This art is geometry "the measuring of Earth. ... In thirteen books he collected The Elements of geometry, starting from the most basic concepts, "a point is that which has no part- and "a line is breadthless length-. ... Focusing our mind on the metaphysical plane where the triangle exists and by following Euclid's reasoning we find that we too can have access to that realm where we'll see true images, rather than likenesses of them. ... The fact that they can only be appreciated outside the material world, in a realm that's only accessible to men and women who trust the p...

• Word Count: 1043
• Approx Pages: 4
• Grade Level: Undergraduate

His interest in mathematics is said to have began from when he observed a solar eclipse on October 18, 320 and then since has focused his work on geometry. ... The purpose of the volumes were to revive geometry and restore it to a level of significance, usually by providing further explanations or supplements to the works of previous geometers. ... Book III distinguishes plane, solid and linear problems and a summary of finding two mean proportionals (a:x=x:y=a:y). ... He writes well, shows great clarity of thought and the Mathematical Collection is a work of very great historical importance i...

• Word Count: 647
• Approx Pages: 3
• Grade Level: Undergraduate

It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. ... In the second book of this work Archimedes' most important result is to show how to cut a given sphere by a plane so that the ratio of the volumes of the two segments has a prescribed ratio. ...

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