## A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |

### From inside the book

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... ten times greater than the third . 1000 3 03

... ten times greater than the third . 1000 3 03

**Hence**it appears , that as the value and denomi- nation of any figure or number of figures in common arithmetic is enlarged , and becomes ten or an hun- 10 DECIMAL FRACTIONS . Page 26

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**hence**it is plain that the radius CD is the greatest possible sine , and thence is called the whole sine . Since the whole sine CD ( fig . 8. ) must be per- pendicular to the diameter ( by def . 22. ) therefore producing DC to E the two ... Page 28

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**Hence**angles are greater or less according as the arc described about the angular point , and termi- nated by the two legs contain a greater or less num- ber of degrees of the whole circle . 31. The sine , tangent , and secant of an arc ... Page 30

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**Hence**all triangles between the same parallels have the same height , since all the perpendiculars are equal from the nature of parallels . 43. Any figure of four sides is called a quadri- lateral figure . 44. Quadrilateral figures ... Page 37

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**Hence**, if one angle of a triangle be known , the sum of the other two is also known : for since the three angles of every triangle contain two right ones , or 180 degrees , therefore 180 - the given angle will be equal to the sum of ...### Other editions - View all

### 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.