Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?
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 is the noblest branch of physics.
When you have to pass a law to make a man let me have a house, or you have to pass a law to make a man let me go to school, or you have to pass a law to make a man let me walk down the street, you have to enforce that law and you'd have to be living actually in a police state. It would take a police state in this country.
I was allergic to school. I was completely befuddled by school. I was trying so hard, but I couldn't succeed. I took geometry for four years, the same course over and over again, and I did not graduate with my senior class. I finally passed geometry after doing summer school, and eventually, I graduated.
Many years ago, it was my opportunity to serve as president of the Canadian Mission. There we had a branch with very limited priesthood. We always had a missionary presiding over the branch. I received a strong impression that we needed to have a member of the branch preside there.
Apparently a great many people have forgotten that the framers of our Constitution went to such great effort to create an independent judicial branch that would not be subject to retaliation by either the executive branch or the legislative branch because of some decision made by those judges.
I am mindful of the difference between the executive branch and the legislative branch. I assured all four of these leaders that I know the difference, and that difference is they pass the laws and I execute them.
The present author confesses that, to him, geometry is nothing at all, if not a branch of art ...
A Treatise on Algebraic Plane Curves
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.
When you treat reprehensible and ludicrous arguments with respect you have elevated the reprehensible and made the ludicrous a bit more reasonable. Having a serious argument with a Nazi makes the horror of the Holocaust a debatable point. Don't wrestle in the mud with pigs. You get dirty and the pig likes it.
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!
You never get to the end of Christ's words. There is something in them always behind. They pass into proverbs--they pass into laws--they pass into doctrines--they pass into consolations; but they never pass away, and, after all the use that is made of them, they are still not exhausted.
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
The early study of Euclid made me a hater of geometry.
People assume that the executive branch has more power than it actually has. Only the legislative branch can create the laws; the executive branch cannot create the laws. So, if the executive branch tries to create a branch one side or the other... you go back to the founders of the nation. They set up a system that ensures that it doesn't happen.