Thursday, September 01, 2005

So there!

If in any figure AacE, terminated by the right lines Aa, AE, and the curve acE, there be inscribed any number of parallelograms Ab, Bc, Cd, &c., comprehended under equal bases AB, BC, CD, &c., and the sides, Bb, Cc, Dd, &c., parallel to one side Aa of the figure; and the parallelograms aKbl, bLcm, cMdn, &c., are completed. Then if the breadth of those parallelograms be supposed to be diminished, and their number to be augmented in infinitum; I say, that the ultimate ratios which the inscribed figure AkbLcMdD, the circumscribed figure AalbmcndoE, and curvilinear figure abased, will have to one another, are ratios of equality.

- Sir Isaac Newton (Principia Mathematica)

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