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 20
... accurately by calculation with Logarithms , or with Natural Sines . TRIGONOMETRY is divided into two Parts , Rectan gular and Oblique - angular . PART I. RECTANGULAR TRIGONOMETRY . This is founded on the following methods of applying a ...
... accurately by calculation with Logarithms , or with Natural Sines . TRIGONOMETRY is divided into two Parts , Rectan gular and Oblique - angular . PART I. RECTANGULAR TRIGONOMETRY . This is founded on the following methods of applying a ...
Page 35
... is the case with a great part of the Land in New - England , it is better to use a Chain of only two Rods in length ; SECTION I. PRELIMINARY PROBLEMS . PROBLEM I. To reduce Two as the Survey can be more accurately taken . SURVEYING. ...
... is the case with a great part of the Land in New - England , it is better to use a Chain of only two Rods in length ; SECTION I. PRELIMINARY PROBLEMS . PROBLEM I. To reduce Two as the Survey can be more accurately taken . SURVEYING. ...
Page 42
... accurately taken . To effect this , the lower end of the Chain must be rais- ed from the ground , so as to have the whole in a hor- izontal Line ; and the end thus raised must be directly over the Point where the Chain begins or ends ...
... accurately taken . To effect this , the lower end of the Chain must be rais- ed from the ground , so as to have the whole in a hor- izontal Line ; and the end thus raised must be directly over the Point where the Chain begins or ends ...
Page 45
... accurately in the first place . f Other methods of taking the Survey of a Field , by the Chain only are mentioned in some Treatises on this subject , but they are rather curious than useful ; and it is much better to ascertain the ...
... accurately in the first place . f Other methods of taking the Survey of a Field , by the Chain only are mentioned in some Treatises on this subject , but they are rather curious than useful ; and it is much better to ascertain the ...
Page 50
... accurately taken . By the RULES for protracting a Field , Page 48 , find the Quantity of the several Angles , and add the whole together ; to their Sum add 360 ° ; divide this Sum by 180 ° ; and , if the Survey is right , the Quotient ...
... accurately taken . By the RULES for protracting a Field , Page 48 , find the Quantity of the several Angles , and add the whole together ; to their Sum add 360 ° ; divide this Sum by 180 ° ; and , if the Survey is right , the Quotient ...
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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.