A Collection of Cambridge Mathematical Examination Papers: Papers in the branches of the mixed mathematicsW. P. Grant, 1831 |
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Resultat 1-5 av 53
Side 1
... acted on by an arm 6 feet long ? 4. If P sustains W on an isosceles wedge , and the wedge be put slightly into motion ; prove that the velocity of P : that of W :: W : P. 5. Explain the construction of the steel - yard . 6. In the ...
... acted on by an arm 6 feet long ? 4. If P sustains W on an isosceles wedge , and the wedge be put slightly into motion ; prove that the velocity of P : that of W :: W : P. 5. Explain the construction of the steel - yard . 6. In the ...
Side 6
... acted upon by a constant force ( ƒ ) , prove that s = tu = } ft2 . 16. The axis of an equilateral hyperbola being vertical , prove that the times of descent from the extremities of the axis to any point in the curve are equal . 17. ( 1 ) ...
... acted upon by a constant force ( ƒ ) , prove that s = tu = } ft2 . 16. The axis of an equilateral hyperbola being vertical , prove that the times of descent from the extremities of the axis to any point in the curve are equal . 17. ( 1 ) ...
Side 13
... acted on by forces in the directions of its edges , viz . AB , AC , AD , BC , CD , DB : reduce these forces to two , and show that the reduction to one is im- possible . 13. Find the centre of gravity of a figure bounded by the arc of a ...
... acted on by forces in the directions of its edges , viz . AB , AC , AD , BC , CD , DB : reduce these forces to two , and show that the reduction to one is im- possible . 13. Find the centre of gravity of a figure bounded by the arc of a ...
Side 20
... acted upon by the forces X , Y , Z , in the directions of x , y , z , respectively ; shew that 1 day X = - Y = - Z = dt2 d2x dt2 d2z dt2 • In the proof make it appear that these equations have become known in consequence of observation ...
... acted upon by the forces X , Y , Z , in the directions of x , y , z , respectively ; shew that 1 day X = - Y = - Z = dt2 d2x dt2 d2z dt2 • In the proof make it appear that these equations have become known in consequence of observation ...
Side 21
... at any point , and the law of its variation at any point for different inclinations of the plane . 11. Shew how the following equations for determining the motion of a body acted on by a constant force Coll . 1821. ] 21 IN MECHANICS .
... at any point , and the law of its variation at any point for different inclinations of the plane . 11. Shew how the following equations for determining the motion of a body acted on by a constant force Coll . 1821. ] 21 IN MECHANICS .
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Vanlige uttrykk og setninger
aberration altitude axis body is projected body moving centre of force centre of gravity chord circle circumference cone convex lens curvature curve cycloid cylinder density descends determine diameter direction distance Earth ecliptic elastic ellipse equal equilibrium Explain Find the centre Find the equation find the position fluid focal length focus force acting force tending force varying given angle given point given velocity given weight horizontal plane hyperbola incident inclined plane JOHN'S COLLEGE latitude latus rectum law of force longitude lowest point magnitude meridian Moon motion Newton's method orifice oscillation parabola paraboloid parallax parallel rays particle passing pencil perpendicular placed pressure prove pulley quantity QUEEN'S COLLEGE radii radius ratio reflected refraction rest revolve right ascension round shew sides sine specific gravity sphere spherical reflector spherical triangle square star straight line string Sun's supposed surface tangent telescope TRINITY COLLEGE vertex vertical vessel
Populære avsnitt
Side 213 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 139 - If a body be acted on by a given force and revolve in a circle, the arc described .in any given time is a mean proportional between the diameter of the circle and the space through which a body would descend in the same time from rest if acted on by the same force.
Side 213 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Side 249 - Prove that the pressure upon any portion of a vessel filled with a fluid of uniform density is equal to the weight of a column of fluid whose base is the area of the surface pressed, and...
Side 141 - In the logarithmic spiral find an expression for the time of a body's descent from a given point to the centre, and prove that the times of successive revolutions are in geometrical progression. 7. A body acted on by a force varying as (dist...
Side 247 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and conversely, triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Side 233 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Side 233 - If a straight line touch a circle, and from the point of contact a...
Side 238 - Csesar and Pope Gregory. 18. Give the theory of the Trade Winds. 19. Prove that part of the equation of time which arises from the obliquity of the ecliptic to be a maximum when the longitude of the Sun equals the complement of its right ascension. 20. Compare the surface of a sphere with the area of its great circle, and its magnitude with that of its circumscribing cylinder. VOL. II.
Side 198 - when a body revolves on an axis, and a force is impressed, tending to make it revolve on another, it will revolve on neither, but on a line in the same plane with them, dividing the angle which they contain so that the sines of the parts are in the inverse ratio of the angular velocities with which the body would have revolved about the said axes separately.