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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[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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            <s xml:id="echoid-s2628" xml:space="preserve">
              <pb o="58" file="0096" n="96" rhead="Apollonij Pergæi"/>
            vt E L ad L D (propter parallelas I D, H L) pariterque D N ad N I eſt, vt E H
              <lb/>
            ad H I (porpter parallelas E D, N H) quare D N ad N I erit vt E L ad L D,
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            & </s>
            <s xml:id="echoid-s2629" xml:space="preserve">propterea D N ad N I minorem proportionem habebit, quàm latus tranſuer-
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            ſum C A ad eius latus rectum, & </s>
            <s xml:id="echoid-s2630" xml:space="preserve">ideo linea breuiſsima ex puncto H ad axim
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">10. huius.</note>
            A D ducta cadet ſupra ramum H I E verſus verticem A, atq; </s>
            <s xml:id="echoid-s2631" xml:space="preserve">E H non erit bre-
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            uiſecans, quod erat primo loco oſtendendum.</s>
            <s xml:id="echoid-s2632" xml:space="preserve"/>
          </p>
          <figure number="72">
            <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0096-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2633" xml:space="preserve">Secundo ducatur ramus E O ſecans maiorem axim in P inter verticem A, & </s>
            <s xml:id="echoid-s2634" xml:space="preserve">
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            breuiſecantem E F; </s>
            <s xml:id="echoid-s2635" xml:space="preserve">Dico E O non eſſe breuiſecantem, & </s>
            <s xml:id="echoid-s2636" xml:space="preserve">breuiſsimam ex puncto
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            O ad axim A D ductam cadere infra ramum O P E; </s>
            <s xml:id="echoid-s2637" xml:space="preserve">Ducantur O Q, O R per-
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            pendiculares ad axes, ſecantes eos in Q, R. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">Manifeſtum eſt Q D minorem eſſe,
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            quàm K D, & </s>
            <s xml:id="echoid-s2639" xml:space="preserve">propterea E D ad D Q maiorem proportionem habebit, quàm ad
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            D K, & </s>
            <s xml:id="echoid-s2640" xml:space="preserve">componendo E Q ad Q D maiorem proportionem habebit, quàm E K
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            ad K D: </s>
            <s xml:id="echoid-s2641" xml:space="preserve">oſtenſa autem fuit E K ad K D, vt latus tranſuerſum C A ad eius la-
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            tus rectum; </s>
            <s xml:id="echoid-s2642" xml:space="preserve">igitur E Q ad Q D maiorem proportionem habebit, quàm latus
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            tranſuerſum ad rectum; </s>
            <s xml:id="echoid-s2643" xml:space="preserve">ſed (propter parallelas P D, O Q) vt E Q ad Q D
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            ita eſt E O ad O P, & </s>
            <s xml:id="echoid-s2644" xml:space="preserve">propter parallelas E D, R O, vt E O ad O P, ita eſt D R
              <lb/>
            ad R P; </s>
            <s xml:id="echoid-s2645" xml:space="preserve">ergo D R ad R P eſt, vt E Q ad Q D, & </s>
            <s xml:id="echoid-s2646" xml:space="preserve">propterea D R ad R P ma-
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            iorem proportionem habebit, quàm latus tranuer ſum C A ad eius latus rectum;
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            </s>
            <s xml:id="echoid-s2647" xml:space="preserve">igitur E O non erit breuiſecans, & </s>
            <s xml:id="echoid-s2648" xml:space="preserve">breuiſsima ex puncto O ad axim ducta cadit
              <lb/>
            infra ramum E O verſus D, quod erat oſtendendum.</s>
            <s xml:id="echoid-s2649" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">ex 10.
            <lb/>
          huius.</note>
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          <head xml:id="echoid-head110" xml:space="preserve">Notæ in Propoſ. LVII.</head>
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            <s xml:id="echoid-s2650" xml:space="preserve">ET dico, quod non repe-
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            riatur vllus alius ramus,
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            &</s>
            <s xml:id="echoid-s2651" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">Ideſt ſit rurſus linea bre-
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            uiſsima C M, quæ producta,
              <lb/>
            concurrat cum perpendiculari E
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            F in E, quæ ſecet axim in F
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            vltra centrum D ad partes ver-
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            ticis A. </s>
            <s xml:id="echoid-s2653" xml:space="preserve">Dico, quod præter </s>
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