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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[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)
[281.] Notæ in Propoſit. XII.
Page: 332 (293)
[282.] Notæ in Propoſit. XIII.
Page: 333 (294)
[283.] Notæ in Propoſit. XXIX.
Page: 334 (295)
[284.] Notæ in Propoſit. XXX.
Page: 334 (295)
[285.] Notæ in Propoſit. XIV. & XXV.
Page: 335 (296)
[286.] Notæ in Propoſit. XXVII.
Page: 335 (296)
[287.] SECTIO QVINTA Continens Propoſit. XXI. XXVIII. XXXXII. XXXXIII. XXIV. & XXXVII.
Page: 337 (298)
[288.] PROPOSITIO XXI. & XXVIII.
Page: 338 (299)
[289.] PROPOSITIO XXVI
Page: 339 (300)
[290.] PROPOSITIO XXXXII.
Page: 340 (301)
[291.] PROPOSITIO XXXXIII.
Page: 341 (302)
[292.] PROPOSITIO XXIV.
Page: 342 (303)
[293.] PROPOSITIO XXXVII.
Page: 343 (304)
[294.] Notę in Propoſit. XXVIII.
Page: 344 (305)
[295.] LEMMA. I.
Page: 345 (306)
[296.] Notę in Propoſit. XXI.
Page: 347 (308)
[297.] Notę in Propoſit. XXXXII.
Page: 349 (310)
[298.] Notæ in Propoſit. XXXXIII.
Page: 350 (311)
[299.] Notæ in Propoſit. XXIV.
Page: 352 (313)
[300.] SECTIO SEXTA Continens Propoſit. XXXIII. XXXIV. XXXV. & XXXVI. PROPOSITIO XXXIII.
Page: 353 (314)
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              <pb o="149" file="0187" n="187" rhead="Conicor. Lib. V."/>
            ergo non congruit portio alicuius
              <lb/>
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            ſectionis portioni alterius ſectionis,
              <lb/>
            cui æqualis non eſt. </s>
            <s xml:id="echoid-s5857" xml:space="preserve">Et hoc erat
              <lb/>
            oſtendendum.</s>
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        <div xml:id="echoid-div558" type="section" level="1" n="181">
          <head xml:id="echoid-head235" xml:space="preserve">Notæ in Propoſit. III.</head>
          <p>
            <s xml:id="echoid-s5859" xml:space="preserve">ETenim ellipſis non eſt æqualis alicui hyperbolæ, &</s>
            <s xml:id="echoid-s5860" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5861" xml:space="preserve">Suppleri debet in
              <lb/>
            textu verbum (parabolæ) dicendo. </s>
            <s xml:id="echoid-s5862" xml:space="preserve">Etenim ellipſis non eſt æqualis alicui
              <lb/>
              <note position="left" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">a</note>
            parabolæ, aut hyperbolæ, quia illa eſt determinata; </s>
            <s xml:id="echoid-s5863" xml:space="preserve">hæ verò ſunt indeterminatæ,
              <lb/>
            ſcilicet ellipſis eſt finita parabole verò, & </s>
            <s xml:id="echoid-s5864" xml:space="preserve">hyperbole in infinitum extendi poſ-
              <lb/>
            ſunt, & </s>
            <s xml:id="echoid-s5865" xml:space="preserve">propterea nulla ratione æquales oſtendentur.</s>
            <s xml:id="echoid-s5866" xml:space="preserve"/>
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        <div xml:id="echoid-div560" type="section" level="1" n="182">
          <head xml:id="echoid-head236" xml:space="preserve">Notæ in Propoſit. VI.</head>
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            <s xml:id="echoid-s5867" xml:space="preserve">QVælibet duæ ſectiones A B C, D E
              <lb/>
              <note position="left" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">a</note>
            F, quarum vnaquæque literarum
              <lb/>
            ſuperpoſita literis alterius con-
              <lb/>
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            gruit; </s>
            <s xml:id="echoid-s5868" xml:space="preserve">vtique ſunt æquales, &</s>
            <s xml:id="echoid-s5869" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5870" xml:space="preserve">Legendum
              <lb/>
            puto. </s>
            <s xml:id="echoid-s5871" xml:space="preserve">Quælibet duæ ſectiones A B C, & </s>
            <s xml:id="echoid-s5872" xml:space="preserve">D
              <lb/>
            E F, quarum portio vnius, alterius portioni
              <lb/>
            ſuperpoſita congruit ſunt æquales inter ſe.</s>
            <s xml:id="echoid-s5873" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div562" type="section" level="1" n="183">
          <head xml:id="echoid-head237" xml:space="preserve">Notæ in Propoſit. VII.</head>
          <p>
            <s xml:id="echoid-s5874" xml:space="preserve">ORdinationes axis in qualibet hyper-
              <lb/>
              <note position="left" xlink:label="note-0187-03" xlink:href="note-0187-03a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0187-03" xlink:href="fig-0187-03a" number="200">
                <image file="0187-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0187-03"/>
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            bolarum abſcindunt à ſectione ex
              <lb/>
            vtraque parte axis duo ſegmenta, quæ,
              <lb/>
            ſi cadit vnum ſuper alterum, ſibi mutuò
              <lb/>
            congruunt, nec excedunt, nec deficiunt,
              <lb/>
            nec congruunt alicui portioni ſectionis,
              <lb/>
            &</s>
            <s xml:id="echoid-s5875" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5876" xml:space="preserve">Expungi debent verba aliqua huius te-
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            xtus ſuperuacanea, & </s>
            <s xml:id="echoid-s5877" xml:space="preserve">aliqua adiungi, vt ſenſus continuus talis ſit. </s>
            <s xml:id="echoid-s5878" xml:space="preserve">Duæ
              <lb/>
            ordinationes axis in qualibet coniſectione abſcindunt à ſectione ex vtraque
              <lb/>
            parte, axis duas portiones, quarum vna alteri ſuperpoſita ſibi mutuò congruent,
              <lb/>
            nec cõgruunt alicui aliæ portioni ſectionis.</s>
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            <s xml:id="echoid-s5880" xml:space="preserve">Quoniam axis B D bifariam diuidit G H, A C, &</s>
            <s xml:id="echoid-s5881" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">Ex eo
              <lb/>
              <note position="left" xlink:label="note-0187-04" xlink:href="note-0187-04a" xml:space="preserve">b</note>
            enim quod omnes applicatæ ad axim B D ſecantur bifariam </s>
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