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

Table of contents

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[71.] Demonſtratio ſecundæ partis. PROPOSITIONIS LI.
Page: 81 (43)
[72.] Notæ in Propoſ. LII. LIII.
Page: 83 (45)
[73.] Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac ratione ſuppleri poteſt.
Page: 87 (49)
[74.] Notæ in Propoſ. LIV. LV.
Page: 92 (54)
[75.] Notæ in Propoſit. LVI.
Page: 93 (55)
[76.] LEMMA VIII.
Page: 95 (57)
[77.] Notæ in Propoſ. LVII.
Page: 96 (58)
[78.] SECTIO NONA Continens Propoſ. LVIII. LIX. LX. LXI. LXII. & LXIII.
Page: 98 (60)
[79.] PROPOSITIO LVIII.
Page: 98 (60)
[80.] PROPOSITIO LIX. LXII. & LXIII.
Page: 98 (60)
[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
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            <s xml:id="echoid-s4450" xml:space="preserve">
              <pb o="111" file="0149" n="149" rhead="Conicor. Lib. V."/>
            ticulam in hyperbole, quæ in textu deſideratur. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">Vocat interpres Arabicus li-
              <lb/>
            neam diſtantem ipſam A E, quæ contingit hyperbolem in vertice axis A, & </s>
            <s xml:id="echoid-s4452" xml:space="preserve">
              <lb/>
            interponitur inter verticem A, & </s>
            <s xml:id="echoid-s4453" xml:space="preserve">continentem, ſeu asymptoton D E.</s>
            <s xml:id="echoid-s4454" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4455" xml:space="preserve">Sit ſectio, D C diameter illius, &</s>
            <s xml:id="echoid-s4456" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4457" xml:space="preserve">Legendum puto; </s>
            <s xml:id="echoid-s4458" xml:space="preserve">Sit hyperbole A B
              <lb/>
              <note position="left" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">b</note>
            eius axis D C. </s>
            <s xml:id="echoid-s4459" xml:space="preserve">Poſtea quia D A, ad A G, ſeu latus tranſuer ſum ad rectum eſt,
              <lb/>
              <note position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">Ex 14.
                <lb/>
              huius.</note>
            vt D H ad H C, atque I A ad A D eſt, vt B H ad H D (propter ſimilitudi-
              <lb/>
            nem triangulorum I A D, & </s>
            <s xml:id="echoid-s4460" xml:space="preserve">B H D) ergo ex æqualitate ordinata I A ad A
              <lb/>
            G eſt vt B H ad H C: </s>
            <s xml:id="echoid-s4461" xml:space="preserve">deinde quia linea A E media proportionalis eſt inter ſe-
              <lb/>
            miaxim tranſuerſum D A, & </s>
            <s xml:id="echoid-s4462" xml:space="preserve">ſemierectum A G, cum quadratum ipſius A E
              <lb/>
            quadrans ſit figuræ quæ ad diametrum per A ductum conſtituitur; </s>
            <s xml:id="echoid-s4463" xml:space="preserve">igitur E A
              <lb/>
              <note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">3. lib. 2.</note>
            ad A G erit, vt D A ad A E, eſt vero E A maior, quàm I A; </s>
            <s xml:id="echoid-s4464" xml:space="preserve">igitur I A ad A
              <lb/>
            G minorem proportionem habet, quàm E A ad A G, ſeu quàm D A ad A E:
              <lb/>
            </s>
            <s xml:id="echoid-s4465" xml:space="preserve">erat autem B H ad H C, vt I A ad A G: </s>
            <s xml:id="echoid-s4466" xml:space="preserve">igitur B H ad H C minorem propor-
              <lb/>
            tionem habet, quàm D A ad A E: </s>
            <s xml:id="echoid-s4467" xml:space="preserve">fiat poſtea L A ad A E, vt B H ad H C
              <lb/>
            circa angulos rectos A, H, coniungaturq; </s>
            <s xml:id="echoid-s4468" xml:space="preserve">L E, manifeſtum eſt, L A minorem
              <lb/>
            eſſe-D A, & </s>
            <s xml:id="echoid-s4469" xml:space="preserve">angulum A E L minorem eſſe angulo A E D: </s>
            <s xml:id="echoid-s4470" xml:space="preserve">ſed propter ſimili-
              <lb/>
            tudinem triangulorum B H C, L A E eſt angulus C æqualis angulo A E L; </s>
            <s xml:id="echoid-s4471" xml:space="preserve">& </s>
            <s xml:id="echoid-s4472" xml:space="preserve">
              <lb/>
            proptrea angulus A E D maior eſt angulo B C H.</s>
            <s xml:id="echoid-s4473" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div416" type="section" level="1" n="128">
          <head xml:id="echoid-head172" xml:space="preserve">Notæ in Propoſ. XXXXII.</head>
          <p>
            <s xml:id="echoid-s4474" xml:space="preserve">QVia eſt linea recta ſecans diametrum paraboles; </s>
            <s xml:id="echoid-s4475" xml:space="preserve">&</s>
            <s xml:id="echoid-s4476" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4477" xml:space="preserve">Addo illam par-
              <lb/>
              <note position="left" xlink:label="note-0149-04" xlink:href="note-0149-04a" xml:space="preserve">a</note>
