Subtangent and Subnormal

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Subtangent and Subnormal

 

the directed line segments QT and QN that are the projections on the x-axis of the segments MT and MN of the tangent and normal, respectively, to some curve at the point M of the curve (see Figure 1). If the curve is the graph of the function y = f(x), the length of the subtangent QT is equal to — f(x) / fʹ (x), and the length of the subnormal QN is equal to f(x)fʹ(x), where x is the abscissa of M. If the curve is defined parametrically— that is, x = Φ(t), y = ψ(t) — the length of QT is– ψ(t)Φʹ (t)/ψ’(t) and the length of QN is ψ(t)ψʹ (t/Φʹ (t), where t is the parameter that determines the position of M on the curve.

Figure 1

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.