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 56 - 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 128 - 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 53 - 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 39 - 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 127 - 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 59 - 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 184 - ... 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 129 - 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 198 - ... 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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