The Method of Fluxions and Infinite Series - With Its Application to the Geometry of Curve-Lines #220071

Now from hence the tell of our Author's Conclufions, in the flame Lemma, may be thus derived fomething more explicite'ly. The Moment of the Rectangle AB being found to be ab-i-db, when the contemporary Moments of A and B are reprefented by a and 6 'retpe'é'tivdy make B A, and therefore b a, and then the Moment of A x A, or A5; will be Arz 4a, or zaa. Again, make B -a4, and therefore Z za'a, and then the Moment of ta or A3, will be 24a+ a — Az, or 34a. Again, make B As, and therefore 5: 34a), and then the Moment of A xa, or 'a*, will 'be 3aa3 or 4dais. Again, make B =a4, and therefore b:_-é 4da3, and then the Moment of A x A4, or A', will be 4da4 +d'aa, or 54a4. And fo on £72 iryfnitum. Therefore in general, affuming m to reprefent any integer affirmative Number, the fimornent of A will be maw.