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-div1080" type="section" level="1" n="341">
          <head xml:id="echoid-head422" xml:space="preserve">Notæ in Propoſit. XXXXX.</head>
          <p style="it">
            <s xml:id="echoid-s12535" xml:space="preserve">SI hyperbole axis A C minor fuerit eius erecto A F, quia H M maior eſt,
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            quàm H E, & </s>
            <s xml:id="echoid-s12536" xml:space="preserve">punctum H cadit inter D, & </s>
            <s xml:id="echoid-s12537" xml:space="preserve">A, ergo H M ad H D ma-
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              <figure xlink:label="fig-0405-01" xlink:href="fig-0405-01a" number="479">
                <image file="0405-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0405-01"/>
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            iorem proportionem habebit, quàm H E ad eandem H D, & </s>
            <s xml:id="echoid-s12538" xml:space="preserve">comparando ante-
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            cedentes ad terminorum ſummas H M ad M D maiorem proportionem habebit,
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              <note position="right" xlink:label="note-0405-01" xlink:href="note-0405-01a" xml:space="preserve">Lem. 17.
                <lb/>
              huius.</note>
            quàm H E ad E D, quare differentia quadratorum ex P Q, & </s>
            <s xml:id="echoid-s12539" xml:space="preserve">ex P R minor
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            erit, quàm differentta quadratorum ex I L, & </s>
            <s xml:id="echoid-s12540" xml:space="preserve">ex I K, ſeu minor quàm dif-
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            ferentia quadratorum ex A C, & </s>
            <s xml:id="echoid-s12541" xml:space="preserve">ex A F.</s>
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            <s xml:id="echoid-s12543" xml:space="preserve">Poſtea, quia vt in precedenti nota dictũ eſt, differentia quadrati A C à rectan-
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            gulo C A F ad ſemidifferentiã quadratorũ ex I L, & </s>
            <s xml:id="echoid-s12544" xml:space="preserve">ex I K eandem proportionẽ
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            habet, quàm rectangulum E H G ad rectangulum ſub E D, & </s>
            <s xml:id="echoid-s12545" xml:space="preserve">ſub G H, eſt-
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            que illud rectangulum minus rectangulo iſto æquè alto, (cum illius baſis E H
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            minor ſit, quàm E D), igitur differentia quadrati A C à rectangulo C A F
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            minor eſt, quàm ſemidifferentia quadratorum ex I L, & </s>
            <s xml:id="echoid-s12546" xml:space="preserve">ex I K.</s>
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          <head xml:id="echoid-head423" xml:space="preserve">Notæ in Propoſit. XXXXXI.</head>
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            <s xml:id="echoid-s12548" xml:space="preserve">IN qualibet ellypſi ſit diameter a b æqualis eius erecto a c, eius latus erit C
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              <note position="right" xlink:label="note-0405-02" xlink:href="note-0405-02a" xml:space="preserve">ex Lem.
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              18. huius.</note>
            D, & </s>
            <s xml:id="echoid-s12549" xml:space="preserve">diametri I L, & </s>
            <s xml:id="echoid-s12550" xml:space="preserve">P Q cadant inter A C, & </s>
            <s xml:id="echoid-s12551" xml:space="preserve">a b, earum </s>
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