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-div533" type="section" level="1" n="174">
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              <pb o="144" file="0182" n="182" rhead="Apollonij Pergæi"/>
            ad D K, & </s>
            <s xml:id="echoid-s5659" xml:space="preserve">propterea etiam conſequentes A I, & </s>
            <s xml:id="echoid-s5660" xml:space="preserve">D K æquales ſunt inter ſe,
              <lb/>
            & </s>
            <s xml:id="echoid-s5661" xml:space="preserve">compræhendunt angulos rectos A, & </s>
            <s xml:id="echoid-s5662" xml:space="preserve">D; </s>
            <s xml:id="echoid-s5663" xml:space="preserve">ergo ſiguræ G A I, & </s>
            <s xml:id="echoid-s5664" xml:space="preserve">H D K ſimi-
              <lb/>
            les ſunt inter ſe, & </s>
            <s xml:id="echoid-s5665" xml:space="preserve">æquales.</s>
            <s xml:id="echoid-s5666" xml:space="preserve"/>
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        <div xml:id="echoid-div538" type="section" level="1" n="175">
          <head xml:id="echoid-head229" xml:space="preserve">Notæ in Propoſit. IV.</head>
          <p style="it">
            <s xml:id="echoid-s5667" xml:space="preserve">I Am ergo demonſtratum eſt, quod duo
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="186">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0182-01"/>
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            vertices tympani ſunt ſimiles, & </s>
            <s xml:id="echoid-s5668" xml:space="preserve">æqua-
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            les, & </s>
            <s xml:id="echoid-s5669" xml:space="preserve">inclinatus communis inter vtrum-
              <lb/>
            que verticem (16. </s>
            <s xml:id="echoid-s5670" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5671" xml:space="preserve">ergo figura eſt
              <lb/>
            communis, &</s>
            <s xml:id="echoid-s5672" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5673" xml:space="preserve">Hæc propoſitio eſt veluti Co-
              <lb/>
            rollarium primæ partis ſecundæ propoſitionis in
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            qua oſtenſum eſt, quod ſi duæ hyperbolæ habue-
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            rint axium ſiguras æquales, & </s>
            <s xml:id="echoid-s5674" xml:space="preserve">ſimiles, erunt
              <lb/>
            quoque ſectiones ipſæ æquales, & </s>
            <s xml:id="echoid-s5675" xml:space="preserve">congruentes;
              <lb/>
            </s>
            <s xml:id="echoid-s5676" xml:space="preserve">habent verò ſectiones oppoſitæ A B, & </s>
            <s xml:id="echoid-s5677" xml:space="preserve">D E
              <lb/>
            (quæ vocantur Vertices Tympani ab Arabico
              <lb/>
            interprete) figuras D A H, & </s>
            <s xml:id="echoid-s5678" xml:space="preserve">A D I axis D
              <lb/>
            A æquales, & </s>
            <s xml:id="echoid-s5679" xml:space="preserve">ſimiles (vt in 14. </s>
            <s xml:id="echoid-s5680" xml:space="preserve">primi libri
              <lb/>
            demonſtrauit Apollonius); </s>
            <s xml:id="echoid-s5681" xml:space="preserve">ergo ſectiones oppo-
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            ſitæ æquales erunt inter ſe, & </s>
            <s xml:id="echoid-s5682" xml:space="preserve">congruentes.</s>
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        <div xml:id="echoid-div540" type="section" level="1" n="176">
          <head xml:id="echoid-head230" xml:space="preserve">Notæ in Propoſit. X.</head>
          <p style="it">
            <s xml:id="echoid-s5684" xml:space="preserve">SImiliter conſtat, quod ſi potentes contineant cum ſuis abſciſſis angu-
              <lb/>
            los equales obliquos, iudicium eſt, quod memorauimus in ſectioni-
              <lb/>
              <note position="right" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">a</note>
            bus, &</s>
            <s xml:id="echoid-s5685" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5686" xml:space="preserve">Senſus huius propoſitionis talis eſt. </s>
            <s xml:id="echoid-s5687" xml:space="preserve">In duabus ſectionibus conicis, ſi
              <lb/>
            cum earum diametris ordinatim applicatæ contineant angulos æquales, non re-
              <lb/>
            ctos, & </s>
            <s xml:id="echoid-s5688" xml:space="preserve">earum latera recta ſint æqualia in parabolis, in reliquis verò ſectioni-
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              <figure xlink:label="fig-0182-02" xlink:href="fig-0182-02a" number="187">
                <image file="0182-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0182-02"/>
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            bus latera recta, & </s>
            <s xml:id="echoid-s5689" xml:space="preserve">tran-
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            ſuerſa æqualia, itaut figuræ
              <lb/>
            ipſæ æquales ſint; </s>
            <s xml:id="echoid-s5690" xml:space="preserve">erunt ſe-
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            ctiones ipſæ inter ſe æqua-
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            les: </s>
            <s xml:id="echoid-s5691" xml:space="preserve">& </s>
            <s xml:id="echoid-s5692" xml:space="preserve">è conuer ſo, ſi ſectio-
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            nes æquales fuerint, habe-
              <lb/>
            bunt latera æqualia earum
              <lb/>
            diametrorum, cum quibus
              <lb/>
            ordinatim applicatæ angulos
              <lb/>
            æquales, non rectos continent.</s>
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            <s xml:id="echoid-s5694" xml:space="preserve">Demonſtrationes non apponuntur ab Apollonio, quia ijſdem verbis omnino in
              <lb/>
            eiſdem figuris ab ſolui poßunt. </s>
            <s xml:id="echoid-s5695" xml:space="preserve">Sint enim primo duæ parabolæ A B, & </s>
            <s xml:id="echoid-s5696" xml:space="preserve">C D, at-
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            que earum diametri A G, & </s>
            <s xml:id="echoid-s5697" xml:space="preserve">C H efficiant æquales angulos F, & </s>
            <s xml:id="echoid-s5698" xml:space="preserve">E, cum ordi-
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            natim ductis D F, & </s>
            <s xml:id="echoid-s5699" xml:space="preserve">B E, ſintque latera recta A I, C N æqualia. </s>
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