Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 pages |
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Page 288
... centre of gravity of a system of bodies , x = ? In the lever , Σ ( P.x ) : y = ( P.y ) Σ ( Ρ ) Σ ( Ρ ) P perpendicular from fulcrum on w's direction - = W perpendicular from fulcrum or P's direction Pressure on fulcrum = [ P2 + w2-2 PW ...
... centre of gravity of a system of bodies , x = ? In the lever , Σ ( P.x ) : y = ( P.y ) Σ ( Ρ ) Σ ( Ρ ) P perpendicular from fulcrum on w's direction - = W perpendicular from fulcrum or P's direction Pressure on fulcrum = [ P2 + w2-2 PW ...
Page 290
... centre of gravity below surface of fluid is h = weight of volume a3 h of the fluid . Specific gravity of a substance = weight of any volume 290 FORMULE . Formulæ in Hydrostatics.
... centre of gravity below surface of fluid is h = weight of volume a3 h of the fluid . Specific gravity of a substance = weight of any volume 290 FORMULE . Formulæ in Hydrostatics.
Page 291
... gravity of a substance = weight of any volume of substance weight of same ... gravity = wh + f . wl : h being the height , the length of plane , whose inclination is very small ... centre o 2 FORMULE . 291 Formulæ in Practical Mechanics.
... gravity of a substance = weight of any volume of substance weight of same ... gravity = wh + f . wl : h being the height , the length of plane , whose inclination is very small ... centre o 2 FORMULE . 291 Formulæ in Practical Mechanics.
Page 293
... centre of gravity of P and Q. 9. A body is projected with a velocity v in a direction making an angle of 30 ° with the horizon ; find its velocity and direction of motion when it has reached a height 2 g . What is the horizontal space ...
... centre of gravity of P and Q. 9. A body is projected with a velocity v in a direction making an angle of 30 ° with the horizon ; find its velocity and direction of motion when it has reached a height 2 g . What is the horizontal space ...
Page 294
... centre of gravity is not affected by the impact . 8. Show that the time of a projectile's describing any arc of its path is the same as would be occupied in moving uni- formly along the chord with the velocity which it has when its ...
... centre of gravity is not affected by the impact . 8. Show that the time of a projectile's describing any arc of its path is the same as would be occupied in moving uni- formly along the chord with the velocity which it has when its ...
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Arithmetic axis ball base bisected body cent centre of gravity circle coefficient of friction compound interest cone cost crown 8vo cube cubic foot curve Define determine diameter Divide dwts ellipse English equal equilibrium expression feet Find the area Find the centre Find the distance Find the equation Find the number Find the sum Find the value fluid forces acting fraction geometrical Grammar horizontal plane hyperbola inches inclined plane inscribed Integrate isosceles latus rectum least common multiple length logarithms miles Multiply parabola parallel particle perpendicular pressure Prove pulleys radius ratio rectangle rectangular Reduce right angles sides simple interest sin² sine spherical triangle square root straight line string subtended Subtract surface tangent theorem tons tower triangle ABC velocity vertical vulgar fraction weight yards
Popular passages
Page 123 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 10 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 184 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Page 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 184 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Page 184 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 163 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 184 - In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.
Page 154 - If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.