An Elementary Treatise on the Application of Trigonometry to Orthographic and Stereographic Projection...together with Logarithmic and Other Tables...

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Printed at the University Press by Hilliard & Metcalf, 1822 - Logarithms - 153 pages
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Page 6 - Every section of a circular cone made by a plane parallel to the base is a circle.
Page 26 - ... for half an hour, &c., insert a rod at the centre perpendicularly to the dial plane, and place the dial so that this rod, representing the axis of the earth, shall be situated like cp, that is, in the plane of the meridian, and making an angle with the horizon equal to the latitude of the place. This would be an equinoctial dial, since its plane is parallel to that of the equator. It would moreover be a horizontal dial at the pole, and a vertical south dial at the equator. 42. To construct a...
Page 13 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 81 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Page 32 - We have here subtracted the logarithm of the first term from the sum of the logarithms of the second and third. But a shorter way would be to take the arithmetical complement (Mg.
Page 93 - It may be remarked that, when the several operations are performed with perfect accuracy, the sum of the northings will be equal to that of the southings, and the, sum of the eastings to that of the westings. This necessarily follows from the circumstance of the surveyor's returning to the place from which he set out ; and it affords a means of judging of the correctness of the work. But it is not to be expected that the measurements and calculations in ordinary surveying will strictly bear this...
Page 86 - ABCD (fig- 64), the breadth or perpendicular distance of either two opposite sides, as CP, is equal to the product of the corresponding oblique side CB by the sine of the angle of the parallelogram, radius being unity (Trig. 30). Hence, the area of a parallelogram is equal to the product of any two contiguous sides multiplied by the sine of the contained angle, radius being unity. Given AB = 59 chains 80 links, or...
Page 33 - Then, as radius = sin 90 .... 10,00000 istoAB 2,29884 so is sin ABC = 46 . . . . 9,85693 to the height AC = 143,14 . . . 2,15577 50. It is required to find the perpendicular height of a cloud or other object, when its angles of elevation, as taken by two observers at the same time, on the same side of it, and in the same vertical plane, were 64 and 35, their distance apart being half a mile, or 880 yards. It is evident from figure 28, that this problem may be solved in the same manner as...
Page 134 - Take the quotients thus obtained, from the scale of equal parts, connected with the line to be constructed, and set them on this line from the right hand toward the left. The extent from the brass pin on the line of meridional parts to any division on this line, applied to the line of equal parts, will give in degrees, the meridional parts answering to the latitude of that division. The extent from one division to another on the line of meridional parts, applied to the line of equal parts, will give...
Page 116 - If one of the objects, viewed from a further station, be a vane or staff in the centre of a steeple, it will frequently happen that such object, when the observer comes near it, is both invisible and inaccessible.

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