...be moved through an angle of 45°. 6. If x, y, be co-ordinates of a point referred to one system of axes, and x, y', the co-ordinates of the same point referred to another system, and x = mx + ny, y = m'x' + riy', shew that m2 + m'2 — 1 _ mm ri' + ri2 — 1 nri...

...through an angle of 45°. 6. If x, y, be co-ordinates of a point referred to one system of oblique axes, and x, y, the co-ordinates of the same point referred to another system of oblique axes, and x = mx' + ny', y = m'x + riy', shew that m* + m" — 1 .•- mm...

...trilinear system, (*) = Ix + my + HZ, in which I, m, n are constant quantities. In Cartesian language, let x, y be the coordinates of any point p referred to oblique axes. For ''axis of y" read "lineX;" for "axis of x" read •' line Y ;" interpret x and y...

...trilinear system, (n) = la + my + nz, iu which /, in, n are constant quantities. In Cartesian language, let x, y be the coordinates of any point p referred to oblique axes. For "axis of y" read "lineX;" for " axis of x " read "line Y;" interpret x and </ as...

...points (r, 0), (~r, 0) are on a straight line through the pole and are equidistant from the pole. 8. Let x, y be the co-ordinates of any point P referred to the rectangular axes OX, OY, and r, 0 the polar co-ordinates of the same point referred to 0 and OX, vectorial angles being...

...points (r, 0), (—r, 0) are on a straight line through the pole and are equidistant from the pole. 8. Let x, y be the co-ordinates of any point P referred to the rectangular axes OX, OY, and r, 0 the polar co-ordinates of MX the same point referred to O and OX, vectorial angles...

...by 6 and ACS by 6'. Let x, y be the co-ordinates of any point P of the hyperbola referred to the old axes, and x', y' the coordinates of the same point referred to the new axes. Now we may use the same process employed in Art 90 ; or, we may simply change (P into —...

...OX', OF' a new set obtained by rotating each of the original axes through an angle 0. Let (x, y) and (x', y') be the coordinates of any point P, referred to the old axes and the new axes, respectively. Draw PM perpendicular to OX and PM' perpendicular to OX'....

...P'v = x' referred to X'Y', where x,y are the coordinates of a point Q referred to the first pair of axes and x', y' the coordinates of the same point referred to the second pair of axes. We find P'z = / = m1x + m2y = miPv + P'v = x' = hx + hy = kPv + kPz which do not...