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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            entes; </s>
            <s xml:id="echoid-s5977" xml:space="preserve">ideoque ſi vnus eorum, nempe Z T extrinſecùs tangit communem portio-
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            nem conicam B C, reliquus V X extrinſecùs quoque eam langet, ſed ex conſtru-
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            ctione intrinſecùs ſectionem tangebat, quod eſt abſurdum: </s>
            <s xml:id="echoid-s5978" xml:space="preserve">Non ergo duæ por-
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            tiones B C, & </s>
            <s xml:id="echoid-s5979" xml:space="preserve">E F non æquè à verticibus axium remotæ ſibi mutuo congruent-
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            Quod erat oſtendendum.</s>
            <s xml:id="echoid-s5980" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5981" xml:space="preserve">Si autem cadit in ellipſi axis A C tranſuerſus ſuper axim rectum illius;
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            <s xml:id="echoid-s5982" xml:space="preserve">
              <note position="right" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">b</note>
            vtique excedit illam, & </s>
            <s xml:id="echoid-s5983" xml:space="preserve">non ſibi mutuò congruunt ſectiones, & </s>
            <s xml:id="echoid-s5984" xml:space="preserve">quædam
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            congruunt, &</s>
            <s xml:id="echoid-s5985" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5986" xml:space="preserve">Senſus eſt. </s>
            <s xml:id="echoid-s5987" xml:space="preserve">Si intelligantur duæ ellipſes, habentes axes tran-
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            ſuerſos A B, & </s>
            <s xml:id="echoid-s5988" xml:space="preserve">G H æquales inier ſe, pariterque
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            axes rectos C D, I K æquales: </s>
            <s xml:id="echoid-s5989" xml:space="preserve">& </s>
            <s xml:id="echoid-s5990" xml:space="preserve">axis A B tran-
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            ſuerſus vnius ponatur ſuper I K axim rectum al-
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            terius, ita vt centra ſibi mutuò congruant in E:
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            </s>
            <s xml:id="echoid-s5991" xml:space="preserve">tunc quidem, quia axes in ellipſi inæquales ſunt
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            (alias eſſet circulus) igitur extremitates axis tran-
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            ſuerſi A B non cadunt ſuper extremitaites axis re-
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            cti K I, neque G, H cadunt ſuper C, D; </s>
            <s xml:id="echoid-s5992" xml:space="preserve">& </s>
            <s xml:id="echoid-s5993" xml:space="preserve">ideo
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            circumferentiæ ellipſium ſe ſe mutuò ſecant qua-
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            tuor in locis, vt in libro 4. </s>
            <s xml:id="echoid-s5994" xml:space="preserve">oſtenſnm eſt.</s>
            <s xml:id="echoid-s5995" xml:space="preserve"/>
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          <head xml:id="echoid-head240" xml:space="preserve">SECTIO TERTIA
            <lb/>
          Continens Propoſit. V. & VIII.
            <lb/>
          PROPOSITIO V.</head>
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            <s xml:id="echoid-s5996" xml:space="preserve">SI per centrum E ellipſis A B, C D tranſeat linea recta A
              <lb/>
            C vſque ad ſectionem; </s>
            <s xml:id="echoid-s5997" xml:space="preserve">vtique bifariam diuidit ſuperſiciem
              <lb/>
            ſectionis, & </s>
            <s xml:id="echoid-s5998" xml:space="preserve">circumferentiam illius, ſcilicet erit ſuperſicies A B
              <lb/>
            C æqualis ſuperficiei A D C.</s>
            <s xml:id="echoid-s5999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6000" xml:space="preserve">Nam ſi A C fuerit axis ſectio-
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            nis, vtique circumferentia A B C
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            congruet A D C, nam ſi non cõ-
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            gruit ſignemus locum B, quod al-
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            teri ſectioni nõ coincidat, & </s>
            <s xml:id="echoid-s6001" xml:space="preserve">pro-
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            ducamus ex illo perpendicularem
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            B F ſuper A C vſque ad D. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">Er-
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            go B D ordinata eſt ad C A, & </s>
            <s xml:id="echoid-s6003" xml:space="preserve">
              <lb/>
            propterea B F ſuperpoſita cõgru-
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            et ipſi D F, & </s>
            <s xml:id="echoid-s6004" xml:space="preserve">cadet B ſuper D,
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            quia B F æqualis eſt D F (8. </s>
            <s xml:id="echoid-s6005" xml:space="preserve">ex
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            1.)</s>
            <s xml:id="echoid-s6006" xml:space="preserve">; </s>
            <s xml:id="echoid-s6007" xml:space="preserve">ſed non cadebat ſuper illum; </s>
            <s xml:id="echoid-s6008" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">Igitur </s>
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