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added angled triangle axis base calculation called capacity chord circle circumference column common cone contains cosine course cubic cylinder departure determined diameter difference of latitude direction distance divided draw drawn earth equal equator Example extend feet field figure four frustum gallons given greater half height hypothenuse inches increase inscribed latter length less logarithm longitude manner measured meridian method middle miles minutes multiplied nearly negative NOTE object observed opposite parallel perimeter perpendicular plane polygon positive prism PROBLEM proportion pyramid quadrant quantity radius ratio regular remaining right angled rods root rule sailing scale secant sector segment ship sides similar sine solidity sphere square subtract supposed surface tables taken taking tangent term theorem third triangle 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 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.