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 = F - F ' , and F : F ' :: BQ : AQ ; .. BQ = F.AB F - F ' ' or R.BQ = F. AB . Hence , we see that as F ' increases , the ...
... length their difference becomes less than any assignable quantity . Let us then reconsider Case 2 . We have found R = F - F ' , and F : F ' :: BQ : AQ ; .. BQ = F.AB F - F ' ' or R.BQ = F. AB . Hence , we see that as F ' increases , the ...
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 ...
... 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 ...
Page 26
... length b . Then if F1 , F2 , F3 ... F be the forces ; and a1 , a2 , a3 ... an the arms of the original couples ; and P1 , P2 , P3 , ... P the forces of the corresponding equivalent couples , we shall have P1b = F1a , P2b = F2a2 ...
... length b . Then if F1 , F2 , F3 ... F be the forces ; and a1 , a2 , a3 ... an the arms of the original couples ; and P1 , P2 , P3 , ... P the forces of the corresponding equivalent couples , we shall have P1b = F1a , P2b = F2a2 ...
Common terms and phrases
a₁ axle balance beam Cambridge catenary centre of gravity College components conditions of equilibrium consequently cos² curve cylinder density direction distance draw dx)² equal to zero equation equi exerts F₁ F₂ find the centre find the conditions find the position fixed axis fixed point forces acting forces F forces which act friction frustum fulcrum Hence horizontal plane inclined plane John Deighton length lever librium m₁ machine magnitude motion parallelogram particle passing perpendicular position of equilibrium pressure proportional pulley pyramid radius represent resolved respectively rest resultant couple right angles rigid body screw shew single force smooth string suppose surface suspended Taylor's theorem tension three forces transposed triangle Trinity College University of Cambridge virtual velocities wheel Wherefore ΣΖ ΣΥ ΣΧ
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