Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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11389 ipſam ABC in puncto L, ſed poſitum fuit eam quoque contingere in H: Er-
go in duobus punctis H, L ſe contingent; quod eſt falſum; nam Parabole
Parabolen, ſiue Hyperbole Hyperbolen concentricam in duobus 1128. 31. 4.
conic. non contingit. Non ergo tales ſectiones ſe tangunt in H; neque in L, ob ean-
dem rationem; quare ipſæ in occurſibus H, & L ſe mutuò ſecant. Quod erat
oſtendendum.

THEOR. XXVIII. PROP. L.

Impoſſibile eſt Hyperbolen Parabolæ, per eundem, vel per
diuerſos vertices inſcribere. Item.

Impoſſibile eſt Parabolen Hyperbolæ, per eundem, vel per di-
uerſos vertices circumſcribere.

ESto Parabole ABC, cui per punctum D in ea ſumptum, vt in prima figu-
ra, vel intra ipſam, vt in ſecunda, adſcripta ſit quæcunque Hyperbole
EDF circa communem diametrum BDG, quæ per aliquas ſuæ peripheriæ
partes DE, DF, hinc inde à diametro ſumptas cadat intra Parabolen ABC.
Dico ipſam Hyperbolen, ſi producatur, ex vtraque parte Parabolen ſecare.

Nam ductis ex D re-
ctis DA, DC vtrique

78[Figure 78] aſymptoto Hyperbolæ
EDF ęquidiſtãtibus, hę;
neceſſariò Parabolen
ſecabunt, vt in A, C; 2227. pri-
mi conic. ſed cum Hyperbola in
alio puncto quàm D
nunquam conuenient: 33Coroll.
11. huius. quare, cum Hyperbola
EDF ex vtraque parte
in infinitum habeat, ſi
producatur, occurret
denique Parabolæ ABC inter puncta B, A, & puncta B, C; eamque ſeca-
bit, nam ſi tantùm eam tangeret, vel non, ſi vlteriùs producatur intra Para-
bolen, ſecaret aliquandò rectas DA, DC; quod eſt impoſſibile. Non 44ibidem. tur inſcribi vnquam poteſt Hyperbole datæ Parabolæ, per punctum in ea,
vel intra ipſa datum, eadem ratione demonſtrabitur non poſſe circumſcribi
Parabolen datæ Hyperbolę per punctum in ea, vel extra ipſam datum. Quod
erat, & c.

COROLL.

HInc patet non dari _MAXIMAM_ Hyperbolen datæ Parabolæ, vel per
eundem verticem, vel per diuerſos inſcriptibilem; itemque non dari
_MINIMAM_ Parabolen datæ Hyperbolæ, vel per eundem, vel per diuerſos
vertices circumſcriptibilem.

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