# Manual Social History of Nineteenth Century Mathematics Contents:

Assume two particles move along separate lines from given initial points.

## Social History of Nineteenth Century Mathematics

The particles begin moving at the same instant with the same velocity. The first particle continues to move with a speed that is decreasing, proportional at each instant to the distance remaining between it and some given fixed point on the line. The second particle moves with a constant speed equal to its initial velocity. Given any increment of time, the distances traveled by the first particle in successive increments form a geometrically decreasing sequence. The corresponding distances traveled by the second particle form an arithmetically increasing sequence.

Napier was able to use this model to derive theorems yielding precise limits to approximate values in the two sequences. Kinematic ideas, which appeared frequently in mathematics of the period, provided a clear and visualizable means for the generation of geometric magnitude.

The conception of a curve traced by a particle moving through space later played a significant role in the development of the calculus. In Briggs published an extensive table of common logarithms , or logarithms to the base He also devised interpolation procedures of great computational efficiency to obtain intermediate values.