A Treatise on Statics: Containing the Theory of the Equilibrium of Forces; and Numerous Examples Illustrative of the General Principles of the Science |
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Page 9
... lengths pro- portional to the magnitudes of the forces . 26. If from a point two lines be drawn representing two forces which act upon a point ; and if upon these lines a parallelogram be constituted , the diagonal drawn from the same ...
... lengths pro- portional to the magnitudes of the forces . 26. If from a point two lines be drawn representing two forces which act upon a point ; and if upon these lines a parallelogram be constituted , the diagonal drawn from the same ...
Page 21
... length their difference becomes less than any assignable quantity . Let us then reconsider Case 2 . We have found R = FF ' , and FF :: BQ : AQ ; .. BQ = F.AB F - F ' or R.BQ F.AB. = Hence , we see that as F " increases , the point Q ...
... length their difference becomes less than any assignable quantity . Let us then reconsider Case 2 . We have found R = FF ' , and FF :: BQ : AQ ; .. BQ = F.AB F - F ' or R.BQ F.AB. = Hence , we see that as F " increases , the point Q ...
Page 23
... length proportional to the moment of a couple , being drawn perpendicular to the plane of the couple , is called " the axis of the couple . " And it is said to be the positive , or the negative axis , according as the perpendicular ...
... length proportional to the moment of a couple , being drawn perpendicular to the plane of the couple , is called " the axis of the couple . " And it is said to be the positive , or the negative axis , according as the perpendicular ...
Page 25
... length : at a , b apply pairs of equal and opposite forces f , g ; f ' , g ' ; of such mag- nitude that F. AB = f.ab , these balance each other , and therefore produce no effect . Now AB and ab being parallel , the lines Ab , Ba lie in ...
... length : at a , b apply pairs of equal and opposite forces f , g ; f ' , g ' ; of such mag- nitude that F. AB = f.ab , these balance each other , and therefore produce no effect . Now AB and ab being parallel , the lines Ab , Ba lie in ...
Page 26
... length b . Then if F1 , F2 , F3 ... F be the forces ; and a , a , a , ... a , the arms of the original couples ; and P1 , P2 , P3 ... P2 the forces of the corresponding equivalent couples , we shall have P1b = F1 a1 , P2b = F2 α2 ...
... length b . Then if F1 , F2 , F3 ... F be the forces ; and a , a , a , ... a , the arms of the original couples ; and P1 , P2 , P3 ... P2 the forces of the corresponding equivalent couples , we shall have P1b = F1 a1 , P2b = F2 α2 ...
Common terms and phrases
A₁ axes axle balance beam Cambridge catenary centre of gravity chain co-ordinates conditions of equilibrium consequently cord cos² couple cylinder density direction distance draw equal to zero equation equi F₁ F₂ find the centre find the position fixed axis fixed point forces acting forces F friction frustum fulcrum given Hence horizontal plane inclined plane length lever librium m₁ machine magnitude motion moveable osculating plane parabola parallelogram parallelopiped particle passing perpendicular position of equilibrium pressure proportional pulley pyramid radii radius represent resolved respectively rest resultant right angles rigid body screw shew smooth string suppose surface suspended T₁ Taylor's theorem tension thread three forces triangle Trinity College University of Cambridge vertex virtual velocities weight wheel Wherefore ΣΖ ΣΥ ΣΧ
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