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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Page 12
... Parallel Lines are such as are equally distant from each other ; as AB and CD . Fig . 8 . 31. A 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 ...
... Parallel Lines are such as are equally distant from each other ; as AB and CD . Fig . 8 . 31. A 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 ...
Page 13
... Figure bounded by four Sides , two of which are parallel though of unequal lengths . Fig . 19. and Fig . 20 . Note . Fig . 19. is sometimes called a Right Angled 47. A Trapezium is a Figure bounded by four un- Trapezium . GEOMETRY . 13.
... Figure bounded by four Sides , two of which are parallel though of unequal lengths . Fig . 19. and Fig . 20 . Note . Fig . 19. is sometimes called a Right Angled 47. A Trapezium is a Figure bounded by four un- Trapezium . GEOMETRY . 13.
Page 14
... parallel Lines is with a parallel Rule . * PROBLEM II . To bisect a given Line ; or to find the middle of it . Fig . 23 . Open the Dividers to any convenient distance , more than half the given Line AB , and with one foot in A describe ...
... parallel Lines is with a parallel Rule . * PROBLEM II . To bisect a given Line ; or to find the middle of it . Fig . 23 . Open the Dividers to any convenient distance , more than half the given Line AB , and with one foot in A describe ...
Page 39
... parallel Sides by the perpendicular distance between them , or the Sum of the two parallel Sides by half the perpen- dicular distance ; the Product will be the Area . PROBLEM XI . To find the Area of a Trapezium , or irregular Four ...
... parallel Sides by the perpendicular distance between them , or the Sum of the two parallel Sides by half the perpen- dicular distance ; the Product will be the Area . PROBLEM XI . To find the Area of a Trapezium , or irregular Four ...
Page 46
... parallel Lines and lay off the sev- eral Sides till the whole is protracted . In protracting a field , let the Top of the Paper be considered as North ; the Bottom , South ; the Right hand , East ; and the Left hand , West : Lay the ...
... parallel Lines and lay off the sev- eral Sides till the whole is protracted . In protracting a field , let the Top of the Paper be considered as North ; the Bottom , South ; the Right hand , East ; and the Left hand , West : Lay the ...
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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 |
Popular passages
Page 28 - 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 27 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 6 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on.
Page 24 - In this case the" hypothenuse may be found by the square root without finding the angles ; according to the following PROPOSITION. IN EVERY RIGHT ANGLED TRIANGLE, THE SUM OF THE SQUARES OF THE TWO LEGS IS EQUAL TO THE SQUARE OF THE HYPOTHENUSE. In the above EXAMPLE, the square of AB 78.7 is 6193.69, the square of BC 89 is 7921 ; these added make 14114,69 the square root of which is nearest 119.
Page 40 - 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 33 - To find the area of a trapezoid. RULE. Multiply half the sum of the two parallel sides by the perpendicular distance between them : the product will be the area.
Page 6 - 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, passing through the centre ; and it divides the circle into two equal parts, called semicircles ; as AB or DE.
Page 40 - 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 23 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.