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 v
... true in fact , the law of the composition of forces acting on a point would still be true ; it is evident , therefore , that to make the truth of the former an essential step in the proof of the latter , is erroneous in principle . In ...
... true in fact , the law of the composition of forces acting on a point would still be true ; it is evident , therefore , that to make the truth of the former an essential step in the proof of the latter , is erroneous in principle . In ...
Page 6
... true , viz . , that one force may be replaced by a system of several forces . When one force is replaced by a system ... true when they act on a rigid body . It is always true , however , that the same force may have different systems of ...
... true , viz . , that one force may be replaced by a system of several forces . When one force is replaced by a system ... true when they act on a rigid body . It is always true , however , that the same force may have different systems of ...
Page 9
... true for Ρ and and also for and r . At the point A apply p in the direction AB : and q , r , both in the direction ... true for the two forces p , q ; and also for the two forces p , r ; it is also true for the forces p and q + r . Now ...
... true for Ρ and and also for and r . At the point A apply p in the direction AB : and q , r , both in the direction ... true for the two forces p , q ; and also for the two forces p , r ; it is also true for the forces p and q + r . Now ...
Page 10
... true for mp and p , and also for mp and p ; therefore it is true for mp and 2p ; and as before for mp and np , n being an integer . Hence our proposition respecting the direction of the resultant is true for any two commensurable forces ...
... true for mp and p , and also for mp and p ; therefore it is true for mp and 2p ; and as before for mp and np , n being an integer . Hence our proposition respecting the direction of the resultant is true for any two commensurable forces ...
Page 14
... 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 . THE ON FORCES WHICH ACT UPON A 14 FORCES ...
... 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 . THE ON FORCES WHICH ACT UPON A 14 FORCES ...
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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