Eureka! (i Have Found It!).

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

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.

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.

It Follows At Once From The Last Proposition That The Centre Of Gravity Of Any Triangle Is At The Intersection Of The Lines Drawn From Any Two Angles To The Middle Points Of The Opposite Sides Respectively.

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