In differential geometry the defining characteristic of a tangent space is that it approximates the smooth manifold to first order near the point of tangency.
32.
The shoulder continuously curves and transitions from the body radius to the neck radius at the point of tangency at the shoulder between the two radii.
33.
However, this advertisement most likely acted as a filter, as Gergonne only stated the circle-tangency problem, not the area-maximizing one.
34.
This standard configuration allows several properties of Steiner chains to be derived, e . g ., its points of tangencies always lie on a circle.
35.
In this configuration, the Steiner-chain circles have the same type of tangency to both given circles, either externally or internally tangent to both.
36.
The same reciprocal relation exists between a point "'P "'outside the circle and the secant line joining its two points of tangency.
37.
The Gergonne triangle or intouch triangle of a reference triangle has its vertices at the three points of tangency of the reference triangle's sides with its incircle.
38.
The extouch triangle of a reference triangle has its vertices at the points of tangency of the reference triangle's excircles with its sides ( not extended ).
39.
The distance from any vertex to the incircle tangency on either adjacent side is half the sum of the vertex's adjacent sides minus half the opposite side.
40.
The term derives from the Latinate root " osculate ", to kiss, because the two curves contact one another in a more intimate way than simple tangency.
