## 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 |

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### Common terms and phrases

according accurately added Angle Arch Arithmetically Base Bearing calculated called Chains Circle Compass contained corresponding Course Decimals describe Diagonal Difference directions Dist Distance divided Draw the Line drawn Eastings equal EXAMPLE Field FIELD BOOK figures find the Area four fourth give given greater half hand Hypothenuse Index Land Latitude and Departure Left Leg BC length less Line Links Logarithm look manner measuring method Minutes multiply Natural Sines North North Areas Note opposite particular Perpendicular PLATE Plot Point preceding PROBLEM Product Proportions protract Quotient Radius Remainder represent Right Angled Rule Scale Secant Secant Co-Secant Side Side BC Sine Sine Sine South Areas Square Square Root Star Station subtract Suppose Surveying Surveyor Table Tang Tangent Tangent Co-Secant third Trapezoid Triangle Trigonometry true West whole

### 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.