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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[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)
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
[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)
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        <div xml:id="echoid-div126" type="section" level="1" n="56">
          <head xml:id="echoid-head85" xml:space="preserve">SECTIO SEPTIMA</head>
          <head xml:id="echoid-head86" xml:space="preserve">Continens XXVI. XXVII. XXVIII. Propoſ.
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          Apollonij.</head>
          <head xml:id="echoid-head87" xml:space="preserve">PROPOSITIO XXVI. & XXVII.</head>
          <p>
            <s xml:id="echoid-s1641" xml:space="preserve">ANgulorum ab axi ſectionis A H, & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">à lineis breuiſſimis F
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            B, H G contentorum proximiores vertici ſectionis mi-
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            nores ſunt remotioribus, nempe angulus AFB minor eſt AHG.</s>
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            <s xml:id="echoid-s1644" xml:space="preserve">SIt itaque centrum D, & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">ſemi inclinatus axis A D, ſiue ſemitranſuer-
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            ſus, & </s>
            <s xml:id="echoid-s1646" xml:space="preserve">dimidium erecti A C: </s>
            <s xml:id="echoid-s1647" xml:space="preserve">educamus itaque duas perpendiculares
              <lb/>
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            GL, BI, & </s>
            <s xml:id="echoid-s1648" xml:space="preserve">ſi ſectio fuerit parabole, erit FI æqualis LH, quia quælibet
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            earum æqualis eſt A C (13. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1650" xml:space="preserve">L G maior eſt, quàm BI; </s>
            <s xml:id="echoid-s1651" xml:space="preserve">an-
              <lb/>
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            gulus igitur F minor quàm H; </s>
            <s xml:id="echoid-s1652" xml:space="preserve">ſi verò ſectio fuerit hyperbole, aut ellipſis,
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            erit FI ad ID, vt HL ad LD, quia quælibet earum eſt, vt AC ad AD
              <lb/>
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            (14. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1655" xml:space="preserve">permutando, erit I D ad L D nempe B I ad M L,
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            vt I F ad L H, & </s>
            <s xml:id="echoid-s1656" xml:space="preserve">anguli I, & </s>
            <s xml:id="echoid-s1657" xml:space="preserve">L ſunt recti; </s>
            <s xml:id="echoid-s1658" xml:space="preserve">igitur duo triangula BIF, M
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            B, & </s>
            <s xml:id="echoid-s1659" xml:space="preserve">hoc erat propoſitum.</s>
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          <head xml:id="echoid-head88" xml:space="preserve">PROPOSITIO XXVIII.</head>
          <p>
            <s xml:id="echoid-s1661" xml:space="preserve">Hinc patet, lineas breuiſſimas ſibi occurrere ad partes axis
              <lb/>
            ſectionis.</s>
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            <s xml:id="echoid-s1663" xml:space="preserve">QVia angulus AFB minor eſt, quàm angulus AHG; </s>
            <s xml:id="echoid-s1664" xml:space="preserve">quare ſibi oc-
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              <note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">26. 27. h.</note>
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            currunt ad partes F, H, & </s>
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