A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 páginas |
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Página 57
... BF , making BF - AE ; through A and B draw the line AB , and it will be parallel to CD . By prob . 2. The angle BAF - AFE , and by theo . 11. BA and CD are parallel . H Plate II . PROBLEM IX . Upon a given line PROBLEMS . 57.
... BF , making BF - AE ; through A and B draw the line AB , and it will be parallel to CD . By prob . 2. The angle BAF - AFE , and by theo . 11. BA and CD are parallel . H Plate II . PROBLEM IX . Upon a given line PROBLEMS . 57.
Página 59
... prob . 8. ) so is CI the third proportional required . For by Cor . 1. theo . 20. CG : CH :: CF : CI . Or , B : A :: A : CI . PROBLEM XII . Three right lines A , B , C , given to find a fourth proportional . Fig . 17 . Plate II . Having ...
... prob . 8. ) so is CI the third proportional required . For by Cor . 1. theo . 20. CG : CH :: CF : CI . Or , B : A :: A : CI . PROBLEM XII . Three right lines A , B , C , given to find a fourth proportional . Fig . 17 . Plate II . Having ...
Página 60
... prob . 5. ) bisect AC in E ( by prob . 4. ) and describe the semicircle ADC ; and from the point D , where its periphery cuts the perpendicular BD , draw the line BD , and that will be the mean proportional required . For if the lines ...
... prob . 5. ) bisect AC in E ( by prob . 4. ) and describe the semicircle ADC ; and from the point D , where its periphery cuts the perpendicular BD , draw the line BD , and that will be the mean proportional required . For if the lines ...
Página 61
... prob . 8. ) so is E the point of division . For , by cor . 1. theo . 20. AC : AD :: AE : AB . Or , C : D :: AE : EB . PROBLEM XV . To describe a circle about a triangle ABC , or ( which is the same thing ) thro ' any three points , A ...
... prob . 8. ) so is E the point of division . For , by cor . 1. theo . 20. AC : AD :: AE : AB . Or , C : D :: AE : EB . PROBLEM XV . To describe a circle about a triangle ABC , or ( which is the same thing ) thro ' any three points , A ...
Página 63
... prob . 8. ) DE , meeting AB produced in E ; then draw CE , and ECB will be the triangle required . For the triangles ADC , AEC being upon the same base AC , and under the same parallel ED ( by cor . to theo . 13. ) will be equal ...
... prob . 8. ) DE , meeting AB produced in E ; then draw CE , and ECB will be the triangle required . For the triangles ADC , AEC being upon the same base AC , and under the same parallel ED ( by cor . to theo . 13. ) will be equal ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 207 - ... that triangles on the same base and between the same parallels are equal...
Página 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.
Página 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 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.
Página 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.
Página 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.
Página 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°.
Página 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.