| Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...and, assuming its truth for the magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium,...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 situated at... | |
| Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...and, assuming its truth for the magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium,...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 situated at... | |
| Stephen Parkinson - 1863 - 408 σελίδες
...the parallelogram of forces we can easily deduce the following theorem first stated by Lami, in 1687. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle contained between the directions of the remaining two. For referring to the fig. of Art. (20),... | |
| 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). For this latter... | |
| 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 represented... | |
| Isaac Todhunter - 1867 - 372 σελίδες
...of a triangle perpendicular to the lines of action. 38. 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. Let forces P, Q, R acting on a particle at 0 keep it in equilibrium. Then,... | |
| Isaac Todhunter - 1867 - 368 σελίδες
...of a triangle perpendicular to the lines of action. 38. 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. Let forces P, Q, R acting on a particle at 0 keep it in equilibrium. Then,... | |
| James Hamblin Smith - 1868 - 102 σελίδες
...similar triangles. Hence and and MN : NO :: AB :: P NO : OH:: BD OM : MN:: DA :: R BD Q DA S, AB P. xxii. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle contained between the directions of the other two. Let P, Q, R be the three forces. a, /8, y... | |
| Ephraim Chambers - 1870 - 872 σελίδες
...substituting the sines of the supplementary angles) : : ein. QAR' : sin. PAH' : sin. PAQ ; that is, each force is proportional to the sine of the angle between the directions of the other tw o. TRIA'NGULAR NUMBERS. See FIOCRAT* NUMBERS. TRIANGULATION is the operation... | |
| bart John Francis Twisden (Sir) - 1870 - 394 σελίδες
...: K : : sin RAP: sin p A Q. These proportions are sometimes expressed by the rule, <If three forces are in equilibrium, each force is proportional to the sine of the angle contained by the other two.(2) Employing the same figure, we have, by a wellknown theorem in... | |
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