:id="echoid-s7115" xml:space="preserve">& </s>
            <s xml:id="echoid-s7116" xml:space="preserve">propte-
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            rea M A ad A P eandem proportionem habebit, quàm C O ad C Q; </s>
            <s xml:id="echoid-s7117" xml:space="preserve">ſed prius
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            oſt enſa fuit P A ad A E, vt Q C ad C F; </s>
            <s xml:id="echoid-s7118" xml:space="preserve">igitur ex æquali ordinata erit M </s>
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