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 21
... Tangent or Secant . Having found the Logarithms of the three given Terms , add together the Log . of the second and third Terms , and from their Sum subtract the Log . of the first Term , the Remainder will be the Log . TRIGONOMETRY . 21.
... Tangent or Secant . Having found the Logarithms of the three given Terms , add together the Log . of the second and third Terms , and from their Sum subtract the Log . of the first Term , the Remainder will be the Log . TRIGONOMETRY . 21.
Page 22
... Subtracted by cancelling the first figure of the Sum of the other two Terms . Making the Leg AB Radius , the Proportions will be : To find the Leg AB . As Secant CAB , 35 ° 30 ′ : Hyp . AC , 25 :: Radius : Leg AB , 20. 35 To find the ...
... Subtracted by cancelling the first figure of the Sum of the other two Terms . Making the Leg AB Radius , the Proportions will be : To find the Leg AB . As Secant CAB , 35 ° 30 ′ : Hyp . AC , 25 :: Radius : Leg AB , 20. 35 To find the ...
Page 23
... subtracted according to the Rule , the result will be found to be the same as the two first Proportions . By Natural Sines . This CASE may be solved by Natural Sines , * ac- cording to the following Proportions : As Unity or 1 ; Is to ...
... subtracted according to the Rule , the result will be found to be the same as the two first Proportions . By Natural Sines . This CASE may be solved by Natural Sines , * ac- cording to the following Proportions : As Unity or 1 ; Is to ...
Page 24
... subtracting Radius , and seek the numbers corres- ponding to the other figures . Making the Leg BC Radius , the Proportions will be ; To find the Hypothenuse As Tang . ACB , 56 ° 45 ′ : Leg AB , 325 :: Sec . ACB , 56 ° 45 ′ To find the ...
... subtracting Radius , and seek the numbers corres- ponding to the other figures . Making the Leg BC Radius , the Proportions will be ; To find the Hypothenuse As Tang . ACB , 56 ° 45 ′ : Leg AB , 325 :: Sec . ACB , 56 ° 45 ′ To find the ...
Page 27
... subtracted from the Square of the Hypothenuse , the Remainder will be the Square of the required Leg . As in the preceding EXAMPLE ; The Square of the Leg AB 40 is 1600 ; this subtracted from the Square of the Hypothenuse 50 which is ...
... subtracted from the Square of the Hypothenuse , the Remainder will be the Square of the required Leg . As in the preceding EXAMPLE ; The Square of the Leg AB 40 is 1600 ; this subtracted from the Square of the Hypothenuse 50 which is ...
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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.