CURVE OF EQUAL APPROACH

CURVE OF EQUAL APPROACH. It was first proposed by Leibnitz, namely, to find a curve, down which a body descending by the force of gravity shall make equal approaches to the horizon in equal portions of time. It has been found by Bernoulli and others, that the curve is the second cubical parabola, placed with its vertex uppermost, and which the descending body must enter with a certain determinate velocity. Varignon rendered the question general for any law of gravity,

gravity, by which a body may approach towards a given point by equal spaces in equal times. And Maupertuis also resolved the problem in the case of a body descending in a medium which resists as the square of the velocity.