The Perimeter Of The Earth Is About

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.

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.

Mathematics Reveals Its Secrets Only To Those Who Approach It With Pure Love, For Its Own Beauty.

Those Who Claim To Discover Everything But Produce No Proofs Of The Same May Be Confuted As Having Actually Pretended To Discover The Impossible.

How Many Theorems In Geometry Which Have Seemed At First Impracticable Are In Time Successfully Worked Out!