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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[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
Page: 229 (191)
[222.] Notæ in Propoſit. XVIII. & XIX.
Page: 230 (192)
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
Page: 231 (193)
[224.] PROPOSITIO XXI.
Page: 233 (195)
[225.] PROPOSITIO XXII.
Page: 235 (197)
[226.] PROPOSITIO XXIII.
Page: 236 (198)
[227.] PROPOSITIO XXIV.
Page: 236 (198)
[228.] Notæ in Propoſit. XX.
Page: 237 (199)
[229.] Notæ in Propoſit. XXI.
Page: 241 (203)
[230.] Notæ in Propoſit. XXII.
Page: 243 (205)
[231.] Notæ in Propoſit. XXIII.
Page: 244 (206)
[232.] Notæ in Propoſit. XXIV.
Page: 245 (207)
[233.] SECTIO NONA Continens Propoſit. XXV.
Page: 245 (207)
[234.] Notæ in Propoſit. XXV.
Page: 246 (208)
[235.] LEMMA IX.
Page: 267 (229)
[236.] SECTIO DECIMA Continens Propoſit. XXVI. XXVII. & XXVIII. PROPOSITIO XXVI.
Page: 275 (237)
[237.] PROPOSITIO XXVII.
Page: 276 (238)
[238.] PROPOSITIO XXVIII.
Page: 278 (240)
[239.] Notæ in Propoſit. XXVI.
Page: 279 (241)
[240.] Notæ in Propoſit. XXVII.
Page: 280 (242)
[241.] Notæ in Propoſit. XXVIII.
Page: 284 (246)
[242.] LEMMAX.
Page: 284 (246)
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
Page: 285 (247)
[244.] PROPOSITIO XXX.
Page: 286 (248)
[245.] PROPOSITIO XXXI.
Page: 289 (251)
[246.] Notæ in Propoſit. XXIX.
Page: 291 (253)
[247.] Notæ in Propoſit. XXX.
Page: 292 (254)
[248.] Notæ in Propoſit. XXXI.
Page: 296 (258)
[249.] LIBRI SEXTI FINIS.
Page: 308 (270)
[250.] DEFINITIONES. I.
Page: 309 (271)
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              <pb o="156" file="0194" n="194" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0194-01" xlink:href="fig-0194-01a" number="210">
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            A B ſimilis eſt figuræ ſectionis E F, erit quadratum H E ad H b in H F,
              <lb/>
            vt quadratum A C ad C a in C B; </s>
            <s xml:id="echoid-s6105" xml:space="preserve">& </s>
            <s xml:id="echoid-s6106" xml:space="preserve">b H in H F ad quadratum H F,
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            vt a C in C B ad quadratum C B (nam poſuimus H F ad F b, vt C B ad
              <lb/>
            B a) ergo ex æqualitate, quadratũ E H ad quadratũ H F eſt, vt quadra-
              <lb/>
            tum A C ad quadratum C B: </s>
            <s xml:id="echoid-s6107" xml:space="preserve">& </s>
            <s xml:id="echoid-s6108" xml:space="preserve">propterea E Z ad H F eſt vt A S ad C
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            B; </s>
            <s xml:id="echoid-s6109" xml:space="preserve">Atque ſic oſtendetur, quod X Y ad N F ſit vt Q R ad L B, & </s>
            <s xml:id="echoid-s6110" xml:space="preserve">T V
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            ad M F ſit vt O P ad K B; </s>
            <s xml:id="echoid-s6111" xml:space="preserve">ergo proportiones ordinationum axis vnius
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            earum ad ſua abſciſſa ſunt eædem rationibus aliarum ordinationum axis
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            ad ſua abſciſſa, & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">alternatiuè. </s>
            <s xml:id="echoid-s6113" xml:space="preserve">Quare duæ ſectiones ſunt ſimiles.</s>
            <s xml:id="echoid-s6114" xml:space="preserve"/>
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          <note position="left" xml:space="preserve">Defin. 2.
            <lb/>
          huius.</note>
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            <s xml:id="echoid-s6115" xml:space="preserve">E contra oſtendetur, quod
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            ſi duæ ſectiones fuerint ſimi-
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                <image file="0194-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0194-02"/>
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            les, earũ figuræ ſimiles quo-
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            que erunt. </s>
            <s xml:id="echoid-s6116" xml:space="preserve">Quia eſt A C ad
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              buius.</note>
            C B, vt E H ad H F, & </s>
            <s xml:id="echoid-s6117" xml:space="preserve">ean-
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            dem proportionem habent
              <lb/>
            earum quadrata, atque
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            quadratum H F ad H F in
              <lb/>
            H b eſt, vt quadratum C B
              <lb/>
            ad C B in C a (eo quod
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            H F ad F b poſita fuit, vt
              <lb/>
            C B ad B a); </s>
            <s xml:id="echoid-s6118" xml:space="preserve">ergo ex æ-
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            qualitate quadratum E H ad
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            b H in H F, nempe I F
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            ad F b (20. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6120" xml:space="preserve">eſt, vt quadratum A C ad a C in C B, nempe vt
              <lb/>
              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">21. lib. 1.
                <lb/>
              Ibidem.</note>
            D B ad B a (20. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s6122" xml:space="preserve">; </s>
            <s xml:id="echoid-s6123" xml:space="preserve">quare figuræ duarum ſectionum ſunt ſimiles.
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            </s>
            <s xml:id="echoid-s6124" xml:space="preserve">Et hoc erat oſtendendum.</s>
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          <head xml:id="echoid-head246" xml:space="preserve">PROPOSITIO XIII.</head>
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            <s xml:id="echoid-s6128" xml:space="preserve">Hyperbolæ, ſeu ellipſis A B ſit axis B C, & </s>
            <s xml:id="echoid-s6129" xml:space="preserve">inclinatus, ſeu tranſuerſus
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            B a, & </s>
            <s xml:id="echoid-s6130" xml:space="preserve">E F ſit ſectio parabolæ, cuius axis F H. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">Dico, quod ſectio E F
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            non eſt ſimilis ſectioni A B hyperbolicæ, aut ellipticæ, alioquin ſit </s>
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