Euclid of Alexandria was an ancient Greek mathematician, who is regarded as the ‘father of geometry’. His work appeared during the time of Ptolemy I. In the history of mathematics, one of the highly esteemed work of all time was his Elements. It served as a prescribed textbook for teaching mathematics from its publication till the 20th century. In this book he highlighted the principles of Euclidean geometry. His other work was based on perspective, conic section, number theory and spherical geometry.
Similar to other Greek scholars of his time, details about his life are barely survived through the ages. In fact, the date of birth, place and circumstances are unknown and estimated roughly. He was born somewhere during the mid-4th century BC and mentioned as the author of Elements in the writings of Archimedes. He was introduced by Proclus in his Commentary on the Elements. It was commented that Euclid was influenced by Plato’s ‘persuasion’ and the work of his pupil. Proclus told a story about Euclid that once Ptolemy I asked him if there is an easier way to learn geometry and to which he responded, “There is no royal road to geometry.” However, the authenticity of this anecdote might be questionable.
Arabian authors wrote Euclid’s biography mentioning his birthplace as town of Tyre. Yet again the biography turned out to be based on fictitious incidents. There is another strange theory proposed by some researchers that Euclid was not an individual but a group of mathematician who called themselves Euclid. On the other hand, there are several scholars who give no credit to such preposterous theory, having no evidence to substantiate it.
Despite the fact that much of the content of Euclid’s Elements is not original and proposed by previous mathematician. The true accomplishment lies in the fact that he compiled all the work in a logically coherent manner which made it easier to access the contents. Moreover, he provided a system of proofs that remained relevant to mathematics even centuries later. The best known content of the book include the geometric results and number theory. It also elucidates the link between Mersenne primes and perfect numbers. Besides these, he also mentioned the use of the Euclidean algorithm for finding the greatest common divisor of two numbers and the fundamental theorem of arithmetic.
The Elements proposed a geometrical system which was considered the only type of geometry possible. Hence, to differentiate between that geometry and the newly discovered geometry during the nineteenth century, it is referred to as Euclidean geometry. Besides Elements, other five of Euclid’s works survived through the ages. The implications and nature of ‘given’ information in geometry is focused upon in his Data. One of his works survived partially in Arabic translation, bearing the title On Divisions of Figures. It discusses the division of geometrical figures into two or several equal parts. The mathematical theory of mirrors and the image formed on concave and spherical mirror is mentioned in Catoptrics.
Another one of Euclid’s treatise, Phaenomena, highlights the spherical astronomy similar to On the Moving Sphere by Autolycus. Optics follows the Platonic tradition describing the way things appear to human eye. The things that are seen at a greater angle appear greater and vice versa. The size of an object can be deduced by factoring in the distance and length of that object from afar, was also cited in the book.