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-div42" type="section" level="1" n="36">
          <p>
            <s xml:id="echoid-s903" xml:space="preserve">
              <pb o="8" file="0046" n="46" rhead="Apollonij Pergæi"/>
            minimo remotiore minor eſt. </s>
            <s xml:id="echoid-s904" xml:space="preserve">Quadratum autem menſuræ mi-
              <lb/>
            nus eſt quadrato cuiuslibet rami aſſignati (4) in parabola qui-
              <lb/>
            dem quadrato ſuæ abſciſſæ (5) & </s>
            <s xml:id="echoid-s905" xml:space="preserve">in hyperbola (6) & </s>
            <s xml:id="echoid-s906" xml:space="preserve">ellipſi
              <lb/>
            exemplari applicato ad abſciſſam illius rami.</s>
            <s xml:id="echoid-s907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div43" type="section" level="1" n="37">
          <head xml:id="echoid-head62" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s908" xml:space="preserve">SIt ſectio A B C, & </s>
            <s xml:id="echoid-s909" xml:space="preserve">axis eius C E, & </s>
            <s xml:id="echoid-s910" xml:space="preserve">inclinatus, ſiue tranſuerſa D C
              <lb/>
            centrum G, atque erectum C F, & </s>
            <s xml:id="echoid-s911" xml:space="preserve">ex C E ſecetur C I æqualis C H
              <lb/>
              <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a" number="13">
                <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/>
              </figure>
            (quæ ſit ſemiſſis erecti) & </s>
            <s xml:id="echoid-s912" xml:space="preserve">ex puncto
              <lb/>
            originis I educantur rami I B perpen-
              <lb/>
            dicularis, & </s>
            <s xml:id="echoid-s913" xml:space="preserve">I K, I L, I A, & </s>
            <s xml:id="echoid-s914" xml:space="preserve">per H, I
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s915" xml:space="preserve">ellipſi ducatur H I P,
              <lb/>
            & </s>
            <s xml:id="echoid-s916" xml:space="preserve">per H, G recta H G T, ad quam ex
              <lb/>
            A, B, K, L extendantur A P E T, B I S,
              <lb/>
            K N R, L M O Q perpendiculares ſuper
              <lb/>
            C E. </s>
            <s xml:id="echoid-s917" xml:space="preserve">Dico, quod C I, comparata mi-
              <lb/>
            nor eſt, quam I L, & </s>
            <s xml:id="echoid-s918" xml:space="preserve">
              <lb/>
            I L, quam I K, & </s>
            <s xml:id="echoid-s919" xml:space="preserve">I K,
              <lb/>
            quam I B, & </s>
            <s xml:id="echoid-s920" xml:space="preserve">maximus
              <lb/>
            ramorum in ellipſi eſt
              <lb/>
            I D, & </s>
            <s xml:id="echoid-s921" xml:space="preserve">quod quadra-
              <lb/>
            tum menſuræ I C mi-
              <lb/>
            nus eſt quadrato I L,
              <lb/>
            in parabola quidem
              <lb/>
            quadrato C M, & </s>
            <s xml:id="echoid-s922" xml:space="preserve">in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s923" xml:space="preserve">ellipſi
              <lb/>
            exemplari applicato
              <lb/>
            ad C M. </s>
            <s xml:id="echoid-s924" xml:space="preserve">Quoniam in
              <lb/>
            parabola L M poteſt
              <lb/>
              <note position="right" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">a</note>
            duplum M C in C H, nempè C I (12. </s>
            <s xml:id="echoid-s925" xml:space="preserve">ex primo) & </s>
            <s xml:id="echoid-s926" xml:space="preserve">quadratum I L ęqua-
              <lb/>
            le eſt aggregato duorum quadratorum L M, & </s>
            <s xml:id="echoid-s927" xml:space="preserve">M I, quadratum itaque L
              <lb/>
            I æquale eſt quadrato M I, & </s>
            <s xml:id="echoid-s928" xml:space="preserve">M C in C I bis, quæ ſunt æqualia duobus
              <lb/>
            quadratis C I, M C. </s>
            <s xml:id="echoid-s929" xml:space="preserve">Quadratum igitur C I minus eſt quadrato L I qua-
              <lb/>
            drato ipſius M C, quæ eſt eius abſciſſa, & </s>
            <s xml:id="echoid-s930" xml:space="preserve">pariter oſtendetur, quod qua-
              <lb/>
            dratum C I minus eſt quadrato I K quadrato N C, & </s>
            <s xml:id="echoid-s931" xml:space="preserve">minus quadrato I
              <lb/>
            B quadrato C I, & </s>
            <s xml:id="echoid-s932" xml:space="preserve">minus quadrato A I quadrato E C.</s>
            <s xml:id="echoid-s933" xml:space="preserve"/>
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          <head xml:id="echoid-head63" xml:space="preserve">PROPOSITIO V. & VI.</head>
          <p>
            <s xml:id="echoid-s934" xml:space="preserve">AT verò in hyperbola, & </s>
            <s xml:id="echoid-s935" xml:space="preserve">ellipſi producantur ex Q, O, H lineæ pa-
              <lb/>
            rallelæ ipſi M C, & </s>
            <s xml:id="echoid-s936" xml:space="preserve">quia I C ex hypotheſi æqualis eſt H C, erit I
              <lb/>
              <note position="right" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">a</note>
            M æqualis M O, quadratum itaque I M duplum eſt trianguli I M O, & </s>
            <s xml:id="echoid-s937" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve">b</note>
            quadratum L M duplum eſt trapezij C M Q H (prima ex 5.) </s>
            <s xml:id="echoid-s938" xml:space="preserve">ergo </s>
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