Leonhard Euler Quotes

In The Meantime, Most Noble Sir, You Have Assigned This Question To The Geometry Of Position, But I Am Ignorant As To What This New Discipline Involves, And As To Which Types Of Problem Leibniz And Wolff Expected To See Expressed In This Way.

If A Nonnegative Quantity Was So Small That It Is Smaller Than Any Given One, Then It Certainly Could Not Be Anything But Zero. To Those Who Ask What The Infinitely Small Quantity In Mathematics Is, We Answer That It Is Actually Zero. Hence There Are Not So Many Mysteries Hidden In This Concept As They Are Usually Believed To Be. These Supposed Mysteries Have Rendered The Calculus Of The Infinitely Small Quite Suspect To Many People. Those Doubts That Remain We Shall Thoroughly Remove In The Following Pages, Where We Shall Explain This Calculus.

Notable Enough, However, Are The Controversies Over The Series 1 - 1 + 1 - 1 + 1 - ... Whose Sum Was Given By Leibniz As 1/2, Although Others Disagree. ... Understanding Of This Question Is To Be Sought In The Word "sum"; This Idea, If Thus Conceived - Namely, The Sum Of A Series Is Said To Be That Quantity To Which It Is Brought Closer As More Terms Of The Series Are Taken - Has Relevance Only For Convergent Series, And We Should In General Give Up The Idea Of Sum For Divergent Series.

A Function Of A Variable Quantity Is An Analytic Expression Composed In Any Way Whatsoever Of The Variable Quantity And Numbers Or Constant Quantities.

Since The Fabric Of The Universe Is Most Perfect And The Work Of A Most Wise Creator, Nothing At All Takes Place In The Universe In Which Some Rule Of Maximum Or Minimum Does Not Appear ... There Is Absolutely No Doubt That Every Affect In The Universe Can Be Explained Satisfactorily From Final Causes, By The Aid Of The Method Of Maxima And Minima, As It Can Be From The Effective Causes Themselves ... Of Course, When The Effective Causes Are Too Obscure, But The Final Causes Are Readily Ascertained, The Problem Is Commonly Solved By The Indirect Method.

After Exponential Quantities The Circular Functions, Sine And Cosine, Should Be Considered Because They Arise When Imaginary Quantities Are Involved In The Exponential.

Thus You See, Most Noble Sir, How This Type Of Solution To The Königsberg Bridge Problem Bears Little Relationship To Mathematics, And I Do Not Understand Why You Expect A Mathematician To Produce It, Rather Than Anyone Else, For The Solution Is Based On Reason Alone, And Its Discovery Does Not Depend On Any Mathematical Principle.

Transcendental [numbers], They Transcend The Power Of Algebraic Methods.

To Those Who Ask What The Infinitely Small Quantity In Mathematics Is, We Answer That It Is Actually Zero. Hence There Are Not So Many Mysteries Hidden In This Concept As They Are Usually Believed To Be.

Although To Penetrate Into The Intimate Mysteries Of Nature And Thence To Learn The True Causes Of Phenomena Is Not Allowed To Us, Nevertheless It Can Happen That A Certain Fictive Hypothesis May Suffice For Explaining Many Phenomena.

Madam, I Have Come From A Country Where People Are Hanged If They Talk.

I Soon Found An Opportunity To Be Introduced To A Famous Professor Johann Bernoulli. ... True, He Was Very Busy And So Refused Flatly To Give Me Private Lessons; But He Gave Me Much More Valuable Advice To Start Reading More Difficult Mathematical Books On My Own And To Study Them As Diligently As I Could; If I Came Across Some Obstacle Or Difficulty, I Was Given Permission To Visit Him Freely Every Sunday Afternoon And He Kindly Explained To Me Everything I Could Not Understand.