The royal road in geometry. Only two anecdotes about Euclid have come down to us, and both are doubtful. In his Eudemiarz 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.
Euclid and the student. The second anecdote about Euclid that has come down to us is an unreliable but pretty story told by Stobaeus in his collection of extracts, sayings, and precepts for his son. One of Euclid's students, when he had learned the first proposition, asked his teacher, "But what is the good of this and what shall I get by learning these things?" Thereupon Euclid called a slave and said, "Give this fellow a penny, since he must make gain from what he learns. "