Jakob Bernoulli was born in Switzerland and received his degree in 1671 after studying philosophy and theology at the request of his father and mathematics and astronomy against the will of his father. His motto became Invito patre sidera verso (“Against my father’s will, I study the stars”) as he began to investigate mathematics and astronomy on his own. His educational pursuits took him to the Netherlands, where he met mathematician Jan Hudde, and to England, where he met Robert Boyle and Robert Hooke. The result of these journeys was his theory of the movement of comets and a theory of gravity. As a result of this work, Bernoulli contributed articles on algebraic subjects to the Acta eruditorum.
By working on problems in optics and mechanics, Bernoulli contributed to important developments in infinitesimal geometry and calculus. Bernoulli showed his mastery of the calculus with his analysis of the solutions given by Huygens in 1687 and by Gottfried Wilhelm Leibniz in 1689 to the problem of the curve of constant descent in a gravitational field. It was in that analysis that he used the term integral. He also studied the catenary, the function that determines the shape of a suspended string or chain. He made use of polar coordinates in several applied problems that he solved. Unfortunately, Jakob had a strained relationship with his younger brother, mathematician Johann Bernoulli. Jakob Bernoulli taught at Basel from 1683 until his death. He was the first mathematician of the Bernoulli family, which became the most famous family in the history of mathematics.