**Euclid's ***Elements* (

*Stoicheia*) is a

mathematical and

geometric treatise consisting of 13 books written by the ancient

Greek mathematician Euclid in

Alexandria,

Ptolemaic Egypt c. 300 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. The work also includes an algebraic system that has become known as

geometric algebra, which is powerful enough to solve many algebraic problems, including the problem of finding the

square root of a number. The

*Elements* is the second oldest extant Greek mathematical treatises after

Autolycus' *On the Moving Sphere*, and it is the oldest extant axiomatic deductive treatment of

mathematics. It has proven instrumental in the development of

logic and modern

science. According to

Proclus the term "element" was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' is in the Greek language the same as 'letter'. This suggests that theorems in the

*Elements* should be seen as standing in the same relation to geometry as letters to language. Later commentators give a slightly different meaning to the term 'element', emphasizing how the propositions have progressed in small steps, and continued to build on previous propositions in a well-defined order.