There is no royal road to any learning, no matter what it is. There is no royal road to any righteous living, no matter who you are or what you are. There is no royal road to anything that is worthwhile. Nothing that is deserving of earning or of cherishing comes except through hard work. I care not how much of a genius you may be, the rule will still hold.
There is no royal road to a successful life, as there is no royal road to learning. It has got to be hard knocks, morning, noon, and night, and fixity of purpose.
Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
What physics tells us is that everything comes down to geometry and the interactions of elementary particles. And things can happen only if these interactions are perfectly balanced.
There is only one royal road for the spiritual journey...Love
Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.
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.
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. (Preface to the French edition).
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
Theoretically, the road to WrestleMania is like an election year. The Royal Rumble usually has 30 people in it, which narrows down to 4 and then finally two. Only one of them can go on to the main event.
The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.