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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[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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            <s xml:id="echoid-s3595" xml:space="preserve">Quod autem infimus ramus breuiſecans D C non ſit neceſſario minimus om-
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            nium ramorum cadentium ad peripheriam ſectionis A B, modò oſtendetur.</s>
            <s xml:id="echoid-s3596" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3597" xml:space="preserve">In coniſectione duos ramos hreuiſecantes, ducere, quorum infimus
              <lb/>
              <note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">PROB.6.
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              Addit.</note>
            maior ſit ramo ſecante poſito in peripheria à vertice, & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">ſuprema bre-
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            uiſecante compræhenſa: </s>
            <s xml:id="echoid-s3599" xml:space="preserve">oportet autem in ellipſi, vt rami ſecantes ad
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            vnum eius quadrantem ducantur à concurſu, inter axim minorem, & </s>
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            verticem collocato.</s>
            <s xml:id="echoid-s3601" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3602" xml:space="preserve">In coniſectione A B C, cuius ver-
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                <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01"/>
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            tex A axis A D, & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">in hyperbola,
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            & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">ellipſi centrum E ducatur quæli-
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              <note position="left" xlink:label="note-0124-02" xlink:href="note-0124-02a" xml:space="preserve">8. 9. 10.
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              huius.</note>
            bet breuiſsima F B: </s>
            <s xml:id="echoid-s3605" xml:space="preserve">poſtea ſecetur
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            F G ex axi, ita vt punctum G non
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            cadat ſupra verticem A, ſeceturque
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            F H non maior, quam F G, ducan-
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            turque rectæ H C, G G parallelæ ipſi
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            F B occurrentes ſectioni in C, & </s>
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            G, coniungaturque recta C G ſecans
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            F B in I: </s>
            <s xml:id="echoid-s3607" xml:space="preserve">patet, C I maiorem non
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            eſſe, quàm I G; </s>
            <s xml:id="echoid-s3608" xml:space="preserve">propterea quod G C,
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            G H à parallelis ſecantur proportio-
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            <s xml:id="echoid-s3609" xml:space="preserve">Deinde ex C ducatur alia
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              26. 27. 28.
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              huius.</note>
            breuiſsima C K, occurrens B F vl-
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            tra axim in L, iungaturque ramus
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            G L: </s>
            <s xml:id="echoid-s3610" xml:space="preserve">oſtendendum eſt L C maiorem
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            eſſe, quàm L G. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Secetur C G bifa-
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            riam in M, atque per M ducatur ſe-
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            ctionis diameter M N parallela axi
              <lb/>
            in parabola, & </s>
            <s xml:id="echoid-s3612" xml:space="preserve">per centrum exſten-
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            ſa in reliquis ſectionibus, occurrens
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            ſectioni in N, ducaturque O N ſe-
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            ctionem contingens in N, iungantur-
              <lb/>
              <note position="left" xlink:label="note-0124-04" xlink:href="note-0124-04a" xml:space="preserve">33. 34.
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              lib. 1.</note>
            que L M, & </s>
            <s xml:id="echoid-s3613" xml:space="preserve">L N, quæ ſecet G C in
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            P. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Quoniam G I æqualis, aut ma-
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            ior eſt, quàm I C, cadet punctum
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            M bipartitæ diuiſionis totius C G,
              <lb/>
            vel in I, vel inter I, G, & </s>
            <s xml:id="echoid-s3615" xml:space="preserve">in vtro-
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            que caſu punctum N cadet inter G,
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            & </s>
            <s xml:id="echoid-s3616" xml:space="preserve">B (eoquod diameter M N paral-
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            lela axi in parabola, aut ex centro
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            E educta in reliquis ſectionibus effi-
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            cit angulum N M L ad partes ver-
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            ticis A) & </s>
            <s xml:id="echoid-s3617" xml:space="preserve">ideo ramus L N cadens
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            ſupra duos breuiſecantes L C, L B
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            ad partes verticis efficit cum </s>
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