Newton's principia, first book sections I, II, III, with notes and illustrations and a collection of problems, principally intended as examples of Newton's methods (1900)
) sec a. 127. To find the area of an equiangular spiral hounded hytwo radii. Employing the same construction as above, AASB-i- aBSG^ AGSn+... : aASB:: 1+\\..+ X~^ : 1 :: 1 - V : 1 - X-^ :: SA - SL: SA - SB% but SB = SA- 2SA.AB cosa -]-AB and a A SB=l SA.AB sina; /. SA - SB^ = 4:AASBycota,… … one another, let FR^ QB, tangents to the spiral at P and Q,intersect in B, and let the normals FO, QO intersect in 0]join OR, SR. 128 NEWTON. Then, since angles SQR^ 8PR are equal to two right angles,and each of the angles OQB, OPB is a right angle, the circlewhich passes through P, i^, and Q will…
Mechanics · Celestial mechanics
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