## 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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**ΣΥ**Consequently in this case the resultant is a single force R acting at the point just found . 66. When the forces are reducible to a single result- ant , to find the equation of the line in which it acts . Let x'y ' be the co ... Page 34

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**ΣΥ ΣΥ**== ΣΤ ' , or y'ΣX - x'ΣY = Σ ( Xy – Yx ) . 67. Any number of forces act in one plane at dif- ferent points of a rigid body ; to find the conditions that they may balance each other . Let the system of forces be that of Art . 64 ... Page 43

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**ΣΥ**, R cos y = ΣΖ , R2 = ( EX ) 2 + ( ΣY ) 2 + ( ΣZ ) 2 : Σ and G cos a ' = ( Zy - Yx ) = L suppose G cos B ' = ( X≈ − Z∞ ) = M ...... G cos y = - ( Yx – Xy ) = N G2 = L2 + M2 + N2 . These eight equations give both the magnitude and ... Page 45

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**ΣΥ**, ΣΖ and add the results we shall find 0 = ΙΣΧ + ΜΣΥ + ΝΣΚ , which being satisfied by hypothesis , the three equations are not independent , but any one is derivable from the other two . Consequently any two of these are the ... Page 46

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**ΣΥ**= y cos B & COS Y y ΣΕ ΣΤ Again , we may suppose the plane of G to pass through the origin . And since a ' , B ' , y ' are the angles which a perpen- dicular upon it makes with the co - ordinate axes , its equation is x ' cos a ' + y ...### 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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