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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
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        <div xml:id="echoid-div268" type="section" level="1" n="89">
          <head xml:id="echoid-head123" xml:space="preserve">PROPOSITIO XXXXV.</head>
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            <s xml:id="echoid-s2914" xml:space="preserve">SI autem fuerit ratio E A ad A D minor,
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              <note position="right" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">a</note>
            quàm proportio figuræ, ponamus E H ad H
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            D in proportione figuræ, & </s>
            <s xml:id="echoid-s2915" xml:space="preserve">producamus per-
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            pendicularem H F, & </s>
            <s xml:id="echoid-s2916" xml:space="preserve">iungamus F E, & </s>
            <s xml:id="echoid-s2917" xml:space="preserve">duca-
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            mus perpendicularem F I. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">Et quoniam E H ad
              <lb/>
            H D, nempe D I ad I G eſt, vt proportio figu-
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            ræ, erit F G linea breuiſſima (10. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2920" xml:space="preserve">Et quo-
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            niam iam educti ſunt ex E duo breuiſecantes
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            F E, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">E A (11. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2923" xml:space="preserve">tunc à terminis ramo-
              <lb/>
            rum egredientium ex E, qui terminantur ad ſe-
              <lb/>
            ctionem B F, linea breuiſſima egrediens erit re-
              <lb/>
            motior ab ipſo B, & </s>
            <s xml:id="echoid-s2924" xml:space="preserve">qui terminatur ad ſectio-
              <lb/>
            nem A F, breuiſſima egrediens ab extremitate illius erit proximior, ipſi
              <lb/>
            B (51. </s>
            <s xml:id="echoid-s2925" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2926" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2927" xml:space="preserve">& </s>
            <s xml:id="echoid-s2928" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s2929" xml:space="preserve"/>
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          <head xml:id="echoid-head124" xml:space="preserve">Notæ in Propoſ. XXXXIV.</head>
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            <s xml:id="echoid-s2930" xml:space="preserve">PVto, numeros 53. </s>
            <s xml:id="echoid-s2931" xml:space="preserve">& </s>
            <s xml:id="echoid-s2932" xml:space="preserve">54. </s>
            <s xml:id="echoid-s2933" xml:space="preserve">Propoſitionum huius ſe-
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            ctionis mendoſos eſſe, nam Propoſitio 53. </s>
            <s xml:id="echoid-s2934" xml:space="preserve">poſita
              <lb/>
            fuit in præmiſſa ſectione, & </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Propoſitio 54. </s>
            <s xml:id="echoid-s2936" xml:space="preserve">inferius
              <lb/>
            appoſita reperitur; </s>
            <s xml:id="echoid-s2937" xml:space="preserve">Cenſeo igitur, eſſe Propoſitiones
              <lb/>
            XXXXIV. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">& </s>
            <s xml:id="echoid-s2939" xml:space="preserve">XXXXV.</s>
            <s xml:id="echoid-s2940" xml:space="preserve"/>
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            <s xml:id="echoid-s2941" xml:space="preserve">Si ex axe recto ellipſis ſumatur menſura, &</s>
            <s xml:id="echoid-s2942" xml:space="preserve">c.
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            <s xml:id="echoid-s2943" xml:space="preserve">
              <note position="right" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">a</note>
            Hoc eſt ſi ex axe minori, recto ellipſis ſumatur menſu-
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            ra, quæ habeat non minorem proportionem ad ſemi-
              <lb/>
            axim rectum, quàm habet axis tranſuerſus ad ſuum
              <lb/>
            latus rectum, quilibet ramus ſecans, ab origine ad ſe-
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            ctionem ductus, abſcindit ex axe tranſuerſo ad ver-
              <lb/>
            ticem ſectionis minorem lineam, quàm ſecat linea breuiſsima ab eius termi-
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            no ad axim tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">Si vero menſura ad minorem ſemiaxim re-
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            ctum proportionem minorem habuerit, quàm latus tranſuer ſum ad rectum, tunc
              <lb/>
            vnicus ramus erit breuiſecans; </s>
            <s xml:id="echoid-s2945" xml:space="preserve">reliqui vero ſequentes terminum tranſuerſi, ha-
              <lb/>
            bent ſuperius expoſitas proprietates, & </s>
            <s xml:id="echoid-s2946" xml:space="preserve">ſequentes extr emitates axis recti, ſecant
              <lb/>
            ex tranſuer ſa maiorem lineam, quàm ſecet breuiſsima ab eius termino ad axim
              <lb/>
            tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Quod autem menſura neceßario ſumi debeat in axe minori
              <lb/>
            ellipſis patet, nàm ex hypotheſi rami ſunt ſecantes non quidem ex concurſu, ſed
              <lb/>
            ex origine ducti igitur origo cadit infra centrum, & </s>
            <s xml:id="echoid-s2948" xml:space="preserve">menſura maior erit medie-
              <lb/>
            tate axis vt in textu habetur; </s>
            <s xml:id="echoid-s2949" xml:space="preserve">debet autem habere menſura ad ſemiaxim rectum
              <lb/>
            maiorem aut eandem proportionem, quàm axis tranſuerſus habet ad eius latus
              <lb/>
            rectum, ergo proportio axis tranſuerſi ad ſuum latus rectum erit maioris inæqua-
              <lb/>
            litatis, & </s>
            <s xml:id="echoid-s2950" xml:space="preserve">propterea tranſuerſus axis erit maior quàm axis rectus.</s>
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