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1603

Cataldi finds the sixth and seventh perfect numbers, 2

1603

Accademia dei Lincei founded in Rome.

1606

Snell makes the first attempt to measure a degree of the meridian arc on the Earth's surface, and so determine the size of the Earth. He publishes *Hypomnemata mathematica* (*Mathematical Memoranda*) which is a Latin translation of Stevin's work on mechanics.

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.

1610

Galileo publishes *Sidereus Nuncius* (*Message from the stars*) which describes the astronomical discoveries he has made with his telescopes. Harriot also observes the moons of Jupiter but does not publish his work.

1612

Bachet publishes a work on mathematical puzzles and tricks which will form the basis for almost all later books on mathematical recreations. He devises a method of constructing magic squares.

1613

Cataldi publishes *Trattato del modo brevissimo di trovar la radice quadra delli numeri* in which he finds square roots using continued fractions.

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.

1615

Mersenne encourages mathematicians to study the cycloid. (See this Famous curve.)

1617

Snell publishes his technique of trigonometrical triangulation which improves the accuracy of cartographic measurements.

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.

1620

Gunter makes a mechanical device, *Gunter's scale*, to multiply numbers based on logarithms using a single scale and a pair of dividers.

1620

Guldin gives *Guldin's Centroid Theorem* which was already known to Pappus.

1621

Bachet publishes his Latin translation of Diophantus's Greek text *Arithmetica*.

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.

List of mathematicians alive in 1600.

List of mathematicians alive in 1625.

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