Francesco Bonaventura Cavalieri

Francesco Bonaventura Cavalieri (1598 to 1647). Cavalieri was a student of Galilei - https://domyhomework.club . He continued the thoughts of Archimedes and Kepler. on the determination of the content of solids and surfaces and created a theory of "indivisibles" (indivisible (lat.) - not divisible).

By indivisibles he imagined infinitely small, indivisible layers of a body or a surface. In his view, they arise in the following way: Any body can be placed between two parallel planes that touch it at a point or boundary surface. If one plane now moves parallel to its initial position towards the other plane (Cavalieri calls this "flowing"), an infinite number of intersections of the plane with the body are created - homework help geometry . The body is the totality of these intersecting surfaces. With this approach, Cavalieri tried to grasp the problem of infinitely small quantities, which had troubled mathematicians since antiquity. However, the further development of mathematics showed that this descriptive idea of infinitely small quantities leads to numerous logical contradictions. Therefore, one had to break away from it again.

Cavalieri did not prove Cavalieri's theorem, which is named after him, but used it as a principle in area and volume calculations - html assignment help . An exact proof is only possible with the means of the infinitesimal calculus. Cavalieri's views led to numerous correct findings and had a strong influence on the development of methods for the determination of area and volume.

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