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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[251.] II.
Page: 309 (271)
[252.] III.
Page: 309 (271)
[253.] IV.
Page: 309 (271)
[254.] V.
Page: 309 (271)
[255.] VI.
Page: 309 (271)
[256.] VII.
Page: 310 (272)
[257.] VIII.
Page: 310 (272)
[258.] NOTÆ.
Page: 310 (272)
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
Page: 311 (273)
[260.] PROPOSITIO V. & XXIII.
Page: 312 (274)
[261.] Notæ in Propoſit. I.
Page: 312 (274)
[262.] Notæ in Propoſit. V. & XXIII.
Page: 313 (275)
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
Page: 314 (276)
[264.] PROPOSITIO IV.
Page: 315 (277)
[265.] PROPOSITIO VI. & VII.
Page: 316 (278)
[266.] Notæ in Propoſit. II. III.
Page: 317 (279)
[267.] Notæ in Propoſit. IV.
Page: 318 (280)
[268.] Notæ in Propoſit. VI. & VII.
Page: 319 (281)
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
Page: 320 (282)
[270.] Notæ in Propoſit. VIII.
Page: 323 (285)
[271.] Notæ in Propoſit. IX.
Page: 324 (286)
[272.] Notæ in Propoſit. X.
Page: 325 (287)
[273.] Notæ in Propoſit. XI.
Page: 325 (287)
[274.] Notæ in Propoſit. XV.
Page: 326 (288)
[275.] Notæ in Propoſit. XIX.
Page: 326 (288)
[276.] Notæ in Propoſit. XVI.
Page: 327 (289)
[277.] Notæ in Propoſit. XVIII.
Page: 327 (289)
[278.] Notæ in Propoſit. XVII.
Page: 328 (290)
[279.] Notæ in Propoſit. XX.
Page: 328 (290)
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
Page: 329 (291)
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            vltra centrum in eadem asymptoti produ{ct}ione A Z; </s>
            <s xml:id="echoid-s7847" xml:space="preserve">aut F I ſupra, & </s>
            <s xml:id="echoid-s7848" xml:space="preserve">G K in-
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            fra centrum A exiſtat: </s>
            <s xml:id="echoid-s7849" xml:space="preserve">In quo libet caſu dicetur, F I vlterius tendere ad partes
              <lb/>
            centri, vel asymptoti A B, quàm G K.</s>
            <s xml:id="echoid-s7850" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7851" xml:space="preserve">Non ſecus ſi ab eadem asymptoto A C educantur quatuor rectæ lineæ inter ſe
              <lb/>
            æquidiſtantes F I, G K, H L, C E, quarum duæ priores F I, G K, centro pro-
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            pinquiores ſint, quando omnes infra centrum A collocantur; </s>
            <s xml:id="echoid-s7852" xml:space="preserve">vel magis à centro
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            recedant, quando omnes in productione A Z exiſtunt; </s>
            <s xml:id="echoid-s7853" xml:space="preserve">aut certe duæ F I, G K
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            ſupra centrum, & </s>
            <s xml:id="echoid-s7854" xml:space="preserve">H L, C E infra centrum exiſtant: </s>
            <s xml:id="echoid-s7855" xml:space="preserve">Tunc ſimiliter in quoli-
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            bet caſu dicentur rectæ lineæ F I, G K vlterius tendere ad partes centri, & </s>
            <s xml:id="echoid-s7856" xml:space="preserve">
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            asympoti A B, quàm duæ aliæ H L, C E.</s>
            <s xml:id="echoid-s7857" xml:space="preserve"/>
          </p>
          <figure number="285">
            <image file="0248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-01"/>
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          <note position="left" xml:space="preserve">PROP.2.
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          Addit.</note>
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            <s xml:id="echoid-s7858" xml:space="preserve">Si in vna aſymptoto A C, hyperboles D E ſumantur duo ſegmenta
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            æqualia F G, H C, & </s>
            <s xml:id="echoid-s7859" xml:space="preserve">à punctis diuiſionum ducantur quatuor rectæ
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            lineæ F I, G K, H L, C E parallelæ inter ſe, vſque ad hyperbolen:
              <lb/>
            </s>
            <s xml:id="echoid-s7860" xml:space="preserve">Dico quod differentia duarum æquidiſtantium F I, G K ad partes cen-
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            tri, & </s>
            <s xml:id="echoid-s7861" xml:space="preserve">alterius aſymptoti A B vlterius tendentium, maior erit differen-
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            tia reliquarum H L, C E.</s>
            <s xml:id="echoid-s7862" xml:space="preserve"/>
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            <s xml:id="echoid-s7863" xml:space="preserve">Ducantnr à punctis E, K rectæ
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                <image file="0248-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-02"/>
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            lineæ E S, K R parallelæ asympto-
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            to A C, quæ efficiant parallelogrã-
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            ma C S, G R. </s>
            <s xml:id="echoid-s7864" xml:space="preserve">Patet I R eſſe dif-
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            ferentiam æquidiſtantium F I, & </s>
            <s xml:id="echoid-s7865" xml:space="preserve">
              <lb/>
            G K; </s>
            <s xml:id="echoid-s7866" xml:space="preserve">pariterque L S eſſe differen-
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            tiam æquidiſtantium H L, C E;
              <lb/>
            </s>
            <s xml:id="echoid-s7867" xml:space="preserve">& </s>
            <s xml:id="echoid-s7868" xml:space="preserve">coniungantur rectæ lineæ E I,
              <lb/>
            & </s>
            <s xml:id="echoid-s7869" xml:space="preserve">K I, ducaturque E O parallela
              <lb/>
            I K, ſecans H L in O. </s>
            <s xml:id="echoid-s7870" xml:space="preserve">Et quia
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            recta linea E I cadit intra curuam
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            ſectionem conicam E K I, & </s>
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            ctum K eiuſdem conicæ </s>
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