An exuberant, enlightening account of Newtonian mechanics by Princeton mathematician turned mystery novelist and essayist (*The Body Shop*, 1996, etc.).

Few, even among scholars, have actually read Newton’s *Principia Mathematica, *yet it is universally acclaimed as one of the pivotal works in modern science, reflecting the genius of its author, who was Lucasian Professor of Mathematics at Cambridge (the chair now held by Stephen Hawking). Enter Berlinski, who takes the reader by the hand and, through simple diagrams and patient prose, unveils some of the mysteries embodied in the concepts of force, mass, acceleration, and velocity symbolized in Newton’s laws. To begin with, he tells us, it was Newton’s gift to take the coordinate system developed by Descartes (which allowed the visualization of algebraic equations as curves) literally to the limit: that is, to see the velocity of a moving particle at a given point on its curve of motion as the measure of the change in distance over the change in time as time approaches zero (the limit). Thus was born the derivative, as defined in the calculus that Newton (and Leibniz) invented. Berlinski moves on from there to capture the mental workings of Newton as he wrestled with the motion of the moon as it circles the earth, neither escaping into space nor plummeting earthward. He also explores Newton’s later work on optics. He makes no excuses for the eccentricities of his subject (the vicious attacks on Hooke and Leibniz, the ruthless persecutions of counterfeiters when Newton was Master of the Mint), and he dutifully records Newton’s religious defection (his disbelief in the Trinity) and his excursions into alchemy and Biblical genealogies. He also reports on the few emotional episodes in Newton’s life, including a two-year mutual attachment between the already rich and famous mathematician and a young Swiss colleague, which may or may not have gone beyond words.

In a short account, Berlinski has wrought an astonishing synthesis—a sort of essential Newton for those not fearing to tread in mathematical waters.