Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">QVod autem in quolibet Sphæroide, inter portiones eius dimidio mi-
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nores, & </
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<
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">æqualium baſium, _MINIMA_ ſit ea, cuius axis ſit ſegmen-
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tum minoris axis Ellipſis datum Sphæroides procreantis, id con-
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ſimili conſtructione, atque argumentis oſtendetur, vti factum fuit in ſecun-
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da parte Prop. </
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<
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">huius, ſi tamen ſuper tertia figura lineæ rectæ, & </
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ibi animaduerſæ, concipiantur tanquam baſes ſolidarum portionum, & </
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<
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luti Sphæroidalia ſolida, &</
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<
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quarum baſes ſint æquales, eam eſſe, cuius axis ſit ſegmentum maio-
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ris axis Ellipſis genitrics; </
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">_MAXIM AM_ autem, cuius axis ſit ſegmentum
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minoris.</
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</
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">Cum ibi ſit A C minor H I, erit quoque dimidium D C minus di-
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midio F I. </
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">Detrahatur ergo F P, quę ſit media proportionalis
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inter F I, D C; </
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<
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rensin R, atque ex R applicetur R Q S, & </
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circa axim B D, concipiantur deſcribiſolida, &</
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<
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rectas A C, H I, S R ductis, & </
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">ad eaſdem genitrices ſectiones erectis, ab-
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ſcindentur portiones ſolidæ A B C, H O I inter ſe æquales, & </
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<
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R. </
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<
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">Nam baſis per H I ad baſim per A C, eſt vt recta H I ad rectam A
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78. h.</
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vel ſumptis dimidijs, vt F I ad D C, vel vt quadratum F I, ad quadratum
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F P, ſiue ad quadratum Q R, vel ſumptis quadruplis, vt quadratum H I ad
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quadratum S R, ſed etiam baſis per H I ad baſim per S R, eſt vt quadra-
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tum H I ad quadratum S R, cum ob planorum æquidiſtantiam ſint
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15. Arch.
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de Co-
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noid.</
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nes ſimiles, ergo baſis per H I ad baſim per A C, erit vt eadem baſis per H
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I ad baſim per S R: </
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facere oportebat.</
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Conoide, aut Sphæroide, & </
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eſt, cuius axis congruat cum maiori axe genitricis ſectionis dati
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ſolidi.</
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<
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">In Sphæroide, MAXIMA eſt, cuius axis cum minori axe eiuſ-
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dem genitricis ſectionis conueniat.</
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roide quocunque ſunt æquales, & </
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