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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...
No preview available - 2016
ABCD altitude axis base breadth calculation circle circular segment circumference column cone cosecant cosine cotangent course cube cylinder decimal departure diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the SOLIDITY frustum given sides gles greater horizon hypothenuse inches inscribed ISOPERIMETRY JEREMIAH DAY lateral surface length line of chords loga logarithm measured Mercator's Merid meridional difference miles multiplied negative number of degrees number of sides object oblique opposite parallel of latitude parallelogram parallelopiped perimeter perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rods secant segment sine sines and cosines slant-height sphere spherical subtracting tables tangent term theorem trapezium triangle ABC Trig trigonometry whole wine gallons 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.