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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[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)
[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)
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            duplum H M in C M minus duobus quadratis ex M H, & </s>
            <s xml:id="echoid-s12026" xml:space="preserve">ex G M: </s>
            <s xml:id="echoid-s12027" xml:space="preserve">& </s>
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            propterea A M in M C bis ſumptum ad H M in M C bis ſumptum, nẽ-
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            pe A M ad M H habebit maiorem proportionem, quam duplum A M
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            in M C ad duo quadrata ex H M, & </s>
            <s xml:id="echoid-s12029" xml:space="preserve">ex G M: </s>
            <s xml:id="echoid-s12030" xml:space="preserve">& </s>
            <s xml:id="echoid-s12031" xml:space="preserve">componendo A H ad
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            H M, ſeu quadratum A H ad A H in H M maiorem proportionem ha-
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            bebit quàm duplum A M in M C cum duobus quadratis ex H M, & </s>
            <s xml:id="echoid-s12032" xml:space="preserve">ex
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            M G (quæ omnia ſimul æqualia ſunt duobus quadratis C G, & </s>
            <s xml:id="echoid-s12033" xml:space="preserve">H C)
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            ad duo quadrata M H, & </s>
            <s xml:id="echoid-s12034" xml:space="preserve">M G; </s>
            <s xml:id="echoid-s12035" xml:space="preserve">igitur quadratum A H ad A H in H M
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            maiorem proportionem habet, quàm duo quadrata C G, & </s>
            <s xml:id="echoid-s12036" xml:space="preserve">C H ad duo
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            quadrata H M, & </s>
            <s xml:id="echoid-s12037" xml:space="preserve">G M, & </s>
            <s xml:id="echoid-s12038" xml:space="preserve">permutando quadratum A H ad duo qua-
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            drata C G, & </s>
            <s xml:id="echoid-s12039" xml:space="preserve">H C, ſcilicet quadratum A C ad quadratum diametri
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            figuræ eius maiorem proportionem habet, quàm A H in H M ad duo
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            quadrata M G, & </s>
            <s xml:id="echoid-s12040" xml:space="preserve">M H, ſeu quàm quadratum A C ad quadratum dia-
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            metri figuræ P Q (19. </s>
            <s xml:id="echoid-s12041" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12042" xml:space="preserve">quapropter diameter figuræ P Q maior
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            eſt diametro figuræ A C. </s>
            <s xml:id="echoid-s12043" xml:space="preserve">Ducatur poſtea diameter S T, & </s>
            <s xml:id="echoid-s12044" xml:space="preserve">ad eam or-
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            dinatim applicata A X, & </s>
            <s xml:id="echoid-s12045" xml:space="preserve">ad axim
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            perpendicularem X V. </s>
            <s xml:id="echoid-s12046" xml:space="preserve">Et ſiqui-
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            dem G M minor eſt, quàm V H
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            cum A G, & </s>
            <s xml:id="echoid-s12047" xml:space="preserve">C H ſint æquales,
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            erunt duo quadrata H M, & </s>
            <s xml:id="echoid-s12048" xml:space="preserve">M G
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            maiora duobus quadratis H V, V
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            G: </s>
            <s xml:id="echoid-s12049" xml:space="preserve">hæc autem maiora ſunt quàm
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            duplum V H in V d: </s>
            <s xml:id="echoid-s12050" xml:space="preserve">ergo duplũ
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            M V in V d ad duplum H V in V
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            d, nempe V M ad V H maiorem
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            proportionem habet, quàm duplũ
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            M V in V d ad duo quadrata ex
              <lb/>
            V H, & </s>
            <s xml:id="echoid-s12051" xml:space="preserve">ex V G: </s>
            <s xml:id="echoid-s12052" xml:space="preserve">& </s>
            <s xml:id="echoid-s12053" xml:space="preserve">componendo
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            M H ad H V, ſeu M H in H A
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            ad V H in H A maiorem propor-
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            tionem habebit, quàm duplum M
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            V in V d cum duobus quadratis ex
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            V H, & </s>
            <s xml:id="echoid-s12054" xml:space="preserve">ex V G, quæ omnia ſi-
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            mul ſunt vt duo quadrata M H, & </s>
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            M G ad duo quadrata V H, & </s>
            <s xml:id="echoid-s12056" xml:space="preserve">V
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            G: </s>
            <s xml:id="echoid-s12057" xml:space="preserve">& </s>
            <s xml:id="echoid-s12058" xml:space="preserve">permutando M H in H A
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            ad duo quadrata H M, & </s>
            <s xml:id="echoid-s12059" xml:space="preserve">G M,
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            ſeu vt quadratum A C ad quadra-
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            tum diametri figuræ P Q (19. </s>
            <s xml:id="echoid-s12060" xml:space="preserve">ex
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            7.) </s>
            <s xml:id="echoid-s12061" xml:space="preserve">maiorem proportionem habebit, quàm V H in H A ad duo quadrata
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            V H, & </s>
            <s xml:id="echoid-s12062" xml:space="preserve">V G, ſeu quàm quadratum A C ad quadratum diametri figuræ
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            S T (19. </s>
            <s xml:id="echoid-s12063" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12064" xml:space="preserve">quare diameter figuræ S T maior eſt diametro figuræ
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            P Q. </s>
            <s xml:id="echoid-s12065" xml:space="preserve">Poſtea quia y O eſt media proportionalis inter A C, & </s>
            <s xml:id="echoid-s12066" xml:space="preserve">A F erit
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            quadratum A C ad quadratum y O, vt A C ad A F, nempe vt C G ad
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            C H, ſeu vt C G in C H ad quadratum C H, & </s>
            <s xml:id="echoid-s12067" xml:space="preserve">quadratum y O ad ſum-
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            <s xml:id="echoid-s12068" xml:space="preserve">O f, nempe ad quadratum diametri ſuæ figuræ
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            eſt vt quadratum H C ad quadratum C G cum quadrato H C: </s>
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