# Calculating differential and integral: Calculating the ancient and middle ages

- Introduction
- Calculating differntial and integral
- Ancient and middle ages
- Analysis
- Conclusion

It is often said that the calculation was invented by two great mathematicians of the seventeenth century, Newton and Leibniz. "In fact, the calculation is the product of a long evolution that has not been started or completed by Newton and Leibniz" (COURANT, 2000, p.481). Its beginning dating from the seventeenth century BC. This season has Egyptian papyri and Babylonian cuneiform tablets that tells us how those civilizations treated certain measurement problems. One of the oldest documents of the history of mathematics is the Rhind papyrus.

It is an Egyptian papyrus in 1600 BC, he was the scribe Ahmes Copilado. In this document we found some mathematical results used in Ancient Egypt, as shown by Boyer (1978):

-The volume of a square pyramid was calculated as 1/3 of the rectangular prism volume.

-The area of a circle was obtained by a square whose side is 8/9 the diameter of the circle.

These rules were accepted, but without a rigorous proof for the same as today.

[...] du, the differential sum; It has also created the symbol an elongated S to indicate the sum of all the infinitesimal areas. Showed that y dx corresponds to an area and that d y dx = y dx, presenting them with inverse of Newton and Leibniz followed different lines in the creation of calculation. Despite the controversy that continues throughout history, the use of different ways to obtain the same theory, indicates that it was two developments independes. In the discoveries of Newton and Leibniz eighteenth century, the efforts of mathematicians focused on the development and applications of calculus. [...]

[...] The scientific activity of the eighteenth century "focused generally in the academies, of which stood out the Paris, Berlin and St. Petersburg. The university had a minor role or no "(STRUIK p.191). Politically, it is the era of enlightened despots: Frederick the Great; Catherine the Great; Louis XV and Louis XVI, who ruled the major European states. Some of these despots around him is learned men. This pleasure was a kind of intellectual snobbery, tempered by a certain understanding of the important role that the natural sciences and applied mathematics played in the modernization of manufacturing and increasing effectiveness of military force (STRUIK p.192). [...]

[...] CALCULATING THE GREEK CIVILIZATION A significant contribution to the Greek calculation came from Eudoxus, mathematician and astronomer who lived in the fourth century BC. It was he who developed the method of exhaustion, combining the concepts of infinitesimal. If any of a quantity subtracted from a portion not less than a half of the remainder is subtracted also a part not less than a half, and so on, it eventually will reach a predetermined magnitude lower than any other of the same species (EVSE p. 419). [...]

[...] He was educated by his grandmother and his uncle's advice was studying at Cambridge in 1661. Early in his first year he bought and studied a copy of Euclid and soon after read the Clavis of Oughtred, Geometry Renato Des Cartes de Schooten, Kepler's Optics, works of Viète, and what was perhaps the most important of all for him, Arithmetica infinitorum Wallis. Furthermore, in this study we acrecentar classes that gave Barrow as "teacher Lucasian 'and Newton seen after 1663 (Boyer p.287). [...]

[...] New York: McGraw-Hill STRUIK, Dirk J. História concisa da Matemática. [...]