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="412" file="0450" n="451" rhead="Archimedis"/>
            pleantur parallelogramma rectangula A L, A K, L B, B K, atque axe
              <lb/>
              <note position="left" xlink:label="note-0450-01" xlink:href="note-0450-01a" xml:space="preserve">Prop. 52.
                <lb/>
              lib. 1.</note>
            F G, latere recto F N deſcribatur parabole F M ſecans H G in M; </s>
            <s xml:id="echoid-s13679" xml:space="preserve">erit
              <lb/>
            igitur in parabola quadratum M G æquale rectangulo G F N ſub abſciſ-
              <lb/>
              <note position="left" xlink:label="note-0450-02" xlink:href="note-0450-02a" xml:space="preserve">Prop. 11.
                <lb/>
              lib. 1.</note>
            ſa, & </s>
            <s xml:id="echoid-s13680" xml:space="preserve">latere recto contento, ideoque idem quadratum F G ad rectangu-
              <lb/>
            lum N F G, atque ad quadratum M G eandem proportionem habebit:
              <lb/>
            </s>
            <s xml:id="echoid-s13681" xml:space="preserve">eſt vero quadratum F G ad rectangulum N F G, vt F G ad F N, cum
              <lb/>
              <figure xlink:label="fig-0450-01" xlink:href="fig-0450-01a" number="525">
                <image file="0450-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0450-01"/>
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            F G ſit illorum altitudo communis, nec non vt C F G ad C F N ſum-
              <lb/>
            pta nimirum C F communi altitudine, ergo rectangulum C F G ad C
              <lb/>
            F N eandem proportionem habebit, quam quadratum F G ad quadra-
              <lb/>
            tum M G, & </s>
            <s xml:id="echoid-s13682" xml:space="preserve">permutando rectangulum C F G ad quadratum F G erit
              <lb/>
            vt rectangulum C F N ad quadratum G M, ſed vt rectangulum C F G
              <lb/>
            ad quadratum F G, ita eſt C F ad F G, & </s>
            <s xml:id="echoid-s13683" xml:space="preserve">E A ad A C, igitur E A ad
              <lb/>
            A C erit vt rectangulum C F N ad quadratum G M, ſeu vt quadratum
              <lb/>
            E B, vel K G ad quadratum G M: </s>
            <s xml:id="echoid-s13684" xml:space="preserve">eſt vero A C minor, quàm A E,
              <lb/>
            quæ triens eſt totius A B, igitur M G minor eſt, quàm G K. </s>
            <s xml:id="echoid-s13685" xml:space="preserve">Poſtea
              <lb/>
            per B circa aſymptotos A C F deſcribatur hyperbole B K, quæ tran-
              <lb/>
              <note position="left" xlink:label="note-0450-03" xlink:href="note-0450-03a" xml:space="preserve">Prop. 4. &
                <lb/>
              12. lib. 2.</note>
            ſibit per punctum K, cum parallelogramma A F, & </s>
            <s xml:id="echoid-s13686" xml:space="preserve">C K æqualia
              <lb/>
            ſint propter diagonalem C E G, quare punctum M paraboles cadet
              <lb/>
            intra hyperbolem B K, ſed parabole F M occurrit aſymptoto C F in ver-
              <lb/>
            tice F, & </s>
            <s xml:id="echoid-s13687" xml:space="preserve">occurrit etiam aſymptoto C A in aliquo alio puncto, cum C
              <lb/>
            A ſit parallela axi F G paraboles, & </s>
            <s xml:id="echoid-s13688" xml:space="preserve">hyperbole ſemper intra aſymptotos
              <lb/>
              <note position="left" xlink:label="note-0450-04" xlink:href="note-0450-04a" xml:space="preserve">Prop. 26.
                <lb/>
              lib. 1.</note>
            incedat, igitur parabola F M bis hyperbolæ occurrit ſupra, & </s>
            <s xml:id="echoid-s13689" xml:space="preserve">inſra pun-
              <lb/>
              <note position="left" xlink:label="note-0450-05" xlink:href="note-0450-05a" xml:space="preserve">ex 1. & 2.
                <lb/>
              lib. 2.</note>
            ctum M: </s>
            <s xml:id="echoid-s13690" xml:space="preserve">ſint occurſus X, à quibus ductis parallelis ad aſymptotos com-
              <lb/>
            pleantur parallelogramma R P, & </s>
            <s xml:id="echoid-s13691" xml:space="preserve">A F, quæ erunt æqualia inter aſym-
              <lb/>
            ptotos, & </s>
            <s xml:id="echoid-s13692" xml:space="preserve">hyperbolen conſtituta, & </s>
            <s xml:id="echoid-s13693" xml:space="preserve">propterea C O S parallelogrammo-
              <lb/>
              <note position="left" xlink:label="note-0450-06" xlink:href="note-0450-06a" xml:space="preserve">Prop. 12.
                <lb/>
              lib. 2.</note>
            rum diameter erit, & </s>
            <s xml:id="echoid-s13694" xml:space="preserve">vna linca recta: </s>
            <s xml:id="echoid-s13695" xml:space="preserve">& </s>
            <s xml:id="echoid-s13696" xml:space="preserve">quia O A ad A C eſt vt C F
              <lb/>
            ad F S, ſiue vt rectangulum C F N ad rectangulum S F N: </s>
            <s xml:id="echoid-s13697" xml:space="preserve">erat autem
              <lb/>
            quadratum E B æquale rectangulo C F N ex conſtructione, & </s>
            <s xml:id="echoid-s13698" xml:space="preserve"/>
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