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Math History Timeline
Baroque Era
1600-1700 A.D.

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1609 Kepler publishes Astronomia nova (New Astronomy). The work contains Kepler's first and second law on elliptical orbits, but only verified for the planet Mars.
1614 Napier publishes his work on logarithms in Mirifici logarithmorum canonis descriptio (Description of the Marvellous Rule of Logarithms).
1615 Kepler publishes Nova stereometria doliorum vinarorum (Solid Geometry of a Wine Barrel), an investigation of the capacity of casks, surface areas, and conic sections. He first had the idea at his marriage celebrations in 1613. His methods are early uses of the calculus.
1617 Briggs publishes Logarithmorum chilias prima (Logarithms of Numbers from 1 to 1,000) which introduces logarithms to the base 10.
1617 Napier invents Napier's bones, consisting of numbered sticks, as a mechanical calculator. He explains their function in Rabdologiae (Study of Divining Rods) published in the year of his death.
1620 Bürgi publishes Arithmetische und geometrische progress-tabulen which contains his version of logarithms discovered independently of Napier.
1623 Schickard makes a "mechanical clock", a wooden calculating machine that add and subtract and aid with multiplication and division. He writes to Kepler suggesting using mechanical means to calculate ephemeredes.
1624 Briggs publishes Arithmetica logarithmica (The Arithmetic of Logarithms) which introduces the terms "mantissa" and "characteristic". It gives the logarithms of the natural numbers from 1 to 20,000 and 90,000 to 100,000 computed to 14 decimal places as well as tables of the sine function to 15 decimal places, and the tangent and secant functions to 10 decimal places.
1626 Albert Girard publishes a treatise on trigonometry containing the first use of the abbreviations sin, cos, tan. He also gives formulas for the area of a spherical triangle.
1629 Fermat works on maxima and minima. This work is an early contribution to the differential calculus.
1631 Harriot's contributions are published ten years after his death in Artis analyticae praxis (Practice of the Analytic Art). The book introduces the symbols > and < for "greater than" and "less than" but these symbols are due to the editors of the work and not Harriot himself. His work on algebra is very impressive but the editors of the book do not present it well.
1635 Cavalieri presents his development of Archimedes' method of exhaustion in his Geometria indivisibilis continuorum nova. The method incorporates Kepler's theory of infinitesimally small geometric quantities.
1635 Descartes discovers Euler's theorem for polyhedra, V - E + F = 2.
1637 Descartes publishes La Géométrie which describes his application of algebra to geometry.
1640 Pascal publishes Essay pour les coniques (Essay on Conic Sections).
1642 Pascal builds a calculating machine to help his father with tax calculations. It performs only additions.
1647 Fermat claims to have proved a theorem, but leaves no details of his proof since the margin in which he writes it is too small. Later known as Fermat's last theorem, it states that the equation x n + y n = z n has no non-zero solutions for x, y and z when n > 2. This theorem is finally proved to be true by Wiles in 1994.
1649 De Beaune writes Notes brièves which contains the many results on "Cartesian geometry", in particular giving the now familiar equations for hyperbolas, parabolas and ellipses.
1649 Van Schooten publishes the first Latin version of Descartes' La géométrie.
1651 Nicolaus Mercator publishes three works on trigonometry and astronomy, Trigonometria sphaericorum logarithmica, Cosmographia and Astronomica sphaerica. He gives the well known series expansion of log(1 + x).
1653 Pascal publishes Treatise on the Arithmetical Triangle on "Pascal's triangle". It had been studied by many earlier mathematicians.
1654 Fermat and Pascal begin to work out the laws that govern chance and probability in five letters which they exchange during the summer.
1656 Huygens patents the first pendulum clock.
1656 Wallis publishes Arithmetica infinitorum which uses interpolation methods to evaluate integrals.
1657 Huygens publishes De ratiociniis in ludi aleae (On Reasoning in Games of Chance). It is the first published work on probability theory, outlining for the first time the concept called mathematical expectation based on the ideas in the letters of Fermat and Pascal from 1654.
1659 Rahn publishes Teutsche algebra which contains ¸ (the division sign) probably invented by Pell.
1660 Viviani measures the velocity of sound. He determines the tangent to a cycloid.
1661 Van Schooten publishes the second and final volume of Geometria a Renato Des Cartes. This work establishes analytic geometry as a major mathematical topic. The book also contains appendices by three of his disciples, de Witt, Hudde, and Heuraet.
1663 Barrow becomes the first Lucasian Professor of Mathematics at the University of Cambridge in England.
1665 Newton discovers the binomial theorem and begins work on the differential calculus.
1667 James Gregory publishes Vera circuli et hyperbolae quadratura which lays down exact foundations for the infinitesimal geometry.
1668 James Gregory publishes Geometriae pars universalis which is the first attempt to write a calculus textbook.
1669 Barrow resigns the Lucasian Chair of Mathematics at Cambridge University to allow his pupil Newton to be appointed.
1670 Barrow publishes Lectiones Geometricae which contains his important work on tangents which forms the starting point of Newton's work on the calculus.
1671 James Gregory discovers Taylor's Theorem and writes to Collins telling him of his discovery. His series expansion for arctan(x) gives a series for p /4.
1673 Leibniz demonstrates his incomplete calculating machine to the Royal Society. It can multiply, divide and extract roots.
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.
1679 Leibniz introduces binary arithmetic. It was not published until 1701.
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.
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".
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.

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