Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 293
... smooth horizontal table by a weight hanging vertically : find ( 1 ) the accelerating force on P , ( 2 ) the accelerating force on the centre of gravity of P and Q. 9. A body is projected with a velocity v in a direction making an angle ...
... smooth horizontal table by a weight hanging vertically : find ( 1 ) the accelerating force on P , ( 2 ) the accelerating force on the centre of gravity of P and Q. 9. A body is projected with a velocity v in a direction making an angle ...
Σελίδα 295
... smooth horizontal plane A C , and the other end B on a smooth plane CB inclined to the horizon at 60 ° . Find the tension of a string CA = CB which keeps the beam from slipping . 5. Two planes of equal altitude are inclined at angles of ...
... smooth horizontal plane A C , and the other end B on a smooth plane CB inclined to the horizon at 60 ° . Find the tension of a string CA = CB which keeps the beam from slipping . 5. Two planes of equal altitude are inclined at angles of ...
Σελίδα 301
... smooth inclined plane , show how to determine the space it will describe in a given time . 8. An inclined plane rises 1 ft . vertically for every 100 ft . in length ; with what velocity must a body be pro- jected up the plane that it ...
... smooth inclined plane , show how to determine the space it will describe in a given time . 8. An inclined plane rises 1 ft . vertically for every 100 ft . in length ; with what velocity must a body be pro- jected up the plane that it ...
Σελίδα 306
... smooth horizontal plane ; find the tension of the string and the pressure on the plane . 4. A bar of iron 15 inches long , which weighs 12 lbs . , and is of uniform thickness , has a weight of 10 lbs . sus- pended from one extremity ...
... smooth horizontal plane ; find the tension of the string and the pressure on the plane . 4. A bar of iron 15 inches long , which weighs 12 lbs . , and is of uniform thickness , has a weight of 10 lbs . sus- pended from one extremity ...
Σελίδα 313
... smooth hemispherical bowl , prove that its pressure on the surface at the lowest point is 3 times the weight of the particle . 8. If the moving force upon a body varies directly as its distance at any time from a given point towards ...
... smooth hemispherical bowl , prove that its pressure on the surface at the lowest point is 3 times the weight of the particle . 8. If the moving force upon a body varies directly as its distance at any time from a given point towards ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.