PYTHAGORAS was born about 582 B.C. at Samos, one of the Grecian isles.  In his youth he came in contact with THALES—­the Father of Geometry, as he is well called,—­and though he did not become a member of THALES’ school, his contact with the latter no doubt helped to turn his mind towards the study of geometry.  This interest found the right ground for its development in Egypt, which he visited when still young.  Egypt is generally regarded as the birthplace of geometry, the subject having, it is supposed, been forced on the minds of the Egyptians by the necessity of fixing the boundaries of lands against the annual overflowing of the Nile.  But the Egyptians were what is called an essentially practical people, and their geometrical knowledge did not extend beyond a few empirical rules useful for fixing these boundaries and in constructing their temples.  Striking evidence of this fact is supplied by the AHMES papyrus, compiled some little time before 1700 B.C. from an older work dating from about 3400 B.C.,[1] a papyrus which almost certainly represents the highest mathematical knowledge reached by the Egyptians of that day.  Geometry is treated very superficially and as of subsidiary interest to arithmetic; there is no ordered series of reasoned geometrical propositions given—­nothing, indeed, beyond isolated rules, and of these some are wanting in accuracy.

[1] See AUGUST EISENLOHR:  Ein mathematisches Handbuch der alten Aegypter (1877); J. Gow:  A Short History of Greek Mathematics (1884); and V. E. JOHNSON:  Egyptian Science from the Monuments and Ancient Books (1891).

One geometrical fact known to the Egyptians was that if a triangle be constructed having its sides 3, 4, and 5 units long respectively, then the angle opposite the longest side is exactly a right angle; and the Egyptian builders used this rule for constructing walls perpendicular to each other, employing a cord graduated in the required manner.  The Greek mind was not, however, satisfied with the bald statement of mere facts—­it cared little for practical applications, but sought above all for the underlying REASON of everything.  Nowadays we are beginning to realise that the results achieved by this type of mind, the general laws of Nature’s behaviour formulated by its endeavours, are frequently of immense practical importance—­ of far more importance than the mere rules-of-thumb beyond which so-called practical minds never advance.  The classic example of the utility of seemingly useless knowledge is afforded by Sir WILLIAM HAMILTON’S discovery, or, rather, invention of Quarternions, but no better example of the utilitarian triumph of the theoretical over the so-called practical mind can be adduced than that afforded by PYTHAGORAS.  Given this rule for constructing a right angle, about whose reason the Egyptian who used it never bothered himself, and the mind of PYTHAGORAS, searching for its full significance, made that gigantic geometrical