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 - 425 من الصفحات
 

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الصفحة 122 - 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.
الصفحة 108 - A and ~B move in opposite directions with velocities, the sum of which is given. 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. 7. If from one extremity of the diameter of a circle, chords are drawn intersecting the radius which is perpendicular to the diameter or that radius produced, and from the points of intersection...
الصفحة 84 - 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.
الصفحة 132 - 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.
الصفحة 168 - ... in the ratio of the sine of incidence to the sine of refraction (Art. 881.) when the light passes from water into air.
الصفحة 102 - ... similar mediums be separated from each other by a space terminated on both sides by parallel planes, and a body in its passage through that space be attracted or impelled perpendicularly towards either of those mediums, and not agitated or hindered by any other force; and the attraction be...
الصفحة 210 - A projectile is to be thrown across a plain 120 feet wide, to strike a mark 30 feet high, the velocity of projection being that acquired down 80 feet j find at what angle it must be projected.
الصفحة 85 - THIRD AND FOURTH CLASSES. 1 . Shew from the principles of the fifth Book of Euclid, that a ratio of greater inequality is diminished, and of less inequality increased by adding a quantity to both its terms. 2. The time of day at a given place determined from observations of the Sun's altitude is9h. 10'. 43''; and a chronometer set to Greenwich time shews 6h
الصفحة 199 - Show that the time in which a heavy body descends down the straight line drawn from any point in the surface of a sphere to the lowest point = the time of descent down the vertical axis of the sphere. 8. A straight line is immersed vertically in a, fluid. Divide it into three portions that shall be equally pressed. 9. A straight line passes through the principal focus of a spherical reflector at right angles to the axis. Determine the conic section that forms the image. Where must the straight line...
الصفحة 202 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...

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