Chronology for 1650 to 1675

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1650
De Witt completes writing Elementa curvarum linearum. It is the first systematic development of the analytic geometry of the straight line and conic. It is not published, however, until 1661 when it appears as an appendix to van Schooten's major work.

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.

1654
Pascal publishes his Treatise on the Equilibrium of Liquids on hydrostatics. He recognizes that force is transmitted equally in all directions through a fluid, and gives Pascal's law of pressure.

1655
Brouncker gives a continued fraction expansion of 4/π . He also computes the quadrature of the hyperbola, a result he will publish three years later.

1656
Wallis publishes Arithmetica infinitorum which uses interpolation methods to evaluate integrals.

1656
Huygens patents the first pendulum clock.

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.

1657
Neile becomes the first to find the arc length of an algebraic curve when he rectified the cubical parabola. (See this Famous curve.)

1657
Frenicle de Bessy publishes Solutio duorm problematum ... which gives solutions to some of Fermat's number theory challenges.

1658
Wren finds the length of an arc of the cycloid. (See this Famous curve.)

1659
Rahn publishes Teutsche algebra which contains divide (the division sign) probably invented by Pell.

1660
De Sluze discusses spirals, points of inflection and the finding of geometric means in his works. He studies curves which Pascal names the "pearls of Sluze". (See this Famous curve.)

1660
Hooke discovers Hooke's law of elasticity.

1660
Viviani measures the velocity of sound. He determines the tangent to a cycloid. (See this Famous curve.)

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.

1662
The Royal Society of London is founded. Brouncker becomes its first President. (See this Article.)

1662
Graunt and Petty publish Natural and Political Observations made upon the Bills of Mortality. It is one of the first statistics books.

1663
Barrow becomes the first Lucasian Professor of Mathematics at the University of Cambridge in England. (See this Article.)

1665
Newton discovers the binomial theorem and begins work on the differential calculus.

1666
The Académie des Sciences in Paris is founded.

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.

1668
Pell gives a table of factors of all integers up to 100000.

1669
Wren publishes his result that a hyperboloid of revolution is a ruled surface.

1669
Barrow resigns the Lucasian Chair of Mathematics at Cambridge University to allow his pupil Newton to be appointed.

1669
Wallis publishes his Mechanica (Mechanics) which is a detailed mathematical study of mechanics.

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
De Witt publishes A Treatise on Life Annuities. It contains the idea of mathematical expectation.

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 π/4.

1672
Mengoli publishes The Problem of Squaring the Circle which studies infinite series and gives an infinite product expansion for π/2.

1672
Mohr publishes Euclides danicus in which he shows that all Euclidean constructions can be carried out with compasses alone.

1673
Leibniz demonstrates his incomplete calculating machine to the Royal Society. It can multiply, divide and extract roots.

1673
Huygens publishes Horologium Oscillatorium sive de motu pendulorum. As well as work on the pendulum he investigates evolutes and involutes of curves and finds the evolutes of the cycloid and of the parabola.

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.


List of mathematicians alive in 1650.

List of mathematicians alive in 1675.



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JOC/EFR August 2001

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