## Tuesday, December 20, 2016

### No Shortcut to Knowledge | Euclid's Elements

 "Ptolemy I. asked Euclid whether there was any shorter way to a knowledge of geometry  than by study of The Elements, whereupon  Euclid answered that there was no royal road  to geometry." Commentary on The Elements. Proclus Diadochus (410-485).
Euclidean geometry is the mathematical system attributed to the Alexandrian Greek mathematician Euclid (365-275 BC), which he described in his textbook The Elements, referred to as the most successful and influential textbook ever written.

The word element in the Greek language is the same as letter, and was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.

The Elements begins with plane geometry, and goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and arithmetic, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute, often metaphysical, sense.

Being first set in type in Venice in 1482, it is one of the very earliest mathematical works to be printed after the invention of the printing press and was estimated to be second only to the Bible in the number of editions published. For centuries, when the Quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.

In 1847 Oliver Byrne (1810–1880), an Irish civil engineer, surveyor, mathematician and teacher, published a notable edition of Euclid’s Elements (HERE). He was an expansive thinker and his aim was to reduce the sheer quantity of text, and to give a visual form to the information. The result is a surprisingly modern layout: a combination of bright blue, red, and yellow woodblock-printed shapes, thoroughly integrated with the black type and rules throughout the book. Byrne's edition has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements.