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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[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)
[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)
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            (qui eſt D B) cadit ſupra breuiſsimam ex puncto I ad axim ductam, quæ per-
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              <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">51. 52.
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            pendicularis eſt ad tangentem L I H, & </s>
            <s xml:id="echoid-s3300" xml:space="preserve">propterea angulus D I L, verticem
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              huius.</note>
            A reſpiciens erit acutus, & </s>
            <s xml:id="echoid-s3301" xml:space="preserve">conſequens angulus D I H obtuſus.</s>
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        <div xml:id="echoid-div315" type="section" level="1" n="105">
          <head xml:id="echoid-head145" xml:space="preserve">LEMMA XI.</head>
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            <s xml:id="echoid-s3303" xml:space="preserve">Iiſdem poſitis, ſi à concurſu D duo breuiſecantes D C, D B ad ſe-
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            ctionem A B duci poſſunt; </s>
            <s xml:id="echoid-s3304" xml:space="preserve">Dico, quod quilibet ramus ſecans D I poſi-
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            tus ſupra breuiſecantem D B vertici proximiorem, vel infra infimum
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            breuiſecantem D C, efficit cum recta L I H tangente ſectionem in I an-
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            gulum D I L, reſpicientem verticem A, acutum, & </s>
            <s xml:id="echoid-s3305" xml:space="preserve">conſequentem D
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            I H obtuſum, & </s>
            <s xml:id="echoid-s3306" xml:space="preserve">quilibet ramus D O inter breuiſecantes poſitus efficit
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            cum recta G O N ſectionem tangente in O angulum D O G verticem
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            reſpicientem obtuſum, conſequentem vero D O N acutum.</s>
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            <s xml:id="echoid-s3308" xml:space="preserve">Quia (ex conuerſa propoſitione 51. </s>
            <s xml:id="echoid-s3309" xml:space="preserve">& </s>
            <s xml:id="echoid-s3310" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3311" xml:space="preserve">huius) perpendicularis D E mi-
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              <note position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">51. 52.
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              huius.</note>
            nor eſſe debet Trutina F, & </s>
            <s xml:id="echoid-s3312" xml:space="preserve">propterea quilibet ramus D I ſupra breuiſecantem
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            D B, vel infra breuiſecãtem D C cadit ſupra breuiſsimam ex puncto I ad axim
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              <note position="right" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">29. 30.
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              huius.</note>
            ductam, cum qua contingens L I angulum rectum conſtituit; </s>
            <s xml:id="echoid-s3313" xml:space="preserve">ergo angulus D I
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            L verticem reſpiciens, eſt acutus, & </s>
            <s xml:id="echoid-s3314" xml:space="preserve">conſequens D I H obtuſus; </s>
            <s xml:id="echoid-s3315" xml:space="preserve">Similiter qui-
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            libet ramus D O inter breuiſecantes poſitus cadit infra breuiſsimam ex puncto
              <lb/>
            O ad axim ductam, & </s>
            <s xml:id="echoid-s3316" xml:space="preserve">cum illa ſectionem contingens G O efſicit angulos rectos,
              <lb/>
              <note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">Ibidem.</note>
            igitur angulus D O G verticem reſpiciens, eſt obtuſus, & </s>
            <s xml:id="echoid-s3317" xml:space="preserve">conſequens D O N
              <lb/>
            acutus.</s>
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        <div xml:id="echoid-div317" type="section" level="1" n="106">
          <head xml:id="echoid-head146" xml:space="preserve">Notæ in Propoſ. LXIV.
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          & LXV.</head>
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            <s xml:id="echoid-s3319" xml:space="preserve">ANtea Apollonius docuit qui nam rami ab origine ad coniſectionem ducti
              <lb/>
            eſſent minimi, & </s>
            <s xml:id="echoid-s3320" xml:space="preserve">quo ordine reliqui rami ſe ſe excederent, modo agit
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            de ramis axim ſecantibus à concurſu ductis, & </s>
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            <s xml:id="echoid-s3322" xml:space="preserve">qui
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            maximus ſit, & </s>
            <s xml:id="echoid-s3323" xml:space="preserve">quo ordine diſponantur.</s>
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            <s xml:id="echoid-s3325" xml:space="preserve">Producamus perpendicularem D E ſuper axim, &</s>
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            <s xml:id="echoid-s3327" xml:space="preserve">Si nullus ramus
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            breuiſecans à concurſu D ad ſectionem A C duci poteſt; </s>
            <s xml:id="echoid-s3328" xml:space="preserve">Dico, quod ramus ter-
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            minatus D A eſt minimus omnium ramorum ſecantium D B, D C, & </s>
            <s xml:id="echoid-s3329" xml:space="preserve">propin-
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            quiores vertici A minores ſunt remotioribus; </s>
            <s xml:id="echoid-s3330" xml:space="preserve">ducatur D E perpendicularis ad
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            axim eum ſecans in E, & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">reperiatur Trutina F. </s>
            <s xml:id="echoid-s3332" xml:space="preserve">Et ſiquidem D A non eſt
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            minor quolibet alio ramo ſecante D B infra ipſum poſito erit æqualis, aut maior
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            illo; </s>
            <s xml:id="echoid-s3333" xml:space="preserve">ſitque prius D A æqualis D B, ſi fieri poteſt, & </s>
            <s xml:id="echoid-s3334" xml:space="preserve">ex puncto A verticis du-
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            catur A G perpendicularis ad axim A E, quæ continget ſectionem in A, pari-
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              <note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">17. lib. 1.
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              32. pr.</note>
            terque ducatur recta A H perpendicularis ad ramum A D inclinatum ad axim;</s>
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