## 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 iii

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**given**at the end of the Treatise has been considerably enlarged , chiefly by the addition of Examples of an elementary character . In the selection of them care has been taken to choose such as illustrate Statical Principles under every ... Page v

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**given**the proof which in the first edition was**given**in the text . The same objection , ( and for the same reason ) lies against the proof of the parallelogram of forces from the properties of the lever . This method , though allowable ... Page vi

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**given**by Lagrange in his Mécanique Analytique , page 22 , et seq . , though highly ingenious , I regard as a fallacy ; and , if not fallacious , deficient in generality . In the last Chapter , I have endeavoured to set before the reader ... Page 9

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**given**forces are equal ; let us assume that p , q and r are three forces , such that this is 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 AD . Take AB , AC , CD to ... Page 12

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**given**and it be required to resolve it into two components acting in directions at right angles to each other , we must employ the equations X - R cose , and Y = R sin 0 , = which are derived from the equations OM = OP cos 0 , and MP ...### 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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