There Are Things Which Seem Incredible To

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.

Eureka! (i Have Found It!).

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.

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

The Diameter Of The Earth Is Greater Than The Diameter Of The Moon And The Diameter Of The Sun Is Greater Than The Diameter Of The Earth.