... calculus remained without logical foundations. In 1821, French mathematician Cauchy began to clarify the basis of calculus with his theory of limits, a purely arithmetic theory that did not depend on geometric intuition or infinitesimals. Cauchy then showed how this could be used to give a logical account of the ideas of continuity, derivatives, integrals, and infinite series. In the next decade ... logical foundations of calculus. The primary motivation behind part one of his book, Continuity and Irrational Numbers, was the desire to replace loose geometrical concepts and intuitive justi...

• Word Count: 2467
• Approx Pages: 10
• Has Bibliography
• Grade Level: Undergraduate

... infinite series. The finite series was recorded in the standard Greek arithmetic notation. Considering the infinite and finite series as one data set, Archimedes stated a rational number problem by a 1/4 geometric infinite series, and calculated a finite series in the standard Greek notation. ----------------------------------------- Bhaskara: His work, the Siddhanta Shiromani, is an astronomical treatise and contains many theories not found in earlier ... learned society Akademie der Wissenschaften, founded by Leibniz, its president for life. In his paper, he introduced the familiar "d...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate

... do not understand the connection, Hume suggests that our findings will probably hold true to our liking because we almost always consider these findings in a similar condition. What about mathematical proofs and geometric theorems? Hume addresses these "Relations of Ideas" that are discoverable through our operations of thought. These findings do not depend on things that exist in the universe. This is ... ...

• Word Count: 1541
• Approx Pages: 6
• Has Bibliography
• Grade Level: Undergraduate

... (Great Work). In Europe, medieval Latin translations reproduced the title as Almagesti, and it has since become known simply as the Almagest. (Toomer, p.p. 190-191) In this work, Ptolemy proposed a geometric theory to account mathematically for the apparent motions and positions of the planets, sun, and moon against a background of unmoving stars. This work did not include any physical descriptions of ... theory." (North, The reluctant revolutionaries, p.131) But, beside religious backing Copernicus had to have a scientific evidence. In an attempt to support his heliocentric model, Cope...

• Word Count: 1299
• Approx Pages: 5
• Grade Level: Undergraduate

... do not understand the connection, Hume suggests that our findings will probably hold true to our liking because we almost always consider these findings in a similar condition. What about mathematical proofs and geometric theorems? Hume addresses these "Relations of Ideas" that are discoverable through our operations of thought. These findings do not depend on things that exist in the universe. This is ... ...

• Word Count: 1525
• Approx Pages: 6
• Has Bibliography
• Grade Level: Undergraduate