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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...
No preview available - 2016
added axis base calculation called chord circle circumference column common considered contains cosine course cylinder decimal departure determined diameter Diff difference of latitude direction distance divided draw drawn earth equal equator Example expressions extend feet field figure four fourth frustum given greater half height horizon hypothenuse inches latter length less logarithm longitude manner measured meridian method middle miles minutes multiplied nearly negative Note object observed opposite parallel perimeter perpendicular plane polygon portion positive PROBLEM proportion pyramid quadrant quantity radius regular rods root rule sailing scale secant segment ship sides similar sine solidity sphere square stations subtracting supposed surface survey tables taken taking tangent term theorem third triangle triangle ABC trigonometry whole zone
Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 61 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
Page 71 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.