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added angled triangle base calculation called chord circle circumference column common contains cosine course 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 increase 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 ratio regular right angled rods root rule sailing scale secant segment ship sides similar sine solidity sphere square stations subtract supposed surface survey tables taken taking tangent term theorem third triangle trigonometry whole
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 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 69 - 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.