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.
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!] On Discovery Of A Method To Test The Purity Of Gold.
Two Magnitudes Whether Commensurable Or Incommensurable, Balance At Distances Reciprocally Proportional To The Magnitudes.
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.
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.
Any Solid Lighter Than A Fluid Will, If Placed In The Fluid, Be So Far Immersed That The Weight Of The Solid Will Be Equal To The Weight Of The Fluid Displaced. On Floating Bodies I, Prop 5.
How Many Theorems In Geometry Which Have Seemed At First Impracticable Are In Time Successfully Worked Out!
