## A Treatise of Practical Surveying, ...1808 - 440 pages |

### From inside the book

Page 94

... a given angle ABC ,

... a given angle ABC ,

**is to their difference , as the tangent of half the sum of**the two unknown angles A and C is to the tangent of half their difference . Fig . 11 . Plate V. Produce AB and make HB = BC , Produce OBLIQUE ANGULAR.### Other editions - View all

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.