Give Me A Place To Stand, And

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

Having Been The Discoverer Of Many Splendid Things, He Is Said To Have Asked His Friends And Relations That, After His Death, They Should Place On His Tomb A Cylinder Enclosing A Sphere, Writing On It The Proportion Of The Containing Solid To That Which Is Contained.

Eureka! Eureka! Supposed To Have Been His Cry, Jumping Naked From His Bath And Running In The Streets, Excited By A Discovery About Water Displacement To Solve A Problem About The Purity Of A Gold Crown.

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.

Equal Weights At Equal Distances Are In Equilibrium And Equal Weights At Unequal Distances Are Not In Equilibrium But Incline Towards The Weight Which Is At The Greater Distance.