A System of Geometry and Trigonometry: Together with a Treatise on Surveying : Teaching Various Ways of Taking the Survey of a Field : Also to Protract the Same and Find the Area : Likewise, Rectangular Surveying, Or, an Accurate Method of Calculating the Area of Any Field Arithmetically, Without the Necessity of Plotting it : to the Whole are Added Several Mathematical Tables, with a Particular Explanation and the Manner of Using Them : Compiled from Various Authors |
From inside the book
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Page 3
... draw- ing a plot of them and measuring with a Scale and Di- viders , as has been the common practice ; and also a more particular explanation of the use of Natural Sines than is contained in most Mathematical Books . The Compiler has ...
... draw- ing a plot of them and measuring with a Scale and Di- viders , as has been the common practice ; and also a more particular explanation of the use of Natural Sines than is contained in most Mathematical Books . The Compiler has ...
Page 9
... drawn between two Points . 6. The inclination of two Lines meeting one an- other , or the opening between them , is called an Angle . Thus at B. PLATE I. Figure 1. is an Angle , formed by the meeting of the Lines AB and BC . 7. If a ...
... drawn between two Points . 6. The inclination of two Lines meeting one an- other , or the opening between them , is called an Angle . Thus at B. PLATE I. Figure 1. is an Angle , formed by the meeting of the Lines AB and BC . 7. If a ...
Page 10
... drawn from the Centre to the Circumference ; as CB . Fig . 4 . Therefore all Radii of the same Circle are equal . 13. The Diameter of a Circle is a Right Line drawn from one side of the Circumference to the other , pass- ing through the ...
... drawn from the Centre to the Circumference ; as CB . Fig . 4 . Therefore all Radii of the same Circle are equal . 13. The Diameter of a Circle is a Right Line drawn from one side of the Circumference to the other , pass- ing through the ...
Page 11
... drawn perpendicular to the Diameter ; and is terminated by a Line drawn from the Centre through the other end of the Arch ; thus BK is the Tangent of the Arch BH . Fig . 7 . Note . The Tangent of an Arch of 45 Degrees is equal in length ...
... drawn perpendicular to the Diameter ; and is terminated by a Line drawn from the Centre through the other end of the Arch ; thus BK is the Tangent of the Arch BH . Fig . 7 . Note . The Tangent of an Arch of 45 Degrees is equal in length ...
Page 13
... drawn from one of the Angles to its opposite Side ; thus the dotted Line AD . Fig . 14. is the per- pendicular height of the Triangle ABC . Note . This Perpendicular may be drawn from either of the Angles ; and whether it falls within ...
... drawn from one of the Angles to its opposite Side ; thus the dotted Line AD . Fig . 14. is the per- pendicular height of the Triangle ABC . Note . This Perpendicular may be drawn from either of the Angles ; and whether it falls within ...
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System of Geometry and Trigonometry: Together with a Treatise on Surveying ... Abel Flint No preview available - 2017 |
System of Geometry and Trigonometry: Together With a Treatise on Surveying ... Abel Flint No preview available - 2017 |
Common terms and phrases
Angle opposite Bearing and Distance C.Tang Chord Circle Circumference Co-Sine Sine Compass contained Angle Decimals Degrees and Minutes Dep Lat Diagonal Difference Dist divided Doub Double Area double the Area draw a Line Draw the Line EXAMPLE FIELD BOOK find the Angles find the Area find the Leg given Leg given number given Side Lat Dep Latitude and Departure Leg AB Leg BC length Loga Logarithmic Sine measuring Meridian multiply Natural Sines North Areas Note number of Acres number of Degrees Offset opposite Angle Parallelogram PLATE Plot PROB PROBLEM protract Quotient Radius Remainder Rhombus Right Angled Triangle RULE Secant Co-Secant Side BC Sine Co-Sine Tangent Sine Sine Sine South Areas Square Chains Square Links Square Root stationary Lines subtract survey a Field Surveyor Table of Logarithms Table of Natural Tangent Co-Secant Secant Tangent or Secant Trapezium Trapezoid Triangle ABC TRIGONOMETRY
Popular passages
Page 10 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 31 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 32 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 10 - The Radius of a circle is a line drawn from the centre to the circumference.
Page 78 - Go to any part of the premises where any two adjacent corners are known ; and if one can be seen from the other, take their bearing ; which, compared with that of the same line in the former survey, shows the difference. But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run and the corner ; then...
Page 44 - Field work and protraction are truly taken and performed ; if not, an error must have been committed in one of them : In such cases make a second protraction ; if this agrees with the former, it is to be presumed the fault is in the Field work ; a re- survey must then be taken.
Page 14 - Figures which consist of more than four sides' are called polygons; if the sides are equal to each other they are called regular polygons, and are sometimes named from the number of their sides, as pentagon, or hexagon, a figure of five or six sides, &c.; if the sides are unequal, they are called irregular polygons.
Page 44 - Let his attention first be directed to the map, and inform him that the top is north, the bottom south, the right hand east, and the left hand west.
Page 27 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 39 - To find the area of a trapezoid. RULE. — Multiply half the sum of the parallel sides by the altitude, and the product is the area.