A Collection of Cambridge Mathematical Examination Papers: Papers in the branches of the mixed mathematics

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W. P. Grant, 1831 - Astronomy
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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.

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