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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.

1630

Oughtred invents an early form of circular slide rule. It uses two Gunter rulers.

1630

Mydorge works on optics and geometry. He gives an extremely accurate measurement of the latitude of Paris.

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.

1631

Oughtred publishes *Clavis Mathematicae* which includes a description of Hindu-Arabic notation and decimal fractions. It has a considerable section on algebra.

1634

Roberval finds the area under the cycloid curve. (See this Famous curve.)

1635

Descartes discovers Euler's theorem for polyhedra, *V* - *E* + *F* = 2.

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.

1636

Fermat discovers the pair of amicable numbers 17296, 18416 which were known to Thabit ibn Qurra 800 years earlier.

1637

Descartes publishes *La Géométrie* which describes his application of algebra to geometry.

1639

Desargues begins the study of projective geometry, which considers what happens to shapes when they are projected on to a non-parallel plane. He describes his ideas in *Brouillon project d'une atteinte aux evenemens des rencontres du Cone avec un Plan* (*Rough draft for an essay on the results of taking plane sections of a cone*).

1640

Pascal publishes *Essay pour les coniques* (*Essay on Conic Sections*).

1641

Wilkins publishes on codes and ciphers.

1642

Pascal builds a calculating machine to help his father with tax calculations. It performs only additions.

1644

Torricelli publishes *Opera geometrica* which contains his results on projectiles. He investigates the point which minimises the sum of its distances from the vertices of a triangle.

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. (See this History Topic.)

1647

Cavalieri publishes *Exercitationes geometricae sex* (*Six Geometrical Exercises*) which contains in print for the first time the integral from 0 to *a* of *x*^{n}.

1648

Wilkins publishes *Mathematical Magic* giving an account of mechanical devices.

1648

Abraham Bosse publishes a work containing Desargues' famous "perspective theorem" - that when two triangles are in perspective the meets of corresponding sides are collinear.

1649

Van Schooten publishes the first Latin version of Descartes' *La géométrie*.

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.

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.

List of mathematicians alive in 1625.

List of mathematicians alive in 1650.

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