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 78
... base AC , are proportional to the perpendiculars from B and D on AC , which are also proportional to BE , DE respectively ; hence , in the above equation , instead of the triangles ABC , ADC , and the trapezium , which is their sum ...
... base AC , are proportional to the perpendiculars from B and D on AC , which are also proportional to BE , DE respectively ; hence , in the above equation , instead of the triangles ABC , ADC , and the trapezium , which is their sum ...
Page 79
... base of the pyramid . E , H the centres of gravity of the base and the face ACD . Join AE , BH , BE , AH . Then , because E is the centre of gravity of the base , therefore BE produced , bisects CD . For a similar reason , AH produced ...
... base of the pyramid . E , H the centres of gravity of the base and the face ACD . Join AE , BH , BE , AH . Then , because E is the centre of gravity of the base , therefore BE produced , bisects CD . For a similar reason , AH produced ...
Page 80
... base , and the centre of gravity of the solid will be at the distance of one - fourth of this line from the base . 151. It may be shewn , by a method very similar to the one in Art . 147 , that if four equal bodies be placed in the four ...
... base , and the centre of gravity of the solid will be at the distance of one - fourth of this line from the base . 151. It may be shewn , by a method very similar to the one in Art . 147 , that if four equal bodies be placed in the four ...
Page 81
... base will be intercepted between this plane and the base . For a fourth part of AE is intercepted , and therefore ( Eucl . xi . 16 ) every line from the vertex to the base is divided in the same proportion . 154. Hence , if a ...
... base will be intercepted between this plane and the base . For a fourth part of AE is intercepted , and therefore ( Eucl . xi . 16 ) every line from the vertex to the base is divided in the same proportion . 154. Hence , if a ...
Page 82
... base , and taking a point in that line at the distance of one - fourth of its length from the base . 157. To find the centre of gravity of the frustum of a cone or pyramid cut off by a plane parallel to the base . Let BCD ( fig . 30 ) ...
... base , and taking a point in that line at the distance of one - fourth of its length from the base . 157. To find the centre of gravity of the frustum of a cone or pyramid cut off by a plane parallel to the base . Let BCD ( fig . 30 ) ...
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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