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 49
—x line, and (x, y) and {x\ j) are the given points. Dem.—Let M N be any right line referred to the rect-angular axes XX, YY. Let P be any point in theline, and designate its co-ordinates, AD and PD, by a;andy. Let P and P be the given points whoseco-ordinates are x, t/, and x, y, respectively.Now… … y—y ■ y—y X : X or y — y = y TT (a;— x). Q. E. D. Cor. 1.—Since PPF = NGX, and y X X PFP F V —y tan PPF, wehave^-7 = the tangent of the angle which the line X —X makes with the axis of abscissas. If x X n y — y __ y — y . , „ ^ — GO, which being the tangent of •JO iv vl 90°, shows that the line is…
Geometry, Analytic · Calculus
Internet Archive · Boston College Libraries · Public Domain Mark 1.0. Free to use for anything.
