A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 pages |
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Page 16
... cyphers as decimals , to the numerator of the vulgar fraction , divide by the denominator ; and the quotient thence arising , will be the decimal fraction required . C EXAMPLES . Reduce to a Decimal Fraction . 4 16 DECIMAL FRACTIONS .
... cyphers as decimals , to the numerator of the vulgar fraction , divide by the denominator ; and the quotient thence arising , will be the decimal fraction required . C EXAMPLES . Reduce to a Decimal Fraction . 4 16 DECIMAL FRACTIONS .
Page 20
... , we place 6 in the divisor and quotient ; the then divisor 1086 is multiplied by the last figure in the quotient 6 , and the product being set under the resolvend and thence deducted leaves nothing : so is 20 THE SQUARE ROOT .
... , we place 6 in the divisor and quotient ; the then divisor 1086 is multiplied by the last figure in the quotient 6 , and the product being set under the resolvend and thence deducted leaves nothing : so is 20 THE SQUARE ROOT .
Page 21
... thence deducted leaves nothing : so is 546 the root sought . For if the root 546 be squared or multiplied by 546 the product will be the square number given . 2. What is the square root of 1710864 ? Root . 1,71,08,64 ( 1308 Answer . 1 ...
... thence deducted leaves nothing : so is 546 the root sought . For if the root 546 be squared or multiplied by 546 the product will be the square number given . 2. What is the square root of 1710864 ? Root . 1,71,08,64 ( 1308 Answer . 1 ...
Page 26
... 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 diameters AB and DE cross one another at right angles , and thus the ...
... 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 diameters AB and DE cross one another at right angles , and thus the ...
Page 43
... thence the lines AD and BC are parallel , by the preceding theorem . Cor . 1. Hence the quadrilateral figure ABCD is a parallelogram , and the diagonal BD bisects the same , inasmuch as the triangle ABD - BCD , as now proved . Cor . 2 ...
... thence the lines AD and BC are parallel , by the preceding theorem . Cor . 1. Hence the quadrilateral figure ABCD is a parallelogram , and the diagonal BD bisects the same , inasmuch as the triangle ABD - BCD , as now proved . Cor . 2 ...
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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.