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 12
... Triangle is a Figure bounded by three Lines ; as ABC . Fig . 9 . 32. An Equilateral Triangle has its three sides equal in length to each other . Fig . 9 . 33. An Isoceles Triangle has two of its sides equal , and the other longer or ...
... Triangle is a Figure bounded by three Lines ; as ABC . Fig . 9 . 32. An Equilateral Triangle has its three sides equal in length to each other . Fig . 9 . 33. An Isoceles Triangle has two of its sides equal , and the other longer or ...
Page 13
... Triangle being added together will amount to 180 Degrees ; con- sequently the two Acute Angles of a Right Angled Triangle amount to 90 Degrees , the Right Angle being also 90 . 40. The perpendicular height of a Triangle is a Line drawn ...
... Triangle being added together will amount to 180 Degrees ; con- sequently the two Acute Angles of a Right Angled Triangle amount to 90 Degrees , the Right Angle being also 90 . 40. The perpendicular height of a Triangle is a Line drawn ...
Page 16
... Triangle of three given Lines , as BO , BL , LO . Fig . 29 . Draw the Line BL from B to L ; from B , with the length of the Line BO , describe an Arch as at O ; from L , with the length of the Line LO , describe another Arch to ...
... Triangle of three given Lines , as BO , BL , LO . Fig . 29 . Draw the Line BL from B to L ; from B , with the length of the Line BO , describe an Arch as at O ; from L , with the length of the Line LO , describe another Arch to ...
Page 17
... Triangle will be completed . Note . The length of the two Legs may be found by measuring them upon the same Scale of equal parts from which the Hypothenuse was taken . PROBLEM X. To make a Right Angled Triangle , the Angles and one Leg ...
... Triangle will be completed . Note . The length of the two Legs may be found by measuring them upon the same Scale of equal parts from which the Hypothenuse was taken . PROBLEM X. To make a Right Angled Triangle , the Angles and one Leg ...
Page 18
... Triangle , two Sides and an Angle opposite to one of them being given . Fig . 35 . Suppose the Side BC 160 , the Side BD 79 , and the Angle at C 29 ° CA. Draw the Side BC in length 160 ; at C make an An- gle of 29 ° 9 ' , and draw an ...
... Triangle , two Sides and an Angle opposite to one of them being given . Fig . 35 . Suppose the Side BC 160 , the Side BD 79 , and the Angle at C 29 ° CA. Draw the Side BC in length 160 ; at C make an An- gle of 29 ° 9 ' , and draw an ...
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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.