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 8
... equal to their sum . : If some act in one direction and some in the opposite direction , then by the first case the ... zero , for in that case their resultant vanishes , and they produce no effect . Hence the condition of equilibrium of any ...
... equal to their sum . : If some act in one direction and some in the opposite direction , then by the first case the ... zero , for in that case their resultant vanishes , and they produce no effect . Hence the condition of equilibrium of any ...
Page 14
... equal to zero . The converse is evidently true also . No other condition is necessary for equilibrium , for if Σ . F cos a = 0 , and . F sin a = 0 , it follows inevitably that R = 0 , and therefore there is equilibrium . CHAPTER II ...
... equal to zero . The converse is evidently true also . No other condition is necessary for equilibrium , for if Σ . F cos a = 0 , and . F sin a = 0 , it follows inevitably that R = 0 , and therefore there is equilibrium . CHAPTER II ...
Page 18
... equal to zero . CHAPTER III . ON FORCES WHICH ACT IN ONE PLANE 18 FORCES NOT IN A PLANE ACTING ON A POINT .
... equal to zero . CHAPTER III . ON FORCES WHICH ACT IN ONE PLANE 18 FORCES NOT IN A PLANE ACTING ON A POINT .
Page 21
... equal to F - F ' , the algebraic sum of the forces , and acts in the direction of the greater force . The word sum ... zero in the limit . Hence , in the ulti- mate state , that is , when F " differs from F by less than any assignable ...
... equal to F - F ' , the algebraic sum of the forces , and acts in the direction of the greater force . The word sum ... zero in the limit . Hence , in the ulti- mate state , that is , when F " differs from F by less than any assignable ...
Page 22
... zero acting at a point infinitely distant from A or B ; yet even then the product R. BQ remains finite , which apart ... equal forces acting in contrary directions on different points of a rigid body is not reducible to a single resultant .
... zero acting at a point infinitely distant from A or B ; yet even then the product R. BQ remains finite , which apart ... equal forces acting in contrary directions on different points of a rigid body is not reducible to a single resultant .
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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