Dreams are the royal road to the unconscious.
It is a happy thing that there is no royal road to poetry. The world should know by this time that one cannot reach Parnassus except by flying thither.
The interpretation of dreams is the royal road to a knowledge of the unconscious activities of the mind.
Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.
The path to perfection is difficult to men in every lot; there is no royal road for rich or poor. But difficulties are meant to rouse, not discourage.
The efforts of a multitude of writers have rather been directed towards producing alternatives for Euclid which shall be more suitable, that is to say, easier, for schoolboys. It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute "a royal road to geometry"; the marvel is that a book which was not written for schoolboys but for grown men (as all internal evidence shows, and in particular the essentially theoretical character of the work and its aloofness from anything of the nature of "practical" geometry) should have held its own as a schoolbook for so long.
Justice, I think, is the tolerable accomodation of the conflicting interests of society, and I don't believe there is any royal road to attain such accomodations concretely.
There is no royal road to learning; no short cut to the acquirement of any art.
There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. …"Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.