The Rationale of Circulating Numbers: With the Investigations of All the Rules And Peculiar ...

Cover The Rationale of Circulating Numbers: With the Investigations of All the Rules And Peculiar ...
The Rationale of Circulating Numbers: With the Investigations of All the Rules And Peculiar ...
Henry Clarke
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Moreover it is evident, that the jl FDG under which the objeft is fcen, is the difference of the angles DFE, DGE, which muft be a max. per qucftipn. Making therefore FE =r a 9 EG 2 J, and ED = t, we have — = the tang, of the greater angle, and / rr that of the left; and the flux, of the difference of thefe angles, exprefled ia terms of the rad. and tang, is Pi abH Trr*p -~ ■avAA t which being made s 0, and reduced, gives t =: Hence it appears that DE the dift. of the pedeftal is a mean proporti...onal between GE and FE.
Now,' it is obvious, from the nature of the queft. that the line PE mttft be the neareft dift. to the curve, or a min. therefore, putting ID 3 r, and the fern, tranfv. 3 x, we have (p*r queft* and Emerfvts Flux. f. 136) — a DH; hence (Euc, *6r* S 47. 1.) *J — I — z: HE% and fir prop, of the Ellipfe, 4 ; «t^ ** 4 J"" «k* . i*» 2 x ** -*• = HE* j V Z x #* — — = ab — *-«* 9 25 9 25 a$ reduced * 3 245*9385, and thence the area of the Ellipfe 3 136681* 1 (qnarcfect*.


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