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-div956" type="section" level="1" n="300">
          <head xml:id="echoid-head371" xml:space="preserve">SECTIO SEXTA</head>
          <head xml:id="echoid-head372" xml:space="preserve">Continens Propoſit. XXXIII. XXXIV.
            <lb/>
          XXXV. & XXXVI.</head>
          <head xml:id="echoid-head373" xml:space="preserve">PROPOSITIO XXXIII.</head>
          <p>
            <s xml:id="echoid-s11236" xml:space="preserve">A Xis inclinatus ſi non fuerit minor dimidio ſui erecti, vti-
              <lb/>
            que eius erectus minor eſt erecto cæterarum diametrorum
              <lb/>
            inclinatarum eiuſdem ſectionis, & </s>
            <s xml:id="echoid-s11237" xml:space="preserve">axi proximioris inclinati ere-
              <lb/>
            ctus minor eſt, quàm erectus remotioris.</s>
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          <p>
            <s xml:id="echoid-s11239" xml:space="preserve">XXXV. </s>
            <s xml:id="echoid-s11240" xml:space="preserve">Et ſi ſuerit axis inclinatus minor dimidio erecti, vti-
              <lb/>
            que ad vtraſque eius partes cadent duæ inclinatæ, quarum quæ-
              <lb/>
            libet æqualis eſt ſemiſſi erecti ipſius, atque eius erectus minor
              <lb/>
            eſt erecto cuiuslibet inclinati ad vtraſque partes eius poſitæ, & </s>
            <s xml:id="echoid-s11241" xml:space="preserve">
              <lb/>
            erectus proximioris minor eſt erecto remotioris.</s>
            <s xml:id="echoid-s11242" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11243" xml:space="preserve">In hyperbole A B N ſint A C,
              <lb/>
              <figure xlink:label="fig-0352-01" xlink:href="fig-0352-01a" number="418">
                <image file="0352-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0352-01"/>
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            I L, P Q, S T diametri inclinatæ,
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            & </s>
            <s xml:id="echoid-s11244" xml:space="preserve">A F ſit erectus ipſius A C, I
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            K ipſius I L, P R ipſius P Q, & </s>
            <s xml:id="echoid-s11245" xml:space="preserve">
              <lb/>
            S Z ipſius S T: </s>
            <s xml:id="echoid-s11246" xml:space="preserve">ſitquè axis A C
              <lb/>
            non minor medietate ipſius A F.
              <lb/>
            </s>
            <s xml:id="echoid-s11247" xml:space="preserve">Dico, quod A F minor eſt, quàm
              <lb/>
            I K, & </s>
            <s xml:id="echoid-s11248" xml:space="preserve">I K minor quàm P R, & </s>
            <s xml:id="echoid-s11249" xml:space="preserve">
              <lb/>
            P R minor quàm S Z. </s>
            <s xml:id="echoid-s11250" xml:space="preserve">Educantur
              <lb/>
            C B parallela I L, & </s>
            <s xml:id="echoid-s11251" xml:space="preserve">C N ipſi P
              <lb/>
            Q & </s>
            <s xml:id="echoid-s11252" xml:space="preserve">C X ipſi S T: </s>
            <s xml:id="echoid-s11253" xml:space="preserve">& </s>
            <s xml:id="echoid-s11254" xml:space="preserve">ducantur
              <lb/>
            B E, N M, X V perpendiculares
              <lb/>
            ad axim C A E. </s>
            <s xml:id="echoid-s11255" xml:space="preserve">Quoniam ſi A C
              <lb/>
            æqualis eſt ipſi A F, etiam I L æ-
              <lb/>
            qualis eſt ipſi I K (21. </s>
            <s xml:id="echoid-s11256" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11257" xml:space="preserve">& </s>
            <s xml:id="echoid-s11258" xml:space="preserve">
              <lb/>
            P Q ipſi P R; </s>
            <s xml:id="echoid-s11259" xml:space="preserve">eſtque A C minor
              <lb/>
              <note position="left" xlink:label="note-0352-01" xlink:href="note-0352-01a" xml:space="preserve">ex 38
                <lb/>
              lib. 5.</note>
            quam I L, & </s>
            <s xml:id="echoid-s11260" xml:space="preserve">I L, quàm P Q;</s>
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