The Centre Of Gravity Of Any Cylinder

Two Magnitudes Whether Commensurable Or Incommensurable, Balance At Distances Reciprocally Proportional To The Magnitudes.

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

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.

Mathematics Reveals Its Secrets Only To Those Who Approach It With Pure Love, For Its Own Beauty.

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.