几何的皇家大道The Royal Road to geometry

DISAPPOINTINGLY little is known about the life and personality of Euclid except that he was the first professor of mathematics at the famed Museum of Alexandria (which opened its doors about 300 B.C.), and apparently the founder of the illustrious and long-lived Alexandrian School of Mathematics. Even his dates and his birthplace are not known, but it seems probable that he received his mathematical training in the Platonic school at Athens. Although he was the author of at least ten works, and fairly complete texts of five of these have come down to us, his reputation rests mainly on his Elements. As soon as this work appeared it was accorded the highest respect. No work, except the Bible, has been more widely used, edited, or studied, and probably no work has exercised greater influence on scientific thinking.

67° The royal road in geometry. Only two anecdotes about Euclid have come down to us, and both are doubtful. In his Eudemian Summary, Proclus (410–485) tells us that Ptolemy Soter, the first King of Egypt and the founder of the Alexandrian Museum, patronized the Museum by studying geometry there under Euclid. He found the subject difficult and one day asked his teacher if there weren't some easier way to learn the material. To this Euclid replied, “Oh King, in the real world there are two kinds of roads, roads for the common people to travel upon and roads reserved for the King to travel upon. In geometry there is no royal road.”

This is an example of an anecdote told also in relation to other people, for Stobaeus has narrated it in connection with Menaechmus when serving as instructor to Alexander the Great.

Since so many students are considerably more able as algebraists than as geometers, analytic geometry, which studies geometry with the aid of algebra, has been described as the “royal road in geometry” that Euclid thought did not exist.