This edition presents Duncan C. Fraser’s new translation of Newton’s interpolation methods, focusing on how descending differences build the foundation of finite differences. It connects historical steps to familiar ideas in today’s calculus and numerical methods.

The text offers a careful look at how Newton’s formulas interpolate between known values, with attention to equal and unequal intervals. Readers will see how central and mean-based forms relate to well‑known results, including Stirling’s and Bessel’s formulas, and how these ideas lead to practical tools for estimating areas and intermediate terms of a series.

Learn the logic behind interpolation by differences, both with equal and with unequal spacing.
See how central and mean ordinates contribute to practical formulas.
Understand historical context for finite differences and their link to early numerical methods.
Discover how Newton’s process evolved into methods used for area estimation and table construction.

Ideal for readers of the history of mathematics, or anyone exploring the origins of interpolation and finite differences in a clear, context-rich presentation.

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