# Mathematics and Euclid's Elements                               The Elements ( Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. undefined 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.

- Euclid's Elements

In the history of mathematics, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements.

- Mathematics 7 related topics ## Euclid

Not to be confused with Euclid of Megara.

Not to be confused with Euclid of Megara.      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. ## Axiom

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".

The classical approach is well-illustrated by Euclid's Elements, where a list of postulates is given (common-sensical geometric facts drawn from our experience), followed by a list of "common notions" (very basic, self-evident assertions). ## Theorem    In mathematics, a theorem is a statement that has been proved, or can be proved.

A proposition is a theorem of lesser importance, or one that is considered so elementary or immediately obvious, that it may be stated without proof. This should not be confused with "proposition" as used in propositional logic. In classical geometry the term "proposition" was used differently: in Euclid's Elements (c. 300 BCE), all theorems and geometric constructions were called "propositions" regardless of their importance. ## Greek mathematics    Greek mathematics refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean.

It has been customary to credit almost half of the material in Euclid's Elements to the Pythagoreans, as well as the discovery of irrationals, attributed to Hippassus (c. ## Apollonius of Perga

Ancient Greek geometer and astronomer known for his work on conic sections.

Ancient Greek geometer and astronomer known for his work on conic sections.      For such an important contributor to the field of mathematics, scant biographical information remains.

4) Ἡ καθόλου πραγματεία, a work on the general principles of mathematics that perhaps included Apollonius's criticisms and suggestions for the improvement of Euclid's Elements ## Area

Quantity that expresses the extent of a region on the plane or on a curved surface.

Quantity that expresses the extent of a region on the plane or on a curved surface.           In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

Subsequently, Book I of Euclid's Elements dealt with equality of areas between two-dimensional figures. ## Pythagorean theorem

The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids.

The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids.                           English mathematician Sir Thomas Heath gives this proof in his commentary on Proposition I.47 in Euclid's Elements, and mentions the proposals of German mathematicians Carl Anton Bretschneider and Hermann Hankel that Pythagoras may have known this proof.

Around 300 BC, in Euclid's Elements, the oldest extant axiomatic proof of the theorem is presented.