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1675

La Hire publishes

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.

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