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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              <pb o="59" file="0097" n="97" rhead="Conicor. Lib. V."/>
            mum E C nullus alius ramus breuiſecans ex concurſu E ad ſectionem duci poteſt,
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            qui cadat in eodem quadrante B L, quem breuiſecans interſecat.</s>
            <s xml:id="echoid-s2654" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2655" xml:space="preserve">Nam ſi producantur E H, E G, &</s>
            <s xml:id="echoid-s2656" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2657" xml:space="preserve">Ducantur quilibet rami E H, E G ad
              <lb/>
              <note position="left" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">h</note>
            vtraſque partes breuiſecantis E C intra quadrantem B L, qui ſecent D B in K,
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            & </s>
            <s xml:id="echoid-s2658" xml:space="preserve">I, & </s>
            <s xml:id="echoid-s2659" xml:space="preserve">producatur per centrum D recta M D L perpendicularis ad axim B A,
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            quæ ſecet ſectionem in L, & </s>
            <s xml:id="echoid-s2660" xml:space="preserve">ramum E C in M.</s>
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            <s xml:id="echoid-s2662" xml:space="preserve">Et quia iam productæ ſunt ex concurſu M duæ breuiſecantes, &</s>
            <s xml:id="echoid-s2663" xml:space="preserve">c.
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              <note position="left" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">i</note>
            Quia C M breuiſsima ex hypotheſi occurrit ſemiaxi minori recto L D breuiſsi-
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            mæ pariter (ex 11. </s>
            <s xml:id="echoid-s2665" xml:space="preserve">huius) in M, ſequitur (non quidem ex 51. </s>
            <s xml:id="echoid-s2666" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2667" xml:space="preserve">huius, ſed
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            ex lemmate 8. </s>
            <s xml:id="echoid-s2668" xml:space="preserve">præmiſſo) quod linea recta ex M ad H coniuncta cadat infra
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            breuiſsimam ex puncto H ad axim B A ductam, & </s>
            <s xml:id="echoid-s2669" xml:space="preserve">coniuncta recta M G cadit
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            ſupra breuiſsimam ex puncto G ad axim ductam.</s>
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            <s xml:id="echoid-s2671" xml:space="preserve">Sed E H, & </s>
            <s xml:id="echoid-s2672" xml:space="preserve">E G efficiunt abſciſsas oppoſito modo, &</s>
            <s xml:id="echoid-s2673" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2674" xml:space="preserve">Quia ab eodem
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            puncto H ſectionis ducuntur tres rectæ lineæ. </s>
            <s xml:id="echoid-s2675" xml:space="preserve">H E, H M, & </s>
            <s xml:id="echoid-s2676" xml:space="preserve">breuiſsima ex H ad
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            axim B A ducta, quarum intermedia eſt H M, eo quod breuiſsima ex H ad
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            axim A B cadit ſupra H M ad partes B, vt dictum eſt, & </s>
            <s xml:id="echoid-s2677" xml:space="preserve">H E cadit
              <lb/>
              <note position="right" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">Lem 8.</note>
            infra H M ad partes A; </s>
            <s xml:id="echoid-s2678" xml:space="preserve">ergo H E cadit infra breuiſsimam ex
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            H ad A B ductam, & </s>
            <s xml:id="echoid-s2679" xml:space="preserve">propterea E H nan erit breuiſecans:
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            </s>
            <s xml:id="echoid-s2680" xml:space="preserve">Similiter breuiſsimaex G ad A B extenſa cadit infra
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            G M ad partes A, vt dictum eſt; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">at E G cadit
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            ſupra G M ad partes B; </s>
            <s xml:id="echoid-s2682" xml:space="preserve">ergo E G cadit
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            ſupra breuiſsimam ex G ad axim
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            A B ductam, quare E G non
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            eſt breuiſecans.</s>
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