Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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omnibus verò per I applicetur ordinatim ad E I recta L I M, quæ rectæ D
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F æquidiſtabit, & </
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<
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">per ipſam L I M concipiatur duci planum, quod plano
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per D F tranſeunti, ſiue baſi portionis ſolidæ D E F æquidiftet, aliam por-
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tionem ſolidam abſcindens L E M, quæ portioni ſolidæ A B C
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erit; </
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<
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">ſed ponitur etiam D E F eidem A B C æqualis; </
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<
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">ergo duæ L E M, D
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E F inter ſe æquales erunt, ſed vtraque eſt de eodem ſolido, circa commu-
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nem axim E H I, & </
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<
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">ſuper baſes parallelas, quare planum baſis ductum per
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L M, congruet cum plano baſis, quod tranſit per D F, vnde, & </
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<
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nus I, cum termino axis H. </
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<
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<
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prima, factus fuit E I æqualis B G, & </
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<
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">in reliquis O E ad E I, vt O B ad
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B G, quare axis quoque E H, in prima, æquabitur axi B G, in alijs verò
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erit O E ad E H, vt O B ad B G, & </
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<
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">conuertendo H E ad E O, vt G B
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ad B O.</
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<
s
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">Sint tandem duæ æquales portiones de eodem Cono recto A B C, D B
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E, quarum recti Canones concipiantur coaptari ſuper eadem ſectione A B
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E per ſolidi axem ducta, & </
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& </
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<
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">diametri B F, B G, (quæ iam ſunt axes ſolidarum portionum.) </
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">3. Schol.
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69. h.</
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F cum aſymptotis B A, B C deſcribatur Hyperbole F G; </
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">quæ omnino
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continget A C in F, termino axis B F. </
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<
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roll. 68. h.</
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G, ad eandem quoque ſectionem pertin-
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gere: </
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metrum B G in puncto G. </
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eſt ſectio F G alibi ſecet axim B G, vt in-
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fra G in puncto H, & </
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<
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H M ipſi D E æquidiſtans: </
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<
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">erit D G ad
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G E, vt L H ad H M, eſtque D G ęqua-
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lis G E, quare L M quoque bifariam ſe-
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cta erit in H: </
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ſectionem, ergo L M ipfam
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">ibidem.</
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in H, quapropter portio plana L B M
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æquabitur portioni A B C, & </
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M agatur planum ſecans Conum, & </
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plano datæ portionis ſolidæ D B E per D E ductum æquidiſtabit, cum hoc
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ad idem planum L B M ponatur rectum eſſe; </
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lis portioni A B C, cum earum recti Canones L B M, A B C
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ſint oſtenſi; </
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">ſed D B E quoque eidem A B C data eſt æqualis, ergo duæ
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portiones L B M, D B E ſimul æquales erunt, totum ſuæ parti, quod eſt
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abſurdum: </
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<
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">non ergo ſectio F G ſecat axim B G infra H; </
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tionem neque ſupra; </
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">ergo ſectio F G omnino tranſibit per G extremum
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axis B G: </
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<
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">ſed facta reuolutione anguli, ac ſectionis circa communem axim
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procreatur Conus, & </
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</
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<
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">ergo F, G, extrema puncta axium æqualium portionum ſolidarum A B C,
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D B E, ex eodem Cono recto, pertingunt ad idem Conoides Hyperboli-
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cum ſimile, & </
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<
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erat.</
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