Mathematical Treatise: Containing I. The Theory of Analytical Functions, II. Spherical Trigonometry, with Practical and Nautical Astronomy

Oliver & Boyd, 1838 - 574 pages
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Page 106 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.
Page 180 - Greenwich for this station ; foreigners, the principal observatories of their respective nations. Some geographers have adopted the island of Ferro. Hereafter, when we speak of longitude, we reckon from Greenwich. The longitude of a place is, therefore, measured by the arc of the equator intercepted between the meridian of the place and that of Greenwich ; or, which is the same thing, by the spherical angle at the pole included between these meridians.
Page ix - ... one another. DEFINITION 7. If it be possible to take equimultiples of the first and the third of four magnitudes and equimultiples of the second and the fourth, such that the multiple of the first is greater than that of the second and the multiple of the third not greater than that of the fourth, the ratio of the first to the second is said to be greater than that of the third to the fourth ; and the ratio of the third to the fourth is said to be less than the ratio of the first to the second....
Page 103 - a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.
Page 57 - To divide a given number (a) into two such parts, that the product of the mth power of the one into the wth power of the other shall be a maximum. We have x'" (a — *•)" a maximum, and therefore mtf" -1 (a — #)" — nxm (a — #)"-' = o ; whence^ m (a — x) = nx.
Page 179 - Azimuth, or vertical circles are great circles passing through the zenith and nadir. They cut the horizon at right ' angles. The altitudes of the heavenly bodies are measured on these circles.
Page 109 - C= 540° — (a' + b' + c'). But a' + b' + c' < 360° (86) ; therefore, A + B + C > 180°; that is, the sum of the three angles is greater than two right angles.
Page 236 - ... soberness of description and precision of language which characterize the science of the nations of Europe. It appears from the astronomical tables that the ancient Hindoos knew that the intersection of the equator and ecliptic is not always in the same point, but that it is constantly retrograding on the ecliptic in a direction contrary to the order of the signs...
Page 181 - Ursa Minoris. This varying direction of the earth's axis is occasioned by the varying influence of the sun and moon on the protuberant matter of the earth's equator, in necessary correspondence with the earth's variations of distance in different parts of its orbit ; and in respect of which varying influence the earth may be described, if I may use a homely figure, as in the situation of a man held by the collar between two policemen, and swayed to the...
Page 250 - ... sun. In eclipses of the moon, the shadow is found to be a little greater than this rule gives it, owing to the atmosphere of the earth. This augmentation of the semidiameter is, according to M. Cassini, 20"; according to M.

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