 | John Radford Young - 1832 - 390 σελίδες
...of their opposite angles, we may say that the intensity of any one of three equilibrating forces in proportional to the sine of the angle between the, directions of the other two. If we represent the sides PC, PC' by P, Q, and the angle CPC' of their direction by a, then, since... | |
 | Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two. Two equal particles, each attracting with a force varying directly as the distance, are... | |
 | Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two. Two equal particles, each attracting with a force varying directly as the distance, are... | |
 | Denison Olmsted - 1861 - 492 σελίδες
...stated in another form, thus : when a body is in equilibrio by the action of three forces, each is as the sine of the angle between the directions of the other two. Let BA, CA, and DA (Fig. 40) hold the particle A at rest ; then the force, BA, FIO. 40. may be represented... | |
 | Stephen Parkinson - 1863 - 408 σελίδες
...however will have no difficulty in proving the following: If each of three forces acting at a point be proportional to the sine of the angle between the directions of the other two, either the three forces are in equilibrium, or they have a resultant double of some one of the forces.... | |
 | Stephen Parkinson - 1863 - 396 σελίδες
...their directions are not parallel : — (i) Their lines of action must meet in a point, Art. (22). (ii) Each force is proportional to the sine of the angle between the other two, the direction of each force lying without the angle formed by the other two, Art. (23).... | |
 | University of Cambridge - 1864 - 694 σελίδες
...it in equilibrium, their directions, if not parallel, shall meet in a point, and each force shall be proportional to the sine of the angle between the directions of the other two. A wire without weight is bent into the form of an arc of a circle. To one extremity is tixed a heavy... | |
 | William Walton - 1864 - 234 σελίδες
...it in equilibrium, their directions, if not parallel, shall meet in a point, and each force shall be proportional to the sine of the angle between the directions of the other two. !v/ A wire without weight is bent into the form of an arc of a circle • To one extremity is fixed... | |
 | Isaac Todhunter - 1866 - 386 σελίδες
...Q:R::AB:AC(oT:BD-):AD POLYGON OP FORCES. Conversely if three forces act on a particle, and each force is as the sine of the angle between the directions of the other two, it may be shewn that one of the forces is equal in magnitude to the resultant of the other two, and... | |
 | James McDowell - 1867 - 120 σελίδες
...(Euc. I. 47) that is, K2 therefore B = </(P* + <?"). QED *24. If three forces acting at a point be in equilibrium, each force is proportional to the sine of the angle between the other two, (Fig. 1. Art. 16.) Let the three forces P, Q, R, acting at 0, be in equilibrium, and be... | |
| |
If three forces acting on a particle keep it in equilibrium, each force is proportional to the sine of the angle between the directions of the other two. 
