The Enchanting Charms Of This Sublime Science

The Higher Arithmetic Presents Us With An Inexhaustible Store Of Interesting Truths - Of Truths, Too, Which Are Not Isolated, But Stand In A Close Internal Connection, And Between Which, As Our Knowledge Increases, We Are Continually Discovering New And Sometimes Wholly Unexpected Ties.

With A Thousand Joys I Would Accept A Nonacademic Job For Which Industriousness, Accuracy, Loyalty, And Such Are Sufficient Without Specialized Knowledge, And Which Would Give A Comfortable Living And Sufficient Leisure, In Order To Sacrifice To My Gods [mathematical Research]. For Example, I Hope To Get The Editting Of The Census, The Birth And Death Lists In Local Districts, Not As A Job, But For My Pleasure And Satisfaction.

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

That This Subject [of Imaginary Magnitudes] Has Hitherto Been Considered From The Wrong Point Of View And Surrounded By A Mysterious Obscurity, Is To Be Attributed Largely To An Ill-adapted Notation. If, For Example, +1, -1, And The Square Root Of -1 Had Been Called Direct, Inverse And Lateral Units, Instead Of Positive, Negative And Imaginary (or Even Impossible), Such An Obscurity Would Have Been Out Of The Question.

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.