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It Is The Invaluable Merit Of The Great Basle Mathematician Leonard Euler, To Have Freed The Analytical Calculus From All Geometric Bounds, And Thus To Have Established Analysis As An Independent Science, Which From His Time On Has Maintained An Unchallenged Leadership In The Field Of Mathematics.

It Is Natural To Men To Judge Of Things Less Known, By Some Similitude They Observe, Or Think They Observe, Between Them And Things More Familiar Or Better Known. In Many Cases, We Have No Better Way Of Judging. And, Where The Things Compared Have Really A Great Similitude In Their Nature, When There Is Reason To Think That They Are Subject To The Same Laws, There May Be A Considerable Degree Of Probability In Conclusions Drawn From Analogy.

For The Perception Of The Beautiful We Have The Term "taste"--a Metaphor Taken From That Which Is Passive In The Body And Transferred To That Which Is Active In The Mind.

And, If We Have Any Evidence That The Wisdom Which Formed The Plan Is In The Man, We Have The Very Same Evidence, That The Power Which Executed It Is In Him Also.

We Find Sects And Parties In Most Branches Of Science; And Disputes Which Are Carried On From Age To Age, Without Being Brought To An Issue. Sophistry Has Been More Effectually Excluded From Mathematics And Natural Philosophy Than From Other Sciences. In Mathematics It Had No Place From The Beginning; Mathematicians Having Had The Wisdom To Define Accurately The Terms They Use, And To Lay Down, As Axioms, The First Principles On Which Their Reasoning Is Grounded. Accordingly, We Find No Parties Among Mathematicians, And Hardly Any Disputes.