Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

in F, G (nam Parabole A B C eſt _MINIMA_ Ellipſi F B G circumſcri- ptibilium) è quorum altero F ducta ſit ordinata F H I communem axem
in H, regulam verò ſecante [?] in I; ſitque F L Parabolen contingens ad F, axemque ſecans in L.

242.1.

ibidem.
2. primi
huius.
24. pri-
mi conic.
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Iam, in triangulo E B D cum ſit E B dupla B D, erit I H dupla H D,
ſed eſt quoque L H dupla H B, quare vt L H ad H B, ita I H ad H D: rectangulum ergo L H D æquale eſt rectangulo B H I, ſiue quadrato F H, eſtque F H ipſi L D perpendicularis, quare angulus D F L rectus eſt, & F L Parabolen contingit in F: vnde D F eſt _MINIMA_ ducibilium ex dato puncto D ad peripheriam Parabolæ F B G. Conſimili ratione oſten-
detur, quamlibet aliam inſcriptam P B R Ellipſis peripheriam B F G D
ſecare, vt in P, R, & iunctam D P, vel D R eſſe _MINIMAM_, & c. Qua-
re ſemita _MINIMARV M_ ex D ad huiuſmodi Parabolarum peripherias, eſt
prædictæ Ellipſis perimeter. Quod oſtendere propoſitum fuit.

242.1.

Coroll.
primæ 1.
huius.
203. Se-
pt. Pappi.
11. huius
ad nu. 1.

243. PROBL. II. PROP. XXII.

A dato puncto, ad datę Hyperbolæ peripheriam, MINI-
MAM rectam lineam ducere.

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SIt data Hyperbole A B C,
cuius axis B D, rectum B E
tranſuerfum verò B G, centrum
H, & datum vbicunque ſit pun-
ctum F. Oportet ex F ad Hyper-
bolæ peripheriam A B C _MINI-_
_MAM_ rectam lineam ducere.

Si primò datum punctum F,
in prima figura fuerit in axe pro-
ducto, extra Hyperbolen, ipſa
F B erit _MINIMA_.

10. h.

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