A Collection of Cambridge Mathematical Examination Papers: Papers in pure mathematics: Supplement

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Page 243 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 240 - 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 12 - If two forces, acting at a point, be represented in magnitude and direction by the...
Page 202 - Nutation of lunar orbit. The action of the bulging matter at the earth's equator on the moon occasions a variation in the inclination of the lunar orbit to the plane of the ecliptic. Suppose the plane N/?
Page 230 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Page 215 - WHAT sum of money must be laid out in the 3 per cent consols, at 63f per cent, to produce an income of £ 400 a year ? 2. The sine of any angle of a plane triangle has to the opposite side a constant ratio. — What is this ratio ? 3. Find by the method of continued fractions a series of fractions converging to V'lp.
Page 282 - Let ABC be a triangle, of which the side AC is greater than the side AB; the angle ABC shall be greater than the angle BCA.
Page 247 - IF a straight line be at right angles to a plane, every plane which passes through it shall be at right angles to that plane.
Page 125 - Upon comparing the observations with each other, it was discovered that in both the fore-mentioned stars, the apparent difference of declination from the maxima was always nearly proportional to the versed sine of the sun's distance from the equinoctial points. This was an inducement to think that the cause, whatever it was, had some relation to the sun's situation with respect to those points.
Page 160 - If two similar mediums are separated from each other by a space terminated on each side by parallel planes ; and a body in its transit through this space, is attracted or impelled perpendicularly towards either medium, and is not agitated or hindered by any other force; and the attraction is every where the same at equal distances from either plane, taken towards the same side of the plane; prove that the velocity of the body before incidence is to its velocity after emergence as the sine of emergence...

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