A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page 3
... equation to the curve will be y2 = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , Szyde falde dx xy a Sy dx 0 ' a dx = Ba [ x + dx fa # 0 a . Archimedes , ' Emédwv iσopponikŵv , Lib . II . Prop . 8 ...
... equation to the curve will be y2 = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , Szyde falde dx xy a Sy dx 0 ' a dx = Ba [ x + dx fa # 0 a . Archimedes , ' Emédwv iσopponikŵv , Lib . II . Prop . 8 ...
Page 8
... equation is y2 = f1 a — x . x = ta . x ( 7 ) To find the centre of gravity of a semi - ellipse , the bisect- ing ... equation to the ellipse will be and we shall have 72 y2 = — ( a2 — x2 ) , a2 4a x = • 3п - Guldin ; Centrobaryca , Lib ...
... equation is y2 = f1 a — x . x = ta . x ( 7 ) To find the centre of gravity of a semi - ellipse , the bisect- ing ... equation to the ellipse will be and we shall have 72 y2 = — ( a2 — x2 ) , a2 4a x = • 3п - Guldin ; Centrobaryca , Lib ...
Page 14
... equation to the circle being we shall have x2 + y2 = a2 , 4a = Зп " y = 4a 3п • ( 5 ) AB ( fig . 7 ) is a parabola , of which the equation is am - ly = x " ; to find the centre of gravity of the area PMNQ , comprised between two ...
... equation to the circle being we shall have x2 + y2 = a2 , 4a = Зп " y = 4a 3п • ( 5 ) AB ( fig . 7 ) is a parabola , of which the equation is am - ly = x " ; to find the centre of gravity of the area PMNQ , comprised between two ...
Page 18
... equation is ym + n = amx " . For any portion of the solid from x = 0 to x = b , x = m + 3n 2m + 4n b . ( 5 ) To find the centre of gravity of the solid generated by the revolution about the axis of x of the curve corresponding to the ...
... equation is ym + n = amx " . For any portion of the solid from x = 0 to x = b , x = m + 3n 2m + 4n b . ( 5 ) To find the centre of gravity of the solid generated by the revolution about the axis of x of the curve corresponding to the ...
Page 31
... equation z ( 1 + p2 + q2 ) 3 = r ; but this equation holds good for the whole class of surfaces generated by the motion of a sphere of invariable radius , of which the centre describes a plane curve traced arbitrarily in the plane of x ...
... equation z ( 1 + p2 + q2 ) 3 = r ; but this equation holds good for the whole class of surfaces generated by the motion of a sphere of invariable radius , of which the centre describes a plane curve traced arbitrarily in the plane of x ...
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Common terms and phrases
absolute force acted angular velocity attraction axes axis body catenary centre of force centre of gravity circle co-ordinates coefficient of friction cos² curve cylinder d²x denote density descends determine direction distance dr² dt dt dt² dx dy dx² elastic ellipse equal equation Euler find the centre fixed point formula given velocity hence horizontal plane inclined plane inertia initial value integrating James Bernoulli John Bernoulli length ma² mass moment of inertia motion oscillation parabola particle perpendicular position of equilibrium pressure problem projection radius of gyration resistance rest right angles Sciences de Paris SECT shews sin² sphere straight line string supposing surface taking moments tan² tangent tension triangle tube vertical plane Vis Viva weight zero δε аф
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