There Are Things Which Seem

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.

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

The Centre Of Gravity Of Any Parallelogram Lies On The Straight Line Joining The Middle Points Of Opposite Sides.

Eureka, Eureka! (i Found It, I Found It!).

Spoken Of The Young Archimedes: . . . [he] Was As Much Enchanted By The Rudiments Of Algebra As He Would Have Been If I Had Given Him An Engine Worked By Steam, With A Methylated Spirit Lamp To Heat The Boiler; More Enchanted, Perhaps For The Engine Would Have Got Broken, And, Remaining Always Itself, Would In Any Case Have Lost Its Charm, While The Rudiments Of Algebra Continued To Grow And Blossom In His Mind With An Unfailing Luxuriance. Every Day He Made The Discovery Of Something Which Seemed To Him Exquisitely Beautiful; The New Toy Was Inexhaustible In Its Potentialities.