...cos ß cos ß1 , r cos у cos ^ , and their sum is r (cos a cos Oj + cos ß cos ß, + cos у cos yj = r cos 0, 0 being the angle between the lines. The...one of whose angular points is at the origin. Let ЛОВ (fig. 10) be such a triangle, and MOMl its projection; then if OM= r, OM1 = r1} MOx = 0, area...

...planes, and then to take the sum of these projections projected on the second plane. (20) To cxpress the area of a triangle in terms of the coordinates...projection; then if OM ' = r, OM, = r,, MOx = 0, area MOM, = | rr, sin (0 - 0,). Let the co-ordinates of M be x, y ; and of M, , x,, y,; then area MOM^ =...

...quadrilateral, PB the positive axis of x, and the points A, B, C, D, respectively, Now the expression for the area of a triangle in terms of the co-ordinates of its three angular points (#1^1, x^y- a .r 3 ^ 3 ) in reference to rectangular axes is ( Young's Analytical...

...r cos/3 cos/3,, r cosy cosy ^ and their sum is r (cosa cosa, + cos/8 cos/9, + cos7 cos7j = r cos0, 0 being the angle between the lines. The same proposition...projection ; then, if OM — r, OM, = r,, MOx — 0, M, Ox = 0^ area MOM, = \rr, sin (0 - 0,). Let the coordinates of M be a;, y ; and of M^ a;,, y, ; then...

...r cos/3 cos/3,, r 00s7 0037,, and their sum is r (cosa cosa, + cos/9 cos/9, + 00s7 00s7,) = r cos0, 0 being the angle between the lines. The same proposition...one of whose angular points is at the origin. Let A OB (fig. 10) be such a triangle, and MOMt its projection; then, if OM = r, OMt = r,, 'M Ox = 0, Mt...

...lines, 36. Find the area included between the lines, x—y = o, x + y = o, x—y = a, x + y=b. 3?. Express the area of a triangle in terms of the coordinates of its angular points a, b ; a', b' ; a", 6". II. CIRCLE. 38. Find the equation to a circle referred to oblique axes. 39....

...drawn, then will these lines meet in the same point on В К produced. Prove this by coordinates. 5. Express the area of a triangle in terms of the coordinates of its three angles. 6. Three lines AB, AC, AD, which emanate from the same point A, are given in position....

...which we require the co-ordinates of a point midway between two given points ; then nl = w2 and 11. To express the area of a triangle in terms of the coordinates of its angular points. Let ABC be a triangle ; let ^ yv be the co-ordinates of x those of B ; x3, y3, those of C. Draw the...

...rfy/r [74. There are two methods of arriving at this result ; we may take the ordinary expression for the area of a triangle in terms of the co-ordinates of its angular points, and substitute the values of the co-ordinates just given. Or we may proceed thus — find the area...

...which we require the co-ordinates of the point midway between two given points ; then и, = n3 and 11. To express the area of a triangle in terms of the coordinates of its angular points. Let ABO be a triangle; let xlt y 'be the co-ordinates of A ; хг, у, those of B; xt, y, those of...