...mechanic. THE PRINCIPLES NATURAL, OR MECHANICAL PHILOSOPHY. No. VI. Statics. PROPOSITION. — If any two forces be represented in magnitude and direction by the sides of a parallelogram, their resultant will be represented in magnitude and direction by the diagonal of the...

...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...

...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...

...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 student...

...of two forces, is called the parallelogram of forces, and is thus concisely expressed : — If t\vo forces be represented, in magnitude and direction, by the sides of a parallelogram, an equivalent force will be represented, in magnitude and direction, by its diagonal....

...of two forces, is called the parallelogram of forces, and is thus concisely expressed : — If two forces be represented, in magnitude and direction, by the sides of a parallelogram, an equivalent force will be represented, in magnitude and direction, by its diagonal....

...then 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...

...then 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...

...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...

...common vertex 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...