A Treatise on Practical Surveying: Which is Demonstrated from Its First Principles. Wherein Everything that is Useful and Curious in that Art, is Fully Considered and Explained

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F. Lucas and Joseph Cushing, 1818 - Surveying - 478 pages


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Page 42 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 99 - ... on a side, denotes its length to be given in feet, yards, perches, or miles, &c. and this mark", either in an angle or on a side, denotes the angle or side to be required. ; From these proportions it may be observed ; that to find a side, when the angles and one side are given, any side may be made the radius; and to find an angle, one of the given sides must be made the radius. So that in the 1st, 2d, and 3d cases, any side as well required as given may be made the radius, and in the first statings...
Page 46 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 93 - 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, &c.
Page 114 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 4 - POMEROY, of the said District, hath deposited in this Office the title of a Book, the right whereof he claims as Proprietor, in the words following, to wit : . . "Biography of the Signers to the Declaration of Independence.
Page 48 - The hypothenuse of a right-angled triangle may be found by having the other two sides ; thus, the square root of the sum of the squares of the base and perpendicular, will be the hypothenuse. Cor. 2. Having the hypothenuse and one side given to find the other; the square root of the difference of the squares of the hypothenuse and given side will be the required side.
Page 175 - ... the two cardinal points of your compass the point of the needle lies between (the north, south, east, and west being called the four cardinal points, and are graved on the bottom of the box), putting down those points together by their initial letters, and thereto annexing the number of degrees, counting from the north or south, as before, thus ; if the point of your needle lies between the north and east, north and west, south and east, or south and west points in the bottom of the box, then...
Page 282 - 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...

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