A Collection of Cambridge Mathematical Examination Papers: Papers in the branches of the mixed mathematicsW. P. Grant, 1831 - Astronomy |
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Page 6
... observe any known law ? Is the quantity of friction affected by an increase of velocity , or by the extent of the surfaces that are in contact ? Explain how friction may be measured , and mention the chief contrivances that are employed ...
... observe any known law ? Is the quantity of friction affected by an increase of velocity , or by the extent of the surfaces that are in contact ? Explain how friction may be measured , and mention the chief contrivances that are employed ...
Page 20
... observation at the Earth's surface of the fact , that gravity communicates the same velocity in the same time in the direction in which it acts , to any body , moving in any direc- tion whatever and with any velocity . ST . JOHN'S ...
... observation at the Earth's surface of the fact , that gravity communicates the same velocity in the same time in the direction in which it acts , to any body , moving in any direc- tion whatever and with any velocity . ST . JOHN'S ...
Page 27
... observed to move off at an angle equal to the angle of in- cidence . Required the sphere's elasticity . 13. A weight ( w ) is connected by a string passing over a fixed pulley with a number of equal balls ( n ) , placed in a vertical ...
... observed to move off at an angle equal to the angle of in- cidence . Required the sphere's elasticity . 13. A weight ( w ) is connected by a string passing over a fixed pulley with a number of equal balls ( n ) , placed in a vertical ...
Page 30
... observations by which it is established . 2. A body is moving in a given direction with a given velocity ; required the direction in which another given velocity less than the former must be communicated to it , so as to make the ...
... observations by which it is established . 2. A body is moving in a given direction with a given velocity ; required the direction in which another given velocity less than the former must be communicated to it , so as to make the ...
Page 52
... observed to spout to the distance m and n respectively from the foot of the cylinder . Find the dimensions of the cylinder . 10. A piston of given area a2 working in a cylinder , forces water through a pipe of given aperture c2 opening ...
... observed to spout to the distance m and n respectively from the foot of the cylinder . Find the dimensions of the cylinder . 10. A piston of given area a2 working in a cylinder , forces water through a pipe of given aperture c2 opening ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 233 - If a straight line touch a circle, and from the point of contact a...
Page 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.
Page 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.