Johann and Jakob Bernoulli, the children of a prominent Basel, Switzerland, couple, were the first in a family line of gifted mathematicians that would endure for three generations. Jakob originally trained as a theologian and was destined to pursue a career in the church, but after studying some of the writings of René Descartes, John Wallis, and Issac Barrow (1630-1677), an English mathematician and theologian, his developing interest in science and mathematics led him away from an ecclesiastical career. After a trip to England in 1676, where he met Robert Boyle and other leading scientists, Jakob decided to devote himself fully to science. In 1677 he began his scientific diary, Meditationes, and thereafter spent two years in France familiarizing himself with the scientific methods of Descartes and his followers. He became interested in the mathematical aspects of astronomy and physics, developing a theory of the origin of comets in...