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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          <head xml:id="echoid-head120" xml:space="preserve">SECTIO DECIMA</head>
          <head xml:id="echoid-head121" xml:space="preserve">Continens Propof. XXXXIV. XXXXV.
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          Apollonij.</head>
          <p>
            <s xml:id="echoid-s2890" xml:space="preserve">SI ex axe recto ellipſis ſumatur menſura ab origine, quæ ad
              <lb/>
              <note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">a</note>
            ſemiaxim rectum non habeat minorem proportionem, quàm
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            habet figura ſuæ tranſuerſæ, tunc quicumque ramus ſecans, ab
              <lb/>
            illa origine ad fectionem ductus, abſcindit ex axe tranſuerſo ad
              <lb/>
            verticem ſectionis lineam minorem ea, quàm abſcindit linea
              <lb/>
            breuiſsima egrediens ab eius termino in ſectione poſito ad tran-
              <lb/>
            ſuerſum axim; </s>
            <s xml:id="echoid-s2891" xml:space="preserve">ſi vero fuerit proportio ad ſemirectum minor,
              <lb/>
            tunc ramorum ſecantium vnus eſt breuiſecans; </s>
            <s xml:id="echoid-s2892" xml:space="preserve">reliqui vero, qui
              <lb/>
            ſequuntur extremum tranſuerſæ habent proprietates ſuperius ex-
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            poſitas, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">qui ſequuntur extremitatem recti, ſecant ex tranſuer-
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            ſa lineam maiorem ea, quàm abſcindit breuiſsima egrediens ab
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            eius termino.</s>
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        <div xml:id="echoid-div265" type="section" level="1" n="88">
          <head xml:id="echoid-head122" xml:space="preserve">PROPOSITIO XXXXIV.</head>
          <p>
            <s xml:id="echoid-s2895" xml:space="preserve">Sit A D dimidium axis recti, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">minoris ſectionis ellipticæ
              <lb/>
              <note position="left" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">b</note>
            A B C, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">meuſura A E, quæ ſit maior, quàm A D, & </s>
            <s xml:id="echoid-s2898" xml:space="preserve">pro-
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            portio illius ad iſtam non ſit minor proportione figuræ ſectionis;
              <lb/>
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            <s xml:id="echoid-s2899" xml:space="preserve">Dico, quod linea breuiſsima egrediens ab extremitate cuiuſcum-
              <lb/>
            que rami ſecantis educti ex E ad ſectionem A B C, ſecat ex
              <lb/>
            tranuerſa B C cum vertice B, vel C lineam maiorem ea, quàm
              <lb/>
            abſcindit ille ramus.</s>
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            <s xml:id="echoid-s2901" xml:space="preserve">Ponatur ramus E F, & </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ducamus ex F ad vtrum-
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                <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0105-01"/>
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              <note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">c</note>
            que axim duas perpendiculares F H, F I. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Et quia
              <lb/>
            proportio E A ad A D non eſt minor proportio-
              <lb/>
            ne ſiguræ, ſed minor eſt, quàm E H ad H D, nem-
              <lb/>
            pe E F ad F G, ſeu D I ad I G, erit proportio ſigu-
              <lb/>
            ræ minor, quàm D I ad I G, & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ponamus D I ad
              <lb/>
            I K, vt eſt proportio figuræ, & </s>
            <s xml:id="echoid-s2905" xml:space="preserve">iungamus F K;
              <lb/>
            </s>
            <s xml:id="echoid-s2906" xml:space="preserve">erit ergo F K linea breuiſſima (10. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2908" xml:space="preserve">& </s>
            <s xml:id="echoid-s2909" xml:space="preserve">iam
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              <note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">10.
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              huius.</note>
            ſecat K B maiorem, quàm B G, & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">G F non erit
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            breuiſſima; </s>
            <s xml:id="echoid-s2911" xml:space="preserve">& </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc erat propoſitum.</s>
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