A Treatise of Practical Surveying, ...1808 - 440 pages |
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Page 2
... proportion : for and which in the decimal form we denote by .3 .03 and .003 , are fractions , of which the first is ten times greater than the second ; and the second ten times than the third . 03 1000 greater Hence it appears , that as ...
... proportion : for and which in the decimal form we denote by .3 .03 and .003 , are fractions , of which the first is ten times greater than the second ; and the second ten times than the third . 03 1000 greater Hence it appears , that as ...
Page 23
... proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D , be equal to B multiplied by C , then A is said to be to B as C is to D. POSTULATES OR PETITIONS . 1. That a right line may be drawn ...
... proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D , be equal to B multiplied by C , then A is said to be to B as C is to D. POSTULATES OR PETITIONS . 1. That a right line may be drawn ...
Page 38
... proportion . So AB : ab :: BC : bc : the same way the rest may be proved to be propor- tional . THE O. XVII . If from a point A without a circle DBCE there be drawn two lines ADE , ABC , each of them cut- ting the circle in two points ...
... proportion . So AB : ab :: BC : bc : the same way the rest may be proved to be propor- tional . THE O. XVII . If from a point A without a circle DBCE there be drawn two lines ADE , ABC , each of them cut- ting the circle in two points ...
Page 39
... proportion between themselves as their bases ABand BD . Let any aliquot part of AB be taken , which will also measure BD : suppose that to be Ag , which will be contained twice in AB , and three times in BD , the parts Ag , gB , Bh , hi ...
... proportion between themselves as their bases ABand BD . Let any aliquot part of AB be taken , which will also measure BD : suppose that to be Ag , which will be contained twice in AB , and three times in BD , the parts Ag , gB , Bh , hi ...
Page 41
... proportion to each ; and ( by theo . 6. ) the triangle A dc ADE , therefore the angle Ade D and Aed - E , but since ed and BC are parallel ( by part 3. theo . 3. ) Ade = B , and Acd = C , therefore B - D and C - E . Q. E. D. * G THE O ...
... proportion to each ; and ( by theo . 6. ) the triangle A dc ADE , therefore the angle Ade D and Aed - E , but since ed and BC are parallel ( by part 3. theo . 3. ) Ade = B , and Acd = C , therefore B - D and C - E . Q. E. D. * G THE O ...
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A Treatise of Practical Surveying: Which Is Demonstrated From Its First ... Robert Gibson No preview available - 2018 |
Common terms and phrases
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-fecant Secant Co-fine Co-tang column contained cyphers decimal decimal fraction diameter difference Dift Diſt distance line divided draw drawn east edge EXAMPLE feet field-book figures fore four-pole chains half the sum height hypothenuse inches instrument latitude logarithm measure meridian distance method multiplied needle number of degrees object off-sets parallel parallelogram perpendicular piece of ground plane Plate pole Portmarnock PROB protractor quotient radius right angles right line scale of equal second station sect semicircle side sights sine square root stationary distance stationary line sun's survey taken tangent thence theo theodolite thro trapezium triangle ABC trigonometry true amplitude two-pole chains vane variation Vulgar Fraction whence ΙΟ
Popular passages
Page 32 - 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 199 - ... that triangles on the same base and between the same parallels are equal...
Page 94 - 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.
Page 23 - Four quantities are said to be in proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D.
Page 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 37 - ABDE+ACGF the sum of the squares —BKLH-\-KCML, the sum of the two parallelograms or square BCMH; therefore the sum of the squares on AB and AC is equal to the square on BC.
Page 24 - Things that are equal to one and the same thing, are equal to each other. 2. Every whole is greater than its part. % 3. Every whole is equal to all its parts taken together. 4 If to equal things, equal things be added, the whole will be equal. 5. If from equal things, equal things be deducted the remainders will be equal.
Page 36 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Page 182 - VI. To find the content of a triangular piece of ground, Multiply the base by half the perpendicular, or the perpendicular by half the base ; or take half the product of the base into the perpendicular. The reason hereof is plain, from cor.
Page 35 - Triangles upon equal bases, and between the same parallels, are equal to one another.