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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              <pb o="258" file="0296" n="296" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0296-01" xlink:href="fig-0296-01a" number="343">
                <image file="0296-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0296-01"/>
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            quadratum Q A; </s>
            <s xml:id="echoid-s9719" xml:space="preserve">ſed in hac poſtrema ſuppoſitione conceditur quadratum B Q
              <lb/>
            ad quadratum Q A habere maiorem proportionem, quàm H E ad E I; </s>
            <s xml:id="echoid-s9720" xml:space="preserve">igitur
              <lb/>
            O N ad N L maiorem proportionem habebit, quàm H E ad E I; </s>
            <s xml:id="echoid-s9721" xml:space="preserve">ſed quia co-
              <lb/>
            nus E R T ponitur continere ſectionem D E F: </s>
            <s xml:id="echoid-s9722" xml:space="preserve">habebit O V ad V R eandem
              <lb/>
            proportionem, quàm H E ad E I (vt ex 53. </s>
            <s xml:id="echoid-s9723" xml:space="preserve">primi deducitur, & </s>
            <s xml:id="echoid-s9724" xml:space="preserve">in hac pro-
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            poſitione denuò factum eſt): </s>
            <s xml:id="echoid-s9725" xml:space="preserve">igitur O N ad N L maiorem proportionem habebit
              <lb/>
            quàm O V ad V R; </s>
            <s xml:id="echoid-s9726" xml:space="preserve">oſtenſa autem fuit O N ad N X, vt O V ad V R; </s>
            <s xml:id="echoid-s9727" xml:space="preserve">ergo O
              <lb/>
            N ad N L maiorem proportionem habebit, quàm O N ad N X: </s>
            <s xml:id="echoid-s9728" xml:space="preserve">quod eſt abſur-
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            dum, nam N X minor eſt, quàm N L.</s>
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          <head xml:id="echoid-head311" xml:space="preserve">Notæ in Propoſit. XXXI.</head>
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            <s xml:id="echoid-s9730" xml:space="preserve">DEinde ſit ſectio elliptica A B C, & </s>
            <s xml:id="echoid-s9731" xml:space="preserve">tranſuerſa illius A C, & </s>
            <s xml:id="echoid-s9732" xml:space="preserve">erectus
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            A D, & </s>
            <s xml:id="echoid-s9733" xml:space="preserve">circunducamus ſuper A C in plano erecto ad ſectionis
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            planum A B C ſegmentum circuli, quod capiat angulum æqualem an-
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            gulo F: </s>
            <s xml:id="echoid-s9734" xml:space="preserve">&</s>
            <s xml:id="echoid-s9735" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9736" xml:space="preserve">Rurſus conus exhiberi debet ſimilis cono dato E F G, qui datam
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            ellipſim A B C contineat, ſitque axis tranſuerſus ellipſis C A, eiuſque latus
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            rectum A D.</s>
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            <s xml:id="echoid-s9738" xml:space="preserve">Quia H I in I K, quod eſt æquale ipſi C I in I A, ad quadratum I A
              <lb/>
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            eſt, vt A C ad A D, & </s>
            <s xml:id="echoid-s9739" xml:space="preserve">C I in A I ad quadratum I K nempe K N ad
              <lb/>
            N O propter ſimilitudinem duorum triangulorum, & </s>
            <s xml:id="echoid-s9740" xml:space="preserve">ex A I, nempe N
              <lb/>
            K ad I K nempe A N vt parallelas conſtituamus lineas, & </s>
            <s xml:id="echoid-s9741" xml:space="preserve">ex his dua-
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            bus proportionibus componitur proportio quadrati N K ad A N in N O,
              <lb/>
            &</s>
            <s xml:id="echoid-s9742" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9743" xml:space="preserve">Senſus huius textus valdè corrupti hic eſt. </s>
            <s xml:id="echoid-s9744" xml:space="preserve">Quia ex conſtructione H I ad
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            I K erat vt C A ad A D, & </s>
            <s xml:id="echoid-s9745" xml:space="preserve">ſumpta communi altitudine I K, erit </s>
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