A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 95
etc., as it should from the construction. OS, JProb.—To produce the equation of the cycloid referred to itsaxis as the axis of abscissas, and a tangent at the vertex of the axis ( B, ^ig.71), as the axis of ordinates. Solution.—Let PM =?/, and BM =ic. Now PM=PL+ LM. But PL-=\/2r.^•—x^, and LM = IF… … For PR = L M = A F — AI = arcHPI —arc PI =arc HP = arc BR. A I F Fig. 71. ScH. 1.—Considering the equation x = versin-y — \/%-y ~~y^, we observe that there are an infinite number of values of x for every value ofy. First of all, the term versin-^ is ambiguous as to its sign, since a nega-tive arc…
Geometry, Analytic · Calculus
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