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-s4915" xml:space="preserve">Erit angulus BHE ma-
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            ior, i
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            quàm E B H, &</s>
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            <s xml:id="echoid-s4917" xml:space="preserve">Eo
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            quod ramorum omnium ab
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            origine E ad ellipſim C B H
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            cadentium maximus ſuppo-
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            nitur E B; </s>
            <s xml:id="echoid-s4918" xml:space="preserve">ergo maior erit,
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            quàm E H, & </s>
            <s xml:id="echoid-s4919" xml:space="preserve">propterea
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            angulus E B H minori late-
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            ri oppoſitus minor erit angu-
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            lo E H B: </s>
            <s xml:id="echoid-s4920" xml:space="preserve">cadit vero recta
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            H F infra H E; </s>
            <s xml:id="echoid-s4921" xml:space="preserve">propterea
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            quod punctum F infra pun-
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            ctum E exiſtit; </s>
            <s xml:id="echoid-s4922" xml:space="preserve">igitur angu-
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            lus F H B maior eſt angulo
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            E H B; </s>
            <s xml:id="echoid-s4923" xml:space="preserve">& </s>
            <s xml:id="echoid-s4924" xml:space="preserve">ideo angulus F H B multo maior erit angulo F B H; </s>
            <s xml:id="echoid-s4925" xml:space="preserve">igitur ramus
              <lb/>
            F B, maiorem angulum ſubtendens, maior erit, quàm F H, &</s>
            <s xml:id="echoid-s4926" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head186" xml:space="preserve">SECTIO DECIMAOCTAVA</head>
          <head xml:id="echoid-head187" xml:space="preserve">Continens XXXII. XXXIII. XXXIV. XXXV.
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          XXXVI. XXXVII. XXXVIII. XXXIX.
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          XXXX. XXXXVII. XXXXVIII.</head>
          <head xml:id="echoid-head188" xml:space="preserve">Propoſit. Apollonij.</head>
          <head xml:id="echoid-head189" xml:space="preserve">PROPOSITIO XXXII.</head>
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            <s xml:id="echoid-s4928" xml:space="preserve">IN ellipſi A B C rami cuiuslibet
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            maximi G H vtrumque axim ſe-
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            cantis portio N H inter axim maio-
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            rem, & </s>
            <s xml:id="echoid-s4929" xml:space="preserve">ſectionem intercepta, eſt li-
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            nea breuiſsima.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4931" xml:space="preserve">Producatur rectus axis minor A D vl-
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            tra centrum D ad I, G, & </s>
            <s xml:id="echoid-s4932" xml:space="preserve">ex I, G ad ſe-
              <lb/>
            ctionem ducantur duo rami maximi G H,
              <lb/>
            I K, qui ſecent tranſuerſum B D in N,
              <lb/>
            M, & </s>
            <s xml:id="echoid-s4933" xml:space="preserve">ſit B E dimidium erecti axis B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s4934" xml:space="preserve">A F dimidium erecti axis A G; </s>
            <s xml:id="echoid-s4935" xml:space="preserve">& </s>
            <s xml:id="echoid-s4936" xml:space="preserve">edu-
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            cantur perpendiculares ad axes H O, H
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            P, K Q, K R. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">Dico, N H breuiſsimum
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            eſſe ramorum egredientium ex H. </s>
            <s xml:id="echoid-s4938" xml:space="preserve">Quia
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            G H eſt linea maxima, erit D A ad A F,
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            nempe B E ad B D, vt D O ad O G (22.
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            </s>
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            ex 5.) </s>
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