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
F. Lucas and Joseph Cushing, 1818 - 478
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acres angle Answer base bearing called centre chains chord circle Co-secant Co-sine Co-tang column contained decimal Deg Dist difference direct Dist distance divided division double draw drawn east edge equal EXAMPLE feet field field-book figures four four-pole give given greater ground half height Hence inches laid land length less logarithm manner measure meridian distance method multiplied needle object observe off-sets opposite parallel parallelogram perches perpendicular plane PROB proceed proportion quantity quotient radius reduce remainder right angles right line root scale Secant sect side sights sine square station stationary suppose survey taken Tang tangent theo THEOREM third triangle triangle ABC true turn variation whole
Strona 44 - 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.
Strona 101 - ... 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...
Strona 48 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Strona 95 - 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.
Strona 116 - 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.
Strona 6 - 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.
Strona 50 - 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.
Strona 117 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Strona 177 - ... 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...