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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[311.] PROPOSITIO XXXIX.
Page: 363 (324)
[312.] PROPOSITIO XXXX.
Page: 364 (325)
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
Page: 366 (327)
[314.] LEMMA VII.
Page: 366 (327)
[315.] LEMMA VIII.
Page: 367 (328)
[316.] LEMMA IX.
Page: 367 (328)
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
Page: 369 (330)
[318.] Notæ in Propoſit. XXXX.
Page: 369 (330)
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
Page: 372 (333)
[320.] PROPOSITIO XXXXVI.
Page: 374 (335)
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
Page: 375 (336)
[322.] LEMM A XI.
Page: 375 (336)
[323.] LEMM A XII.
Page: 376 (337)
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
Page: 378 (339)
[325.] Notæ in Propoſit. XXXXVI.
Page: 378 (339)
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
Page: 380 (341)
[327.] PROPOSITIO XXXXI.
Page: 382 (343)
[328.] PROPOSITIO XXXXVII.
Page: 383 (344)
[329.] PROPOSITIO XXXXVIII.
Page: 386 (347)
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
Page: 388 (349)
[331.] LEMMA XIV.
Page: 389 (350)
[332.] LEMMA XV.
Page: 389 (350)
[333.] Notæ in Propoſit. XXXXI.
Page: 392 (353)
[334.] Notæ in Propoſit. XXXXVII.
Page: 393 (354)
[335.] Notæ in Propoſit. XXXXVIII.
Page: 394 (355)
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
Page: 397 (358)
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
Page: 400 (361)
[338.] LEMMA XVII.
Page: 400 (361)
[339.] LEMMA XVIII.
Page: 403 (364)
[340.] Notæ in Propoſit. XXXXIX.
Page: 404 (365)
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          <pb o="72" file="0110" n="110" rhead="Apollonij Pergæi"/>
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            <s xml:id="echoid-s3066" xml:space="preserve">Patet ex hoc, quod ſi producantur ex duo-
              <lb/>
              <note position="right" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">d</note>
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                <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-01"/>
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            bus punctis contactus in ellipſi perpendiculares
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            E M, A L; </s>
            <s xml:id="echoid-s3067" xml:space="preserve">& </s>
            <s xml:id="echoid-s3068" xml:space="preserve">fuerit E M minor, exempli gra-
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            tia, tunc tangens educta ab eius extremitate,
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            quæ eſt in ſectione, minor quoque eſt, &</s>
            <s xml:id="echoid-s3069" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Si
              <lb/>
            enim ex punctis E, A contactuum in ellipſi ducan-
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            tur ad axim minorem K C perpendiculares E M,
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            & </s>
            <s xml:id="echoid-s3071" xml:space="preserve">A L ſecantes eum in M, & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">L, fueritque E M
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            minor, quàm A L, tunc quidem punctum E magis
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            recedit à vertice B axis maioris, quàm punctum
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            A; </s>
            <s xml:id="echoid-s3073" xml:space="preserve">& </s>
            <s xml:id="echoid-s3074" xml:space="preserve">propterea, ex præmiſſa 70. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">huius libri, erit
              <lb/>
            tangens E F minor, quàm A F. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Expungo deter-
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            minationem ab aliquo incaute additam (quæ eſt in
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            ſectione) manifeſtum enim eſt ducinon poſſe contin-
              <lb/>
            gentem ellipſim à perpendicularis termino M in axi minori poſito, ſed à termi-
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            no E in ſectionis peripheria conſtituto.</s>
            <s xml:id="echoid-s3077" xml:space="preserve"/>
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        <div xml:id="echoid-div290" type="section" level="1" n="96">
          <head xml:id="echoid-head132" xml:space="preserve">SECTIO DVODECIMA</head>
          <head xml:id="echoid-head133" xml:space="preserve">Continens XXIX. XXX. XXXI.</head>
          <head xml:id="echoid-head134" xml:space="preserve">Propoſ. Appollonij.</head>
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            <s xml:id="echoid-s3078" xml:space="preserve">Q Vælibet linea recta A E D tangens fectionem aliquam A
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            F B in A extremitate lineæ breuiſſimæ A C eſt perpeudi-
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            cularis ſuper illam, nẽpe D A C eſt angulus rectus.
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            </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Et ſi fuerit perpendicularis ſuper illam vtique tanget ſectio-
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            nem.</s>
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            <s xml:id="echoid-s3081" xml:space="preserve">Alioquin producatur perpendicu-
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              <figure xlink:label="fig-0110-02" xlink:href="fig-0110-02a" number="92">
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            laris C E ſuper A D, erit A C maior,
              <lb/>
            quàm E C, ergo maior eſt, quàm F
              <lb/>
            C; </s>
            <s xml:id="echoid-s3082" xml:space="preserve">ſed eſt minor, cũ ſit minor, quàm
              <lb/>
            C F, quod eſt abſurdum. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Igitur an-
              <lb/>
            gulus D A C, eſt rectus, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s3084" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3085" xml:space="preserve">Si verò fuerit D A C rectus, erit
              <lb/>
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            A D tangens, alioquin ſit tangens A
              <lb/>
            G; </s>
            <s xml:id="echoid-s3086" xml:space="preserve">ergo C A G erit rectus, ſed erat
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            C A D rectus, quod eſt abſurdum;
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            <s xml:id="echoid-s3087" xml:space="preserve">ergo A D eſt tangens, & </s>
            <s xml:id="echoid-s3088" xml:space="preserve">hoc erat
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            probandum.</s>
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