A Treatise on Surveying: Containing the Theory and Practice : to which is Prefixed a Perspicuous System of Plane Trigonometry : the Whole Clearly Demonstrated and Illustrated by a Large Number of Appropriate Examples, Particularly Adapted to the Use of Schools |
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Page 26
... ABC , Fig . 6 . 18. A right angled triangle has one right angle , as ABC , Fig . 9 ; in which the side AC , opposite to the right angle , is called the hypothenuse . 19. An obtuse angled triangle has one obtuse angle , 26 GEOMETRY .
... ABC , Fig . 6 . 18. A right angled triangle has one right angle , as ABC , Fig . 9 ; in which the side AC , opposite to the right angle , is called the hypothenuse . 19. An obtuse angled triangle has one obtuse angle , 26 GEOMETRY .
Page 27
... opposite sides are paral- lel , is called a parallelogram , as D , Fig . 11 . 24. A parallelogram , whose angles are all right angles , is called a rectangle , as E , Fig . 12 . 25. A parallelogram whose sides are all equal , and angles ...
... opposite sides are paral- lel , is called a parallelogram , as D , Fig . 11 . 24. A parallelogram , whose angles are all right angles , is called a rectangle , as E , Fig . 12 . 25. A parallelogram whose sides are all equal , and angles ...
Page 42
... opposite 10 on the line of numbers . - Tangents . The line of tangents , marked Tan . , begins at the left hand , and is numbered 1 , 2 , 3 , & c . to 10 , then 20 , 30 , 40 , 45 , where there is a brass pin , just under 90 in the line ...
... opposite 10 on the line of numbers . - Tangents . The line of tangents , marked Tan . , begins at the left hand , and is numbered 1 , 2 , 3 , & c . to 10 , then 20 , 30 , 40 , 45 , where there is a brass pin , just under 90 in the line ...
Page 43
... opposite angles will be equal : thus AEC - BED , and AED = CEB . Fig . 36 . 4. The sum of the three angles of a plane triangle is equal to two right angles , or 180 ° . 5. If the sum of two angles of a triangle be subtracted from 180 ...
... opposite angles will be equal : thus AEC - BED , and AED = CEB . Fig . 36 . 4. The sum of the three angles of a plane triangle is equal to two right angles , or 180 ° . 5. If the sum of two angles of a triangle be subtracted from 180 ...
Page 44
... opposite the given side , Is to the sine of the angle opposite the required side , So is the given side , To the required side . * • DEMONSTRATION . Let ABC , Fig . 49 , be any plane triangle ; take BFAC and upon AB let fall the ...
... opposite the given side , Is to the sine of the angle opposite the required side , So is the given side , To the required side . * • DEMONSTRATION . Let ABC , Fig . 49 , be any plane triangle ; take BFAC and upon AB let fall the ...
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Common terms and phrases
100 Distance AB² ABCD acres adjacent angles axis bearings and distances centre changed bearing Co-secant Secant Co-sine Co-tang compass decimal Degrees DEMONSTRATION diff difference of latitude difference of level dist divide division line draw equal EXAMPLES feet find the angles find the area fourth term given angle given area given side Given the bearings half height Hence horizontal hypothenuse instrument last problem latitude and departure length line FE line of collimation line of level logarithm measured meridian multiplier natural number off-sets parallel parallelogram parture perches perpendicular pole star prob quired quotient radius Required the area right angles right line right-angled triangle RULE screws side AC Sine square root stake station stationary lines straight line subtract survey take the difference Tangent theodolite tract of land trapezium triangle ABC trigonometry upper telescope vane vernier plate
Popular passages
Page 36 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 71 - A maypole, whose top was broken off by a blast of wind, struck the ground at 15 feet distance from the foot of the pole: what was the height of the whole maypole, supposing the broken piece to measure 39 feet in length ? Ans.
Page 17 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 20 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 28 - Sine, or Right Sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter which passes through the other extremity. Thus, BF is the sine of the arc AB, or of the supplemental arc BDE.
Page 112 - PROBLEM I. To find the area of a parallelogram ; whether it be a square, a rectangle, a rhombus, or a rhomboid**. RULE.* Multiply the length by the perpendicular height, and the product will be the area.
Page 18 - Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.
Page 119 - From half the sum of the three sides, subtract each side severally ; multiply the half sum, and the three remainders together, and the square root of the product will be the area required.
Page 54 - To find a side. Call any one of the sides radius, and write upon it the word