# Chronology for 1675 to 1700

1675
La Hire publishes Sectiones conicae which is a major work on conic sections.

1675
Leibniz uses the modern notation for an integral for the first time.

1676
Leibniz discovers the differentials of basic functions independently of Newton.

1677
Leibniz discovers the rules for differentiating products, quotients, and the function of a function.

1678
Giovanni Ceva publishes De lineis rectis containing "Ceva's theorem".

1678
Cocker's Arithmetic is published two years after Cocker's death. It would run to more than 100 editions over a period of about 100 years.

1679
Leibniz introduces binary arithmetic. It was not published until 1701.

1680
Cassini studies the "Cassinian curve" which is the locus of a point the product of whose distances from two fixed foci is constant. (See this Famous curve.)

1682
Tschirnhaus studies catacaustic curves, being the envelope of light rays emitted from a point source after reflection from a given curve.

1683
Seki Kowa publishes a treatise that first introduces determinants. He considers integer solutions of ax - by = 1 where a, b are integers.

1684
Leibniz publishes details of his differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus. In contains the familiar d notation, and the rules for computing the derivatives of powers, products and quotients.

1685
Wallis publishes De Algebra Tractatus (Treatise of Algebra) which contains the first published account of Newton's binomial theorem. It made Harriot's remarkable contributions known.

1685
Kochanski gives an approximate method to find the length of the circumference of a circle.

1687
Newton publishes The Principia or Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy). In this work, recognised as the greatest scientific book ever written, Newton presents his theories of motion, gravity, and mechanics. His theories explain the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon.

1690
Jacob Bernoulli uses the word "integral" for the first time to refer to the area under a curve.

1690
Rolle publishes Traité d'algèbre on the theory of equations.

1691
Jacob Bernoulli invents polar coordinates, a method of describing the location of points in space using angles and distances.

1691
Rolle publishes Méthods pour résoudre les égalités which contains Rolle's theorem. His proof uses a method due to Hudde.

1692
Leibniz introduces the term "coordinate".

1693
Halley publishes his mortality tables for the city of Breslau (now Wroclaw) in Poland. His attempts to relate mortality and age in a population and proves highly influential in the future production of actuarial tables in life insurance.

1694
Johann Bernoulli discovers "L'Hôpital's rule".

1696
Johann Bernoulli poses the problem of the brachristochrone and challenges others to solve it. Johann Bernoulli, Jacob Bernoulli and Leibniz all solve it.

List of mathematicians alive in 1675.

List of mathematicians alive in 1700.

 JOC/EFR May 2015 The URL of this page is: School of  Mathematics and Statistics University of  St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/history/Chronology/1675_1700.html