The method of integration can be traced back to the Egyptians, in the Moscow Mathematical Papyrus circa 1800 BC, which gives the formula for finding the volume of a pyramidal frustrum.[1] Greek geometers are credited with a significant use of infinitesimals. Democritus is the first person recorded to consider seriously the division of objects into an infinite number of cross-sections, but his inability to rationalize discrete cross-sections with a cone's smooth slope prevented him from accepting the idea. At approximately the same time, Zeno of Elea discredited infinitesimals further by his articulation of the paradoxes which they create. Antiphon and later Eudoxus are generally credited with implementing the method of exhaustion, which made it possible to compute the area and volume of regions and solids by breaking them up into an infinite number of recognizable shapes. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts somewhat. (See Archimedes' Quadrature of the Parabola and Archimedes on Spheres & Cylinders.) It was not until the time of Newton that these methods were made obsolete. It should not be thought that infinitesimals were put on rigorous footing during this time, however. Only when it was supplemented by a proper geometric proof would Greek Mathematicians accept a proposition as true. (See Archimedes' use of infinitesimals.) The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere.[1]
Related Rate
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ตอบ อัตราการเปลี่ยนแปลงความสูง ลดลง 4 นิ้ว/นาที |
Created Date: 2007-03-03 03:03:03
Last Update: 2007-06-16 23:25:30
Comment: 3
แก้แล้วคราบ
น้องนี่ตาไวจริงๆ
Surachai U.
2009-09-26 14:34:15
Comment: 2
โจทย์ บอกเป็นทรงกระบอกตรงไม่ใช่หรอครับ ในรูปมันทรงกรวยครับ
DDD
2009-09-26 01:34:14
Comment: 1
โจทย์ บอกเป็นทรงกระบอกตรงไม่ใช่หรอครับ ในรูปมันทรงกรวยครับ
DDD
2009-09-26 01:34:13
-   1
In differential calculus, related rates problems involve finding the rate at which a quantity is changing by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time.