            ticulam breuiſſimam, quæ in textu deſiderari videtur.</s>
            <s xml:id="echoid-s4478" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div418" type="section" level="1" n="129">
          <head xml:id="echoid-head173" xml:space="preserve">Notæ in Propoſit. XXXXIII.</head>
          <p style="it">
            <s xml:id="echoid-s4479" xml:space="preserve">INclinatum ſi non excedit erectum, nulla linearum, &</s>
            <s xml:id="echoid-s4480" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4481" xml:space="preserve">Addo, quæeui-
              <lb/>
              <note position="left" xlink:label="note-0149-05" xlink:href="note-0149-05a" xml:space="preserve">a</note>
            denter deſiciunt in textu, legi enim debet: </s>
            <s xml:id="echoid-s4482" xml:space="preserve">Axis inclinatus ideſt tranſuer-
              <lb/>
            ſus ſi non excedit erectum, &</s>
            <s xml:id="echoid-s4483" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4484" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4485" xml:space="preserve">Et quia D A ad A G eſt vt quadratum D A ad quadratum A E, &</s>
            <s xml:id="echoid-s4486" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4487" xml:space="preserve">
              <note position="left" xlink:label="note-0149-06" xlink:href="note-0149-06a" xml:space="preserve">b</note>
            Eo quod quadratum A E æquale eſt quartæ parti figuræ, quæ ad duplam ſemia-
              <lb/>
              <note position="right" xlink:label="note-0149-07" xlink:href="note-0149-07a" xml:space="preserve">3. lib. 2.</note>
            xis D A applicatur, ſcilicet æquale eſt rectangulo D A G; </s>
            <s xml:id="echoid-s4488" xml:space="preserve">igitur D A, A E,
              <lb/>
            A G ſunt continuæ proportionales: </s>
            <s xml:id="echoid-s4489" xml:space="preserve">ponitur vero D A æqualis, aut minor, quàm
              <lb/>
            A G; </s>
            <s xml:id="echoid-s4490" xml:space="preserve">igitur D A æqualis, aut minor quoque erit, quàm A E; </s>
            <s xml:id="echoid-s4491" xml:space="preserve">& </s>
            <s xml:id="echoid-s4492" xml:space="preserve">propterea in
              <lb/>
            triangulo D E A erit angulus D E A æqualis, aut maior angulo A D E, ſeu
              <lb/>
            A D F (cum angulus continentiæ ſecetur bifariam ab axi) & </s>
            <s xml:id="echoid-s4493" xml:space="preserve">prius erat an-
              <lb/>
              <note position="right" xlink:label="note-0149-08" xlink:href="note-0149-08a" xml:space="preserve">41. huius.</note>
            gulus C minor angulo A E D; </s>
            <s xml:id="echoid-s4494" xml:space="preserve">igitur angulus B C D minor erit alterno angulo
              <lb/>
            F D C; </s>
            <s xml:id="echoid-s4495" xml:space="preserve">vnde conſtat rectas lineas F D, C B concurrere poſſe, ſi vlterius pro-
              <lb/>
            ducantur ad partes D, B; </s>
            <s xml:id="echoid-s4496" xml:space="preserve">non autem ad partes C, & </s>
            <s xml:id="echoid-s4497" xml:space="preserve">F.</s>
            <s xml:id="echoid-s4498" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4499" xml:space="preserve">Quia ſi occurreret illi occurreret D F (7. </s>
            <s xml:id="echoid-s4500" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s4501" xml:space="preserve">ſecaretque ſectionem
              <lb/>
              <note position="left" xlink:label="note-0149-09" xlink:href="note-0149-09a" xml:space="preserve">c</note>
            in duobus punctis, &</s>
            <s xml:id="echoid-s4502" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4503" xml:space="preserve">Senſus huius textus talis eſt. </s>
            <s xml:id="echoid-s4504" xml:space="preserve">Quoniam, vt oſtensũ
              <lb/>
            eſt, recta B C inſinite producta non occurrit asymptoto D F ad partes F C; </s>
            <s xml:id="echoid-s4505" xml:space="preserve">igi-
              <lb/>
              <note position="right" xlink:label="note-0149-10" xlink:href="note-0149-10a" xml:space="preserve">8. lib. 2.</note>
            tur recta C B producta non ſecabit peripheriam hyperboles ad partes K; </s>
            <s xml:id="echoid-s4506" xml:space="preserve">nam
              <lb/>
            ſi ipſam ſecaret, ſecaret quoque asymptoton D F ad partes F, quod non poni-
              <lb/>
              <note position="right" xlink:label="note-0149-11" xlink:href="note-0149-11a" xml:space="preserve">Ibidem.</note>
            tur. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">Ex his inferri debet concluſio principalis, nimirum, quod B C non occurrit
              <lb/>
            ſectioni duobus in punctis: </s>
            <s xml:id="echoid-s4508" xml:space="preserve">& </s>
            <s xml:id="echoid-s4509" xml:space="preserve">hac ratione textum alioqui corruptum emendaui.</s>
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