A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |
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Page 80
... remainder is the tangent . ( By part 1. theo . 24. ) EXAMPLE . 1. Suppose the tangent of 41 ° . 20 ' , was defaced , but the sine and co - sine of it visible . From the sine of 41 ° . 20 ' + 10.00000 , or radius , Take the co - sine of ...
... remainder is the tangent . ( By part 1. theo . 24. ) EXAMPLE . 1. Suppose the tangent of 41 ° . 20 ' , was defaced , but the sine and co - sine of it visible . From the sine of 41 ° . 20 ' + 10.00000 , or radius , Take the co - sine of ...
Page 81
... remainder is the co - tangent , ( by theo . 24. part . 5. ) EXAMPLE . Required , the tangent of 29 ° . 50 ′ being defaced , as also the sine and co - sine defaced , by the co - tan- gent only . From twice the radius , Take the co ...
... remainder is the co - tangent , ( by theo . 24. part . 5. ) EXAMPLE . Required , the tangent of 29 ° . 50 ′ being defaced , as also the sine and co - sine defaced , by the co - tan- gent only . From twice the radius , Take the co ...
Page 82
... remainder will be the secant , ( by theơ , 24. part 7. ) EXAMPLE . Required , the secant of 57 ° . 20 ′ by help of the sine and tangent . From the tan . of 57 ° . 20 ' + 10.00000 the radius , Take the sine of 57 ° . 20 ′ 20.19303 ...
... remainder will be the secant , ( by theơ , 24. part 7. ) EXAMPLE . Required , the secant of 57 ° . 20 ′ by help of the sine and tangent . From the tan . of 57 ° . 20 ' + 10.00000 the radius , Take the sine of 57 ° . 20 ′ 20.19303 ...
Page 104
... remainder will be the least of them . Fig . 13 . Let the two quantities be represented by AB and BC ; ( making one continued line ; ) whereof AB is the greatest , and BC the least ; bisect the whole line AC in E ; and make AD - BC ...
... remainder will be the least of them . Fig . 13 . Let the two quantities be represented by AB and BC ; ( making one continued line ; ) whereof AB is the greatest , and BC the least ; bisect the whole line AC in E ; and make AD - BC ...
Page 122
... remainder will be the other inter- nal opposite one , thus ; CBD 55 ° --A 37 ° -AÇB 18 ° Therefore in the triangle ABC we have the angles A , and ACB , with the side AB given to find BC . Plate V. fig . 23 . S.ACB : AB :: 122 OF HEIGHTS .
... remainder will be the other inter- nal opposite one , thus ; CBD 55 ° --A 37 ° -AÇB 18 ° Therefore in the triangle ABC we have the angles A , and ACB , with the side AB given to find BC . Plate V. fig . 23 . S.ACB : AB :: 122 OF HEIGHTS .
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Common terms and phrases
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-sec Co-sine Co-tang Tang column contained cyphers decimal decimal fraction diameter difference distance line divided divisor draw drawn east edge EXAMPLE feet field-book figures fore four-pole chains half the sum height hypothenuse inches instrument Lat Dep Lat latitude line of numbers logarithm measure meridian distance multiplied needle number of degrees off-sets parallel parallelogram perpendicular piece of ground plane Plate prob PROBLEM proportion protractor quotient radius right angles right line scale of equal SCHOLIUM Secant second station sect semicircle side sights sine square root stationary distance sun's suppose survey taken tance tangent thence theo theodolite THEOREM trapezium triangle ABC trigonometry true amplitude two-pole chains vane variation whence
Popular passages
Page 25 - 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 207 - ... that triangles on the same base and between the same parallels are equal...
Page 40 - 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 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 31 - Figures which consist of more than four sides are called polygons ; if the sides are all equal to each other, they are called regular polygons. They sometimes are named from the number of. their sides, as a five-sided figure is called a pentagon, one of six sides a hexagon, &"c.
Page 31 - ... they are called regular polygons. They sometimes are named from the number of their sides, as a five-sided figure is called a pentagon, one of. six sides a hexagon, &c. but if their sides are not equal to each other, then they are called irregular polygons, as an irregular pentagon, hexagon, &c.
Page 45 - 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 265 - As the length of the whole line, Is to 57.3 Degrees,* So is the said distance, To the difference of Variation required. EXAMPLE. Suppose it be required to run a line which some years ago bore N. 45°.
Page 32 - Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders are equal.