Cambridge Problems: Being a Collection of the Printed Questions Proposed to the Candidates for the Degree of Bachelor of Arts at the General Examinations, from 1801 to 1820, Inclusive

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J. Deighton and sons, 1821 - Mathematics - 425 pages
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Page 112 - The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides.
Page 318 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Page 69 - ... move in its intersection with the other. 19. Let the position of the "axis of a spherical surface of known refracting power, perpendicular to, and bisecting, a very distant object, be given, and in it the position of the eye and image, and also the apparent magnitudes of the object and image; to determine the magnitude and position of the refracting surface. 20. A body is projected in a given direction, at a known distance from an horizontal plane, with a given velocity, acted on by a force perpendicular...
Page 304 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.
Page 280 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Page 89 - If a body revolves in an ellipse it is required to find the law of the centripetal force tending to the focus of the ellipse . . . . . . And therefore the centripetal force is inversely as the square of the distance.
Page 191 - Find the inclination of the bar to the horizon, upon supposition that the semi-circle is devoid of weight. 2. Prove, from a property of the circle, that if four quantities are proportionals, the sum of the greatest and least is greater than the sum of the other two. 3. Given the area of any plane surface, it is required to find the content of a solid, formed ' by drawing lines from a given point without the plane, to every part of its surface.
Page 328 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.
Page 421 - A sets off from London to York, and B at the same time from York to London : they travel uniformly; A reaches York 16 hours, and B London 36 hours, after they have met on the road ; find in what time each has performed the journey.
Page 364 - ... in the ratio of the sine of incidence to the sine of refraction (Art. 881.) when the light passes from water into air.

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