MATHEMATICIAN

Life
As extraordinary as it may seem, almost nothing is known of the life of the man who was the most celebrated mathematician of all time and the outstanding figure of his age. Some sources suggest that he was born in Alexandria; certain doubtful Arab sources give his birthplace as Tyre, describing him as the son of Naucrates, a Greek originally from Damascus. His active life, which encompassed the period from 330 - 270 BC (essentially the period of the reign of Ptolemy I Soter), was devoted to the study of mathematics and to the school he founded in the Museum in Alexandria. Pappus of Alexandria (3rd century AD) tells us that he was a mild-tempered man and a natural teacher.


Work
Euclid's mathematical genius is reflected in his most important work, the famous "Elements of Geometry", which built upon and superseded the works of his predecessors and remained the authoritative work on geometry until the 19th century. It is a work that in number of editions and translations can only be compared to Dante's "Divine Comedy" - first published, as a matter of interest, in 1472, just ten years before the "Elements". The "Elements" are preserved in 13 books, which contain 93 problems and 372 theorems in addition to the many initial propositions. Successive copyings and publications have introduced certain changes to the original text, but these are insignificant, and do not modify the initial form of the work in any real way.

Book I, contains definitions, common notions and postulates, using constructions with the ruler and compasses. The fifth postulate, "If a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles" is particularly important, for this is the famous crux geometrica, the unsolved hypothesis that drove later geometers to work out new, wholly non-Euclidean, geometries.

Books II, III and IV give the elements of "geometric algebra" (by way of example, the number a² was used to represent the square whose side was a). Book V contains a rigorous theory of proportion, and Book VI a development of the theory of similar plane figures. Books VII, VIII and IX are devoted to the arithmetic of rational numbers, where numbers are represented by segments of straight lines; this also foreshadows the development of epagoge, a method of deduction by successive logical inference. Euclid's method for determining the least common denominator of two numbers has also remained classical. Book X contains his theory of incommensurables, which he developed from his solution to the quadratic equation ÷4+á÷2+â=0. The three final books of the "Elements" are devoted to solid geometry.

Although Euclid is best known for the "Elements", he also wrote a number of other equally important works, including "Data", an introduction to geometry described by both Pappus and Marinos (5th century) as "very useful for those who wish to familiarise themselves with the difficult art of solving geometrical problems", "On Divisions" (of numbers), also used as a supplement to the "Elements", "Porisms", "Fallacies", "Surface Loci" and "Conics". He also wrote a treatise on musical intervals that many consider to be part of an entire "Elements of Music".

His wide range of interests also included physics, aspects of which are treated in his works "Optics", "Catoptrica" (the rectilinear propagation of light) and "Phenomena", a cosmography.