Pietro Mengoli was an Italian mathematician and clergyman from Bologna, where he studied with Bonaventura Cavalieri at the University of Bologna, and succeeded him in 1647. He remained as professor there for the next 39 years of his life.
Title-page from Novae quadraturae arithmeticae, by Pietro Mengoli. 1650.
Jacob Bernoulli was one of the many prominent mathematicians in the Swiss Bernoulli family. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus, which he made numerous contributions to; along with his brother Johann, he was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.
Jacob Bernoulli
Image from Acta Eruditorum (1682) wherein was published the critique of Bernoulli's Conamen novi systematis cometarum
Jacob Bernoulli's tombstone in Basel Münster
De gravitate aetheris, 1683