An Elementary Course of Mathematics: Designed Principally for Students of the University of Cambridge

John Deighton, 1849 - Mathematics - 528 pages

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Page 427 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 512 - The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances...
Page 534 - Mathematical Tracts. On La Place's Coefficients ; the Figure of the Earth ; the Motion of a Rigid Body about its Centre of Gravity ; Precession and Nutation. 8vo. 4s. 6d. An Elementary Treatise on the Differential Calculus, in which the Method of Limits is exclusively made use of.
Page 256 - To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal and directed to contrary pans.
Page iv - The elementary parts of Astronomy ; so far as they are necessary for the explanation of the more simple phenomena, without calculation.
Page 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 318 - ... velocity with which the body arrives at its last place, and with which the motion ceases. And in like manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish.
Page iv - ... logarithms. The elementary parts of Plane Trigonometry, so far as to include the solution and properties of triangles. The elementary parts of Conic Sections, treated geometrically, but not excluding the method of orthogonal projections ; curvature.
Page 529 - Mathematical Tracts on the Lunar and Planetary Theories. The Figure of the Earth, Precession and Nutation, the Calculus of Variations, and the Undulatory Theory of Optics.
Page 73 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...