 | William Whewell - 1837 - 226 pages
...forces AB,BC, which act at a point A, are equivalent to a force AC. PROP. XV. If any number of forces, represented in magnitude and direction by the sides of a polygon taken in order, act on a point, they \ri\\ it in equilibrium. Let forces AB, BC, CD, DE, EA act upon a point A ; they... | |
 | William Whewell - Mechanics - 1847 - 208 pages
...P : R :: sin RAQ : sin PAQ, whence, Q : R :: sin RAP : sin QAP. 59. PROP. If any number of forces, represented in magnitude and direction by the sides of a polygon taken in order, act on a point, they will keep it in equilibrium.. Let forces AB, BC, CD, DE, EA act upon a point A... | |
 | Harvey Goodwin (Bishop of Carlisle.) - 1851 - 414 pages
...velocities be supposed to be impressed simultaneously upon a particle at rest, and if these velocities be represented in magnitude and direction by the sides of a polygon taken in order, then the particle will remain at rest. 17. It is to be observed, that in what has been here said, the... | |
 | Augustus William Smith - Mechanics, Analytic - 1855 - 368 pages
...AE =AB cos. BAE, and AF=AB cos. BAF. POLYGON OF FORCES. 24. PBOP. If any number of concurring forces be represented in magnitude and direction by the sides of a polygon, taken in order, they will be in equilibrium. Let the sides of the polygon ABCDEA represent the magnitudes and have the directions respectively... | |
 | Augustus William Smith - Mechanics, Analytic - 1855 - 340 pages
...AE ^AB cos. BAE, and AF^AB cos. BAF. POLYGON OF FORCES. 24. PROP. If any number of concurring forces be represented in magnitude and direction by the sides of a polygon, taken in order, they will be in equilibrium. Draw the diagonals AC and AD. By Art. 22, AC, the third side of the triangle ABC, represents... | |
 | John Bradford Cherriman - Mechanics - 1858 - 108 pages
...Q' = B » + P » + 2 RP cos (B, P). Polygon of 30. Polygon of Forces. T/ 7 Forces acting on a point be represented in magnitude and direction by the sides of a polygon, taken in order, they will keep the point at rest. For if ABCDEF be the polygon, the forces AB, BC, have for their resultant AC;... | |
 | George RAWLINSON (Professor of Applied Sciences, Elphinston College, Bombay.) - 1860 - 168 pages
...of the planes. Find the ratio of the inclinations of the planes. 21. Shew that if a system of forces be represented in magnitude and direction by the sides of a polygon taken in order, the moment of the forces about any point may be represented by twice the area of the polygon. 22. A... | |
 | Augustus William Smith - Mechanics, Analytic - 1863 - 340 pages
...AE =AB cos. BAE, and AF=AB cos. BAF. POLYGON OF FORCES. 24. PROP. If any number of concurring forces be represented in magnitude and direction by the sides of a polygon, taken in order, they will be in equilibrium. STATICS. Draw the diagonals AC, and AD. By Art. 22, AC, the third side of the triangle... | |
 | Stephen Parkinson - Mechanics - 1863 - 408 pages
...22, and is called the Polygon of Forces. Polygon of Forces. If any number of forces acting at a point be represented in magnitude and direction by the sides of a polygon taken in order, they will be in equilibrium. If the forces be represented in magnitude and direction by the sides of the polygon ABCDE,... | |
 | Stephen Parkinson - Dynamics - 1863 - 396 pages
...22, and is called the Polygon of Forces. Polygon of Forces. If any number of forces acting at a point be represented in magnitude and direction by the sides of a polygon taken in order, tfiey will be in equilibrium. If the forces be represented in magnitude and direction by the sides... | |
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If any number of forces acting at a point can be represented in magnitude and direction by the sides of a POLYGON taken in order, they are in equilibrium. 
