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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            <s xml:id="echoid-s11407" xml:space="preserve">
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            ducatur N n occurrens ſectioni in N, & </s>
            <s xml:id="echoid-s11408" xml:space="preserve">n, à quibus iungantur N C, n C, & </s>
            <s xml:id="echoid-s11409" xml:space="preserve">
              <lb/>
            eis æquidiſtantes diametri P Q, & </s>
            <s xml:id="echoid-s11410" xml:space="preserve">p q extendantur, quarũ erecta P R, & </s>
            <s xml:id="echoid-s11411" xml:space="preserve">p r.
              <lb/>
            </s>
            <s xml:id="echoid-s11412" xml:space="preserve">Oſtendendum eſt P Q ſubduplam eſſe ipſius P R, atq; </s>
            <s xml:id="echoid-s11413" xml:space="preserve">P R, & </s>
            <s xml:id="echoid-s11414" xml:space="preserve">p r æquales eße
              <lb/>
            inter ſe, & </s>
            <s xml:id="echoid-s11415" xml:space="preserve">minima eſſe erectorum quarumlibet Diametrorum eiuſdem ſectio-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s11416" xml:space="preserve">Quoniam vt H M ad M G ita eſt P Q ad P R, & </s>
            <s xml:id="echoid-s11417" xml:space="preserve">p q ad p r, erat au-
              <lb/>
              <note position="left" xlink:label="note-0360-01" xlink:href="note-0360-01a" xml:space="preserve">Prop. 6.
                <lb/>
              huius.</note>
            tem H M ſubdupla ipſius M G, ergo Diameter P Q ſubdupla eſt erecti eius P R,
              <lb/>
            pariterque p q ſubdupla eſt ipſius p r: </s>
            <s xml:id="echoid-s11418" xml:space="preserve">atque Diametri P Q, & </s>
            <s xml:id="echoid-s11419" xml:space="preserve">p q æquales
              <lb/>
            ſunt inter ſe, cum æque recedant ab axi A C, atque earum commune latus ſit
              <lb/>
            C M. </s>
            <s xml:id="echoid-s11420" xml:space="preserve">Poſtea quia tam E H, quàm M H maiores non ſunt eadem H M, vel
              <lb/>
            G H, ergo rectangulum ſub M G E in E H minus eſt quadrato E G, & </s>
            <s xml:id="echoid-s11421" xml:space="preserve">ex
              <lb/>
              <note position="left" xlink:label="note-0360-02" xlink:href="note-0360-02a" xml:space="preserve">Lem. 2.
                <lb/>
              huius.</note>
            lem. </s>
            <s xml:id="echoid-s11422" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11423" xml:space="preserve">P R minor eſt I K.</s>
            <s xml:id="echoid-s11424" xml:space="preserve"/>
          </p>
          <figure number="429">
            <image file="0360-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0360-01"/>
          </figure>
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            <s xml:id="echoid-s11425" xml:space="preserve">Similiter quia tam E H, quàm A H minor eſt eadem H M, ergo rectan-
              <lb/>
              <note position="left" xlink:label="note-0360-03" xlink:href="note-0360-03a" xml:space="preserve">Lem. 2.
                <lb/>
              & 5. hui.</note>
            gulum ſub E G A in A H minus eſt quadrato A G, & </s>
            <s xml:id="echoid-s11426" xml:space="preserve">I K minor erit, quàm
              <lb/>
            A F. </s>
            <s xml:id="echoid-s11427" xml:space="preserve">tandem, quia tam V H, quàm M H non eſt minor eadem G H, ergo re-
              <lb/>
            ctangulum V G M in M H maius erit quadrato G M, & </s>
            <s xml:id="echoid-s11428" xml:space="preserve">ideo S Z maior erit,
              <lb/>
              <note position="left" xlink:label="note-0360-04" xlink:href="note-0360-04a" xml:space="preserve">Lem. 3.</note>
            quàm P R, & </s>
            <s xml:id="echoid-s11429" xml:space="preserve">ſic vlterius: </s>
            <s xml:id="echoid-s11430" xml:space="preserve">quare P R minimum eſt laterum rectorum quarum-
              <lb/>
              <note position="left" xlink:label="note-0360-05" xlink:href="note-0360-05a" xml:space="preserve">Lem 5.</note>
            libet Diametrorum eiuſdem hyperboles.</s>
            <s xml:id="echoid-s11431" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11432" xml:space="preserve">In hyperbole latus rectum alicuius Diametri reperire, quod æquale
              <lb/>
              <note position="left" xlink:label="note-0360-06" xlink:href="note-0360-06a" xml:space="preserve">PROP. 1.
                <lb/>
              Addit</note>
            ſit lateri recto axis; </s>
            <s xml:id="echoid-s11433" xml:space="preserve">ſed oportet, vt axis tranſuerſus A C minor ſit me-
              <lb/>
            dietate eius erecti A F.</s>
            <s xml:id="echoid-s11434" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11435" xml:space="preserve">Reperiatur Diameter P Q, quæ ſubdupla ſit eius erecti P R, ſitque C M la-
              <lb/>
              <note position="left" xlink:label="note-0360-07" xlink:href="note-0360-07a" xml:space="preserve">ex 35. hu.</note>
            tus, & </s>
            <s xml:id="echoid-s11436" xml:space="preserve">fiat e G ad G A, vt M H ad H A, & </s>
            <s xml:id="echoid-s11437" xml:space="preserve">ducatur ordinatim applicata
              <lb/>
            ad axim e d, coniungaturque recta d C, & </s>
            <s xml:id="echoid-s11438" xml:space="preserve">extendatur diameter a b paralle-
              <lb/>
            la ipſi d C, cuius latus rectum ſit a c. </s>
            <s xml:id="echoid-s11439" xml:space="preserve">Dico a c æquale eſſe A F: </s>
            <s xml:id="echoid-s11440" xml:space="preserve">quia e G
              <lb/>
            ad G A facta fuit vt M H, ſiue G H ad H A, ergo rectangulum ſub e G A in
              <lb/>
              <note position="left" xlink:label="note-0360-08" xlink:href="note-0360-08a" xml:space="preserve">Lem. 4.
                <lb/>
              huius.</note>
            A H æquale eſt quadrato G A, ideoque erectum a c æquale erit erecto A F,
              <lb/>
              <note position="left" xlink:label="note-0360-09" xlink:href="note-0360-09a" xml:space="preserve">Lem. 5.
                <lb/>
              huius.</note>
            quod erat propoſitum.</s>
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