Euclid's Elements and Algorithms

Euclid, fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry”. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.
"Euclid" is the anglicized version of the Greek name meaning "Good Glory".

Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. Euclid's Elements has been referred to as the most successful and influential textbook ever written. It is one of the very earliest mathematical works to be printed.

Contents of the books
Books 1 through 4 deals with plane geometry:
  * Book 1 contains Euclid's 10 axioms (5 named postulates—including the parallel postulate—and 5 named axioms) and the basic propositions of geometry: the pons asinorum (proposition 5) , the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area).
  * Book 2 is commonly called the "book of geometrical algebra," because most of the propositions can be seen as geometric interpretations of algebraic identities, such as a(b + c + ...) = ab + ac + ... or (2a + b)2 + b2 = 2(a2 + (a + b)2).
  * Book 3 deals with circles and their...