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.
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
[93.] PROPOSITIO LXX.
[94.] PROPOSITIO LXXI.
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
[99.] PROPOSITIO LXVI.
[100.] PROPOSITIO LXVII.
[101.] PROPOSITIO LXXII.
[102.] MONITVM.
[103.] LEMMA IX.
[104.] LEMMA X.
[105.] LEMMA XI.
[106.] Notæ in Propoſ. LXIV. & LXV.
[107.] Notæ in Propoſ. LXVI.
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
[109.] Notæ in Propoſ. LXVII.
[110.] COROLLARIVM PROPOSIT. LXVII.
[111.] Notæ in Propoſit. LXXII.
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
[113.] PROPOSITO LXXIV.
[114.] PROPOSITO LXXV.
[115.] PROPOSITIO LXXVI.
[116.] PROPOSITIO LXXVII.
[117.] Notæ in Propoſit. LXXIII.
[118.] LEMMA XII.
[119.] Notæ in Propoſ. LXXIV.
[120.] Notæ in Propoſit. LXXV.
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            in ellipſi, vt menſura ſumatur in maiori duorum axium, & </s>
            <s xml:id="echoid-s1791" xml:space="preserve">rami
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            egrediantur ad eius ſectionem.</s>
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        <div xml:id="echoid-div143" type="section" level="1" n="63">
          <head xml:id="echoid-head95" xml:space="preserve">PROPOSITIO IL. & L.</head>
          <p>
            <s xml:id="echoid-s1793" xml:space="preserve">EXE concurſu ſuper perpendicularem ED educamus E B ſe-
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            cantem menſuram A D in F, & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">ſectionem A B in B, & </s>
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              <lb/>
              <note position="left" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">b</note>
            ſit A H dimidium erecti; </s>
            <s xml:id="echoid-s1796" xml:space="preserve">ſitque menſura A D non maior, quàm
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            H A. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">Dico quod BF non erit breuiſſima, & </s>
            <s xml:id="echoid-s1798" xml:space="preserve">minima egrediens
              <lb/>
              <note position="left" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">c</note>
            ex B abſcindit ex ſagitta maiorem lineam, quàm F A: </s>
            <s xml:id="echoid-s1799" xml:space="preserve">at ſi fue-
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            rit A D maior , quàm A H, tunc B F poteſt eſſe linea breuiſ-
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            ſima.</s>
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            <s xml:id="echoid-s1801" xml:space="preserve">EDucamus iam B I perpendicularem ad axim, & </s>
            <s xml:id="echoid-s1802" xml:space="preserve">ſupponamus prius A
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            D non maiorem quàm A H , & </s>
            <s xml:id="echoid-s1803" xml:space="preserve">ſit ſectio parabole ; </s>
            <s xml:id="echoid-s1804" xml:space="preserve">igitur D I mi-
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              <note position="left" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">d</note>
            nor eſt , quàm A H, & </s>
            <s xml:id="echoid-s1805" xml:space="preserve">ponatur G I æqualis A H, erit B G minima (8.
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            </s>
            <s xml:id="echoid-s1806" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1807" xml:space="preserve">abſcindit G A ex ſagitta maiorem , quàm A F; </s>
            <s xml:id="echoid-s1808" xml:space="preserve">ſi verò ſe-
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            ctio fuerit hyperbole, aut ellipſis, ſit centrum C; </s>
            <s xml:id="echoid-s1809" xml:space="preserve">ergo A C ad A H non
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            habet maiorem proportionem, quàm ad A D, quare C I ad I F maiorem
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            proportionem habet, quàm C A ad A H; </s>
            <s xml:id="echoid-s1810" xml:space="preserve">ponatur ergo I C ad I G , vt
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            A C ad A H; </s>
            <s xml:id="echoid-s1811" xml:space="preserve">ergo B G eſt minima , & </s>
            <s xml:id="echoid-s1812" xml:space="preserve">abſcindit (9. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">& </s>
            <s xml:id="echoid-s1814" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">ex quinto)
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            G A maiorem , quam F A, quod erat oſtendendum.</s>
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