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Subtangent and subnormal

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The directed segments and which are the projections on the -axis of the segments of the tangent line and the normal to a certain curve at a point (see Fig.).

Figure: s091040a

If the curve is the graph of a function , the values of the subtangent and subnormal are equal to

respectively, where is the abscissa of the point . If the curve is given parametrically by

then

where is the value of the parameter defining the point on the curve.


Comments

References

[a1] M. Berger, "Geometry" , II , Springer (1989)
[a2] F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
[a3] H. Lamb, "Infinitesimal calculus" , Cambridge (1924) pp. 118
How to Cite This Entry:
Subtangent and subnormal. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Subtangent_and_subnormal&oldid=14018
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098