Mathematics Is The Queen Of The Sciences.

It Is Not Knowledge, But The Act Of Learning, Not Possession But The Act Of Getting There, Which Grants The Greatest Enjoyment. When I Have Clarified And Exhausted A Subject, Then I Turn Away From It, In Order To Go Into Darkness Again; The Never-satisfied Man Is So Strange If He Has Completed A Structure, Then It Is Not In Order To Dwell In It Peacefully,but In Order To Begin Another. I Imagine The World Conqueror Must Feel Thus, Who, After One Kingdom Is Scarcely Conquered, Stretches Out His Arms For Others.

As Is Well Known The Principle Of Virtual Velocities Transforms All Statics Into A Mathematical Assignment, And By D'alembert's Principle For Dynamics, The Latter Is Again Reduced To Statics. Although It Is Is Very Much In Order That In Gradual Training Of Science And In The Instruction Of The Individual The Easier Precedes The More Difficult, The Simple Precedes The More Complicated, The Special Precedes The General, Yet The Min, Once It Has Arrived At The Higher Standpoint, Demands The Reverse Process Whereby All Statics Appears Only As A Very Special Case Of Mechanics.

I Am Coming More And More To The Conviction That The Necessity Of Our Geometry Cannot Be Demonstrated, At Least Neither By, Nor For, The Human Intellect. . . Geometry Should Be Ranked, Not With Arithmetic, Which Is Purely Aprioristic, But With Mechanics.

The Infinite Is Only A Manner Of Speaking.

Less Depends Upon The Choice Of Words Than Upon This, That Their Introduction Shall Be Justified By Pregnant Theorems.