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 11
... proportional to the sine of the angle between the directions in which the other two act . Let the forces be P , Q , R ( fig . 5 ) acting in the directions ОА , ОВ , ОС . In OA , OB , take points A , B , such that OA , OB represent the ...
... proportional to the sine of the angle between the directions in which the other two act . Let the forces be P , Q , R ( fig . 5 ) acting in the directions ОА , ОВ , ОС . In OA , OB , take points A , B , such that OA , OB represent the ...
Page 20
... proportional to those sides ( Art . 27 ) . Similarly .. F : f :: PQ : AQ f ' : F ' :: BQ : PQ .. F : F ' :: BQ : AQ ; · :: f = f ' . Consequently Q divides AB into two parts which are in- versely proportional to the forces adjacent to ...
... proportional to those sides ( Art . 27 ) . Similarly .. F : f :: PQ : AQ f ' : F ' :: BQ : PQ .. F : F ' :: BQ : AQ ; · :: f = f ' . Consequently Q divides AB into two parts which are in- versely proportional to the forces adjacent to ...
Page 23
... 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 stands on ...
... 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 stands on ...
Page 28
... proportional to their moments , are in this case proportional to their arms OA , OB , OD ; we may therefore consider OA , OB , OD as being equal to the axes . If therefore from O in the plane OBA , we draw three lines respectively ...
... proportional to their moments , are in this case proportional to their arms OA , OB , OD ; we may therefore consider OA , OB , OD as being equal to the axes . If therefore from O in the plane OBA , we draw three lines respectively ...
Page 70
... proportional to the accelerating force of gravity , at the re- spective places . This force is generally denoted by g ; and hence we have for a given body Wag . Consequently , for different bodies at different places W & Mg . For ...
... proportional to the accelerating force of gravity , at the re- spective places . This force is generally denoted by g ; and hence we have for a given body Wag . Consequently , for different bodies at different places W & Mg . For ...
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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