Galileo's aphorism that "the Book of Nature is written in the characters of Geometry" is as old as Plato, as old as Pythagoras, and as old perhaps as the wisdom of the Egyptians.
But is geometry, like the idea of nature as a book, a human invention? Interestingly enough, Euclid's Elements was one of the first books printed. After being lost to the West when the Northern tribes overran the Roman Empire, the original Greek texts were preserved in Byzantium and were translated into Latin during the Renaissance. Not only was Euclid's Elements one of the first published books, but after the bible, it is one of the most often republished.
"Geometry lies at the crossroads of a physics problem and an affair of the State." (Thousand Plateaus, p.489)
"We owe geometry to the tax collector." (J.L. Heilbron, Geometry Civilized, p.1) According to the Greek historian Herodotus, the Egyptian king Sesostris divided all the land in Egypt equally among its inhabitants in return for an annual rent. But every year the flood of the Nile washed away parts of the plots. Those whose lands had disappeared naturally objected to paying the rent on what they had lost. 'Upon which, the king sent persons to examine and determine by measurement the exact extent of the loss; and thenceforth only such a rent was demanded of him as was proportionate to the reduced size of his land. From this practice, I think, geometry first came to be known in Egypt, whence it passed into Greece.' "Geometry expresses in Greek what the Greeks received from the Egyptians, retaining its root meaning of land measurement." (Heilbron)
The Greeks, or rather Euclid, gave geometry a second meaning. By treating geometry as a deductive science, the Greeks transformed it into a mental discipline, an abstract discourse, and the exemplar of rigorous reasoning. In his commentary on Euclid, Proclus preserved a statement of Eudemos, according to which Pythagoras was the first to raise mathematics to the dignity of a liberal education by returning to its general principles and treating its problems as purely intellectual, with no restrictions to partiucular matters. This was the real stroke by which an empirical art of mensuration was made all at once at the very center of a true, philosophical knowledge. According to Proclus' Commentary on the first book of Euclid's elements, Ptolemy I, king of Egypt once asked Euclid for a shorter way to mastering geometry than working through the Elements. Euclid answered, "There is no royal road to geometry."
Plato and Euclid developed an indissoluble partnership between geometrical and philosophical ideas of truth. The Platonic concept of the theory of ideas was possible only because Plato had continually in mind the static shapes discovered by Greek mathematics. On the other hand, Greek gemetry did not achieve completion as a real system until it adopted Plato's manner of thinking. (see Ernst Cassirer, The Problem of Knowledge.) The concepts and propositions that Euclid placed at the apex of his system were a prototype and pattern for what Plato called the process of synopsis in idea. What is grasped in such synopsis is not the peculiar, fortuitous, or unstable; it possesses universal necessary and eternal truth. (see transcendence / immanence)
Critics of Euclid, such as the Greek philosopher Epicurus, used the pack donkey's geometric intuitions to ridicule Euclid's insistence on "proving things that have no need of proof." Euclid's science is ridiculous, Epicurus claimed, pointing to a proposition half way through the first book of the Elements, in which Euclid labors to show that no side of a triangle can be longer than the sum of the other two sides. "It is evident even to an ass." For a hungry ass will go directly to a bale of hay at B, without passing through any point C outside the straight line.
The exemplary role of geometry after Euclid enjoyed uncontested supremacy for centuries, until the discovery of non-Euclidean geometry introduced entirely new questions for mathematical thought and forced it to a new interpretation of its own logical structure. (see scientific space)