Sinopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: ...of the new method as thus far developed, is to the determination of the centre of gravity of areas and solids. We shall confine ourselves to areas only, merely observing that all the principles hitherto developed apply equally well to forces in space. The forces being given by their orthographic projections upon two planes after the manner of descriptive geometry, the projections upon each plane may be dealt with as forces lying in that plane, and thus the projections of the force and equilibrium polygons, the resultant, etc., determined. A body under the action of gravity may be considered as a body acted upon by parallel forces. The resultant of these forces being found for one position of the body or the body being considered as fixed, for one common direction of the forces may have its point of application anywhere in its line of direction. For a new position of the body or another direction of the forces there is another position for the resultant. Among all the points which may be considered as points of application of these two resultants there is one which remains unchanged in position, whatever the change in direction of the parallel forces. This point must evidently lie upon all the resultants, and is therefore given by the intersection of any two. It is hardly necessary to give illustrations of the method of procedure. Generally, we divide up the given area into triangles, trapezoids, rectangles, etc., and reduce the area of each of these figures to a rectangle of assumed base. The heights of these reduced rectangles will then be proportional to the areas, and hence to the force of gravity acting upon them; i. e., to their weights. Consider then these heights as forces. Construct the force polygon by laying them off one after the other. Choose a ...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: ...of the new method as thus far developed, is to the determination of the centre of gravity of areas and solids. We shall confine ourselves to areas only, merely observing that all the principles hitherto developed apply equally well to forces in space. The forces being given by their orthographic projections upon two planes after the manner of descriptive geometry, the projections upon each plane may be dealt with as forces lying in that plane, and thus the projections of the force and equilibrium polygons, the resultant, etc., determined. A body under the action of gravity may be considered as a body acted upon by parallel forces. The resultant of these forces being found for one position of the body or the body being considered as fixed, for one common direction of the forces may have its point of application anywhere in its line of direction. For a new position of the body or another direction of the forces there is another position for the resultant. Among all the points which may be considered as points of application of these two resultants there is one which remains unchanged in position, whatever the change in direction of the parallel forces. This point must evidently lie upon all the resultants, and is therefore given by the intersection of any two. It is hardly necessary to give illustrations of the method of procedure. Generally, we divide up the given area into triangles, trapezoids, rectangles, etc., and reduce the area of each of these figures to a rectangle of assumed base. The heights of these reduced rectangles will then be proportional to the areas, and hence to the force of gravity acting upon them; i. e., to their weights. Consider then these heights as forces. Construct the force polygon by laying them off one after the other. Choose a ...
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