Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ipſam ABC in puncto L, ſed poſitum fuit eam quoque contingere in H: </
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go in duobus punctis H, L ſe contingent; </
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<
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<
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Parabolen, ſiue Hyperbole Hyperbolen concentricam in duobus
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conic.</
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non contingit. </
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<
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">Non ergo tales ſectiones ſe tangunt in H; </
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<
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dem rationem; </
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<
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">quare ipſæ in occurſibus H, & </
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<
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oſtendendum.</
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diuerſos vertices inſcribere. </
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<
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">Impoſſibile eſt Parabolen Hyperbolæ, per eundem, vel per di-
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uerſos vertices circumſcribere.</
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<
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">ESto Parabole ABC, cui per punctum D in ea ſumptum, vt in prima figu-
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ra, vel intra ipſam, vt in ſecunda, adſcripta ſit quæcunque Hyperbole
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EDF circa communem diametrum BDG, quæ per aliquas ſuæ peripheriæ
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partes DE, DF, hinc inde à diametro ſumptas cadat intra Parabolen ABC.
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</
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ctis DA, DC vtrique
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aſymptoto Hyperbolæ
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EDF ęquidiſtãtibus, hę;
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ſecabunt, vt in A, C;</
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mi conic.</
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ſed cum Hyperbola in
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alio puncto quàm D
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nunquam conuenient:</
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11. huius.</
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quare, cum Hyperbola
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EDF ex vtraque parte
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in infinitum habeat, ſi
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producatur, occurret
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denique Parabolæ ABC inter puncta B, A, & </
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<
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bit, nam ſi tantùm eam tangeret, vel non, ſi vlteriùs producatur intra Para-
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bolen, ſecaret aliquandò rectas DA, DC; </
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<
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tur inſcribi vnquam poteſt Hyperbole datæ Parabolæ, per punctum in ea,
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vel intra ipſa datum, eadem ratione demonſtrabitur non poſſe circumſcribi
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Parabolen datæ Hyperbolę per punctum in ea, vel extra ipſam datum. </
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erat, &</
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eundem verticem, vel per diuerſos inſcriptibilem; </
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_MINIMAM_ Parabolen datæ Hyperbolæ, vel per eundem, vel per diuerſos
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vertices circumſcriptibilem.</
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