Ceva, Giovanni
,
Geometria motus
,
1692
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Tab.
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2.
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Fig.
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9.</
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PROP. XI. THEOR. XI.
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<
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">IIſdem adhuc manentibus, idem de Angelis monſtrat eo
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dem illo tractatu pr. 3. ſi quæcunque ex dictis parabo
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lis ſecta ſit qualibet recta parallela baſi BC, eſſe parabolam
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ad reſectam portionem verſus verticem, vt poteſtas baſis,
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cuius exponens eſt numerus parabolæ vnitate auctus ad
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ſimilem poteſtatem ex baſi reſectæ portionis; itaque iņ
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prima parabola eſt vt quadratum ad quadratum, in ſecun
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da vt cubus ad cubum, & ſic de cæteris. </
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tur quodlibet ex infinitis trilineis linea GF baſi CD paral
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lela, erit trilineum ad ſuperius ſui ſegmentum vt poteſtas
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ex DA, cuius exponens eſt numerus trilinei vnitate auctus
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ad ſimilem poteſtatem ex AF. quare trilineum primum̨
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CAD ad GAF erit vt quadratum ex DA ad quadratum
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ex FA, ſecundum CHAD ad ſegmentum HAF vt cubus
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ad cubum, & ita in cæteris eodem ordine. </
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PROP. XII. THEOR. XII.
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Tab.
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3.
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fig.
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1.</
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<
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">SIt modò ACD angulus rectus, & linea FE talis naturæ,
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vt deductis ad libitum rectis AF, BE parallelis ipſi
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CD, poteſtas ex CA ad ſimilem poteſtatem ex CB ſit reci
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procè vt alia quædam poteſtas ex BE ad ſimilem huic po
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teſtatem ex AF; patet rectas CA, CD nondum iungi cum
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EF, quamuis in immenſum vnà producerentur. </
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<
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">Ab hoc
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proprietate VValliſius & Fermatius ſubtiliſſimi authores
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vocauerunt curuam FE nouam hyperbolam, & eius aſ
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ſymptotos AC, CD. </
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<
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">Omnes huiuſmodi hyperbolæ, quæ
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infinitæ numero ſunt, terminantur ad vnam partem ma
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gnitudine, cum hyperbola
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, ſeu Apolloniaca ſit in
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vtranque partem magnitudine infinita. </
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<
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">Quod ergo exi
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mium eſt, oſtenderunt ipſi authores rectangulum FA iņ </
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