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 |
From inside the book
Results 1-5 of 38
Page 35
... measured by the arc DE , and contains the same number of degrees that the arc does . The measure of a right angle is therefore 90 degrees ; for DH , Fig . 31 , which measures the right angle DCH , is one fourth part of the circumference ...
... measured by the arc DE , and contains the same number of degrees that the arc does . The measure of a right angle is therefore 90 degrees ; for DH , Fig . 31 , which measures the right angle DCH , is one fourth part of the circumference ...
Page 45
... measured by the same scale of equal parts , is 162 , and BC is 95 . • the angles A and B to the equal radii AC and BF . Now the triangles BDC and BEF being similar , we have CD : FE :: BC : BF : or AC ; that is sin . A : sin . B : · BC ...
... measured by the same scale of equal parts , is 162 , and BC is 95 . • the angles A and B to the equal radii AC and BF . Now the triangles BDC and BEF being similar , we have CD : FE :: BC : BF : or AC ; that is sin . A : sin . B : · BC ...
Page 47
... measured by the same scale of equal parts , will be 288 , and BC will be 384 . By Calculation . As sine of B 90 ° 10.00000 Is to sine of A 53 ° 8 ' 9.90311 So is AC 480 2.68124 12.58435 To BC 384 · 2.58435 · · · 10.00000 9.77812 As sine ...
... measured by the same scale of equal parts , will be 288 , and BC will be 384 . By Calculation . As sine of B 90 ° 10.00000 Is to sine of A 53 ° 8 ' 9.90311 So is AC 480 2.68124 12.58435 To BC 384 · 2.58435 · · · 10.00000 9.77812 As sine ...
Page 49
... measured by the scale of equal parts will be 1.54 , and the angles A and B , mea- sured by a scale of chords will be 26 ° 21 ′ and 120 ° 18 ′ . Here the arc ab cuts AC in one point only , because AB is greater than BC ; therefore the ...
... measured by the scale of equal parts will be 1.54 , and the angles A and B , mea- sured by a scale of chords will be 26 ° 21 ′ and 120 ° 18 ′ . Here the arc ab cuts AC in one point only , because AB is greater than BC ; therefore the ...
Page 57
... The angles measured by a scale of chords , will be A = 32 ° 39 ′ , B = 58 ° 56 ' , and C = 88 ° 25 ′ . By Calculation . AC · 365 BC 230 Sum 595 Difference - 135 As the base AB 426 2.62941 Is to the sum PLANE TRIGONOMETRY . 57.
... The angles measured by a scale of chords , will be A = 32 ° 39 ′ , B = 58 ° 56 ' , and C = 88 ° 25 ′ . By Calculation . AC · 365 BC 230 Sum 595 Difference - 135 As the base AB 426 2.62941 Is to the sum PLANE TRIGONOMETRY . 57.
Other editions - View all
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