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-div656" type="section" level="1" n="219">
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            <s xml:id="echoid-s7118" xml:space="preserve">
              <pb o="188" file="0226" n="226" rhead="Apollonij Pergæi"/>
            ad A E, vt O C ad C F, ſuntque anguli E, & </s>
            <s xml:id="echoid-s7119" xml:space="preserve">F æquales, vt dictum eſt. </s>
            <s xml:id="echoid-s7120" xml:space="preserve">Et
              <lb/>
            hoc erat propoſitum.</s>
            <s xml:id="echoid-s7121" xml:space="preserve"/>
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        <div xml:id="echoid-div659" type="section" level="1" n="220">
          <head xml:id="echoid-head277" xml:space="preserve">Notæ in Propoſit. XVII.</head>
          <p style="it">
            <s xml:id="echoid-s7122" xml:space="preserve">DEinde ſint ſectiones hyperbolicæ, aut ellipticæ, & </s>
            <s xml:id="echoid-s7123" xml:space="preserve">reliqua in ſuo
              <lb/>
              <note position="right" xlink:label="note-0226-01" xlink:href="note-0226-01a" xml:space="preserve">a</note>
            ſtatu, &</s>
            <s xml:id="echoid-s7124" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7125" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s7126" xml:space="preserve">Supponantur ſectiones hyperbolicæ, vel ellipticæ A B,
              <lb/>
            & </s>
            <s xml:id="echoid-s7127" xml:space="preserve">C D ſimiles inter ſe, ſcilicet figuræ axium V B, & </s>
            <s xml:id="echoid-s7128" xml:space="preserve">γ D ſint ſimiles inter ſe,
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            atque à verticibus A, & </s>
            <s xml:id="echoid-s7129" xml:space="preserve">C duarum diametrorum A M, & </s>
            <s xml:id="echoid-s7130" xml:space="preserve">C O ductæ ſint re-
              <lb/>
              <figure xlink:label="fig-0226-01" xlink:href="fig-0226-01a" number="254">
                <image file="0226-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0226-01"/>
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            ctæ lineæ contingentes A E, & </s>
            <s xml:id="echoid-s7131" xml:space="preserve">C F, efficientes cum axibus angulos A E B, & </s>
            <s xml:id="echoid-s7132" xml:space="preserve">
              <lb/>
            C F D æquales, ſintque H G, & </s>
            <s xml:id="echoid-s7133" xml:space="preserve">K I ordinatim ad diametros applicatæ, ſcili-
              <lb/>
            cet æquidiſtantes contingentibus verticalibus; </s>
            <s xml:id="echoid-s7134" xml:space="preserve">& </s>
            <s xml:id="echoid-s7135" xml:space="preserve">habeat abſciſſa M A ad portio-
              <lb/>
            nem contingentis A E eandem proportionem, quàm abſcißa O C habet ad por-
              <lb/>
            tionem contingentis C F; </s>
            <s xml:id="echoid-s7136" xml:space="preserve">Dico ſegmenta H A G, & </s>
            <s xml:id="echoid-s7137" xml:space="preserve">K C I ſimlia eſſe inter ſe.</s>
            <s xml:id="echoid-s7138" xml:space="preserve"/>
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            <s xml:id="echoid-s7139" xml:space="preserve">Ergo Y c C ſimile eſt V a A, &</s>
            <s xml:id="echoid-s7140" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7141" xml:space="preserve">Quoniam duæ ordinatim ad axes ap-
              <lb/>
              <note position="right" xlink:label="note-0226-02" xlink:href="note-0226-02a" xml:space="preserve">b</note>
            plicatæ A a, & </s>
            <s xml:id="echoid-s7142" xml:space="preserve">C c perpendiculares ſunt ad axes, erunt in triangulis A a E,
              <lb/>
            & </s>
            <s xml:id="echoid-s7143" xml:space="preserve">C c F duo anguli a, & </s>
            <s xml:id="echoid-s7144" xml:space="preserve">c recti: </s>
            <s xml:id="echoid-s7145" xml:space="preserve">atque ex hypotheſi duo reliqui anguli E, & </s>
            <s xml:id="echoid-s7146" xml:space="preserve">
              <lb/>
            F æquales quoque ſunt; </s>
            <s xml:id="echoid-s7147" xml:space="preserve">igitur tertius angulus a A E æqualis eſt tertio angulo c
              <lb/>
            C F, cumque in duobus triangulis V A E, atque γ C F ab eorum verticibus A,
              <lb/>
            & </s>
            <s xml:id="echoid-s7148" xml:space="preserve">C ducuntur ad baſes V E, & </s>
            <s xml:id="echoid-s7149" xml:space="preserve">γ F duæ rectæ lineæ A a, & </s>
            <s xml:id="echoid-s7150" xml:space="preserve">C c continentes
              <lb/>
            cum baſibus angulos æquales, nempe rectos, & </s>
            <s xml:id="echoid-s7151" xml:space="preserve">rectangulum V a E ad quadra-
              <lb/>
            tum a A eandem proportionem habet, quàm rectangulum γ c F ad quadratum
              <lb/>
            c C, vt in textu oſtenſum eſt: </s>
            <s xml:id="echoid-s7152" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s7153" xml:space="preserve">duo anguli a A E, & </s>
            <s xml:id="echoid-s7154" xml:space="preserve">c C F æquales oſten-
              <lb/>
              <note position="left" xlink:label="note-0226-03" xlink:href="note-0226-03a" xml:space="preserve">ex 37.
                <lb/>
              lib. 1.</note>
            ſi ſunt inter ſe; </s>
            <s xml:id="echoid-s7155" xml:space="preserve">igitur erunt triangula V A E, & </s>
            <s xml:id="echoid-s7156" xml:space="preserve">γ C F ſimilia inter ſe; </s>
            <s xml:id="echoid-s7157" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0226-04" xlink:href="note-0226-04a" xml:space="preserve">Propoſ. 6
                <lb/>
              præmiſſ.</note>
            angulus V æqualis eſt angulo γ, atque angulus E A V æqualis erit angulo F </s>
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