Concept

Gilles de Roberval

Gilles Personne de Roberval (August 10, 1602 – October 27, 1675), French mathematician, was born at Roberval near Beauvais, France. His name was originally Gilles Personne or Gilles Personier, with Roberval the place of his birth. Like René Descartes, he was present at the siege of La Rochelle in 1627. In the same year he went to Paris, and in 1631 he was appointed the philosophy chair at Gervais College, Paris. Two years after that, in 1633, he was also made the chair of mathematics at the Royal College of France. A condition of tenure attached to this particular chair was that the holder (Roberval, in this case) would propose mathematical questions for solution, and should resign in favour of any person who solved them better than himself. Notwithstanding this, Roberval was able to keep the chair until his death. Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, which would today be solved by calculus. He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented. Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines.

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Evangelista Torricelli
Evangelista Torricelli (ˌtɒriˈtʃɛli ; evandʒeˈlista torriˈtʃɛlli; 15 October 1608 - 25 October 1647) was an Italian physicist and mathematician, and a student of Galileo. He is best known for his invention of the barometer, but is also known for his advances in optics and work on the method of indivisibles. The torr is named after him. Torricelli was born on 15 October 1608 in Rome, the firstborn child of Gaspare Torricelli and Caterina Angetti. His family was from Faenza in the Province of Ravenna, then part of the Papal States.
Quadrature (mathematics)
In mathematics, quadrature is a historical term for the process of determining area. This term is still used in the context of differential equations, where "solving an equation by quadrature" or "reduction to quadrature" means expressing its solution in terms of integrals. Quadrature problems served as one of the main sources of problems in the development of calculus. They introduce important topics in mathematical analysis.
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri (Bonaventura Cavalerius; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus. Born in Milan, Cavalieri joined the Jesuates order (not to be confused with the Jesuits) at the age of fifteen, taking the name Bonaventura upon becoming a novice of the order, and remained a member until his death.
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