For Since The Fabric Of The Universe

Nothing Takes Place In The World Whose Meaning Is Not That Of Some Maximum Or Minimum.

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.

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.

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

The Kind Of Knowledge Which Is Supported Only By Observations And Is Not Yet Proved Must Be Carefully Distinguished From The Truth; It Is Gained By Induction, As We Usually Say. Yet We Have Seen Cases In Which Mere Induction Led To Error. Therefore, We Should Take Great Care Not To Accept As True Such Properties Of The Numbers Which We Have Discovered By Observation And Which Are Supported By Induction Alone. Indeed, We Should Use Such A Discovery As An Opportunity To Investigate More Exactly The Properties Discovered And To Prove Or Disprove Them; In Both Cases We May Learn Something Useful.