Eureka! (i Have Found It!).

There Are Things Which Seem Incredible To Most Men Who Have Not Studied Mathematics.

Give Me But A Firm Spot On Which To Stand, And I Shall Move The Earth.

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

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.

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.