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altitude attraction axis base bisecting body centre of gravity chord circular arc circumference cone conic section consequently cosine curve cycloid denote described determine diameter difference distance draw drawn ellipse equal equation expression Find the fluents fluxion formula given circle given point given ratio hence horizontal hyperbola inscribed intersection John F. W. Herschel John Pond latitude Lemma length logarithm Mathematical meet method orbit ordinate PALABA parabola parallel pendulum perpendicular prime numbers Prop Proposer Prove quadrant quantities QUESTION R. M. College radius rectangle right angles right ascension roots shew sides sine ſº Solution specific gravity sphere spherical spherical reflector spheroid square straight line subtangent supposed surface tangent theorem tion velocity vertex vertical whence wherefore
Page 11 - If the force vary inversely as the square of the distance, and a body be projected...
Page 23 - 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 35 - 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 11 - 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 39 - 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 20 - ... 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 21 - «)". ( (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.