# Euclid's Elements

## Who was Euclid?

Euclid

Euclid of Alexandria (19th Century)

Greek mathematician Euclid lived in Alexandria, Egypt around 300 BCE, it is thought he attended Plato’s academy in Athens before moving here. Euclid is often referred to as the “Father of Geometry” and wrote possibly the most important and successful mathematical textbook in history, known as the “Elements” - a comprehensive compilation and explanation of all the known mathematics of his time and the earliest known discussion of geometry, the branch of mathematics relating to the study of space and the relationships between points, lines, curves and surfaces.

The thirteen volumes of Euclid’s “Elements” contains 465 formulas and proofs, described in a clear, logical style using only a compass and a straight edge, it contains formulas for calculating the volumes of solids such as cones, pyramids and cylinders. The books discuss perfect numbers and primes; proof and generalization of Pythagoras’ Theorem, Euclid proved that the diagonals of the regular pentagon cut each other in "extreme and mean ratio", which is now more commonly known as the golden ratio or golden section.

Euclidean geometry is still as valid today as it was 2,300 years ago, it is widely used in many disciplines, including art, architecture, science and engineering, to name but a few.

References

Cambridge University, P. (1999) 'Cambridge dictionaries online'. Cambridge: Cambridge University Press.

Euclid of Alexandria, 19th Century (engraving), Cook, J.W., Private Collection, Bridgeman Images.

Mastin, L. (2010) The story of mathematics. Available at: http://www.storyofmathematics.com/hellenistic_euclid.html (Accessed: 29/02/18).

O'Connor, J. and Robertson, E. (July 2001 ) The Golden ratio. Available at: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Golden_ratio.html (Accessed: 08/03/18).

## Euclid's Elements

Euclid - The thirteen books of the Elements

Contents

Book I – Foundations of Plane Geometry

Book II – The Geometry of Rectangles

Book III – The Geometry of the Circle

Book IV – Regular Polygons in Circles

Book V – The General Theory of Magnitudes in Proportion

Book VI – The Plane Geometry of Similar Figures

Book VII – Basic Arithmetic

Book VIII – Numbers in Continued Proportion

Book IX - Numbers in Continued proportion; the Theory of Even and Odd Numbers, Perfect Numbers

Book X – Incommensurable Line Segments

Book XI – Foundations of Solid Geometry

Book XII – Areas and Volume; Eudoxus’s Method of Exhaustion

Book XIII – The Platonic Solids

Reference

Euclid (1956) The thirteen books of Elements. 2d ed. New York: Dover Publications.