How Many Theorems In Geometry

Archimedes To Eratosthenes Greeting. ... Certain Things First Became Clear To Me By A Mechanical Method, Although They Had To Be Demonstrated By Geometry Afterwards Because Their Investigation By The Said Method Did Not Furnish An Actual Demonstration. But It Is Of Course Easier, When We Have Previously Acquired By The Method, Some Knowledge Of The Questions, To Supply The Proof Than It Is To Find It Without Any Previous Knowledge.

I Am Persuaded That This Method [for Calculating The Volume Of A Sphere] Will Be Of No Little Service To Mathematics. For I Foresee That Once It Is Understood And Established, It Will Be Used To Discover Other Theorems Which Have Not Yet Occurred To Me, By Other Mathematicians, Now Living Or Yet Unborn.

Two Magnitudes Whether Commensurable Or Incommensurable, Balance At Distances Reciprocally Proportional To The Magnitudes.

Man Has Always Learned From The Past. After All, You Can't Learn History In Reverse!

It Follows At Once From The Last Proposition That The Centre Of Gravity Of Any Triangle Is At The Intersection Of The Lines Drawn From Any Two Angles To The Middle Points Of The Opposite Sides Respectively.