Euclid

I worked in Alexandria in the days of Ptolemy son of Lagus. Little else of my life is secure, and that is fitting; what mattered were the proofs. I taught quietly: a room, a board, a straightedge, a compass, and students willing to grant a few simple things. From what is given, more is drawn; this is the discipline I practiced and demanded.

I composed the Elements to set geometry and number in order. I began with definitions, postulates, and common notions; from these I derived propositions, one after another, each depending only on what had been granted. My demonstrations end with hoper edei deixai—what was required to be shown. The straight line, the circle, equality, superposition: I asked little at the start so that necessity could labor much thereafter.

Within those thirteen books lie plane figures and ratios, the Pythagorean theorem, similar triangles, properties of circles, prime numbers, and the method for finding a greatest common measure. I adopted Eudoxus’ doctrine of proportion to treat incommensurables, and I set out the five regular solids shaped already by Theaetetus. I stated, too, a postulate about parallels, plainly and without disguise, though many would later quarrel with it.

I wrote other treatises—Data on what follows from what is given, Optics on visual rays and apparent size, Phaenomena on the sphere. Some works are mentioned now only by name: Porisms, Surface Loci, Division of Figures. They repeat that I told a king there is no royal road to geometry, and that I sent a coin to a student who asked for profit. Let the stories stand; the proofs suffice.