# The Mathematical Repository, Volume 4

W. Glendinning., 1819 - Mathematics

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Page 9 - If the force vary inversely as the square of the distance, and a body be projected...
Page 28 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 21 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when trie velocities are reciprocally proportional to the quantities of matter in the bodies.
Page 54 - Having given the radius of an arc of any colour in the secondary rainbow, find the ratio of the sine of incidence to the sine of refraction when rays of that colour pass out of air into water.
Page 33 - 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 9 - 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 is 9h. 10'.45"; and a chronometer set to Greenwich time shews 6h. 3'.
Page 37 - New Mathematical Tables, containing the Factors, Squares, Cubes, Square Roots, Cube Roots, Reciprocals, and Hyperbolic Logarithms, of all Numbers from 1 to 10,000; Tables of Powers and Prime Numbers; an extensive Table of Formula;, or General Synopsis of the most important Particulars relating to the Doctrines of Equations, Series, Fluxions, Fluents, &c.
Page 18 - ... 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...
Page 19 - «)". ( (l— *"0 .2V(2*'*— 1) 14. If the middle points of any two edges of a triangular pyramid which do not meet, be joined ; shew that the middle point of the connecting line is the centre of gravity of the pyramid. 15. If parallel rays be incident on a spherical surface of a plano-convex glass mirror, whose thickness is a semi-diameter and a half of the spherical surface, prove that they will...
Page 70 - ... =.b. 3. Draw through a given point a straight line, making a given angle with a given straight line. 4. A straight line can cut a circle in only two points. Required proof. 5. Trace the changes of algebraic sign, in the sine of an arc, the tangent and secant ; and explain why sec. A, and sec. (180°+ A) which coincide, should be one positive and the other negative. 6. In the direct impact of a row of perfectly elastic bodies A, B, C, &.c.