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.