A Treatise of Practical Surveying, ...1808 - 440 pages |
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Page 21
... . fig . 13 . 39. Or obtuse angled , having one obtuse angle , as E. fig . 14 . 40. Or acute angled , having all the angles acute , as F. fig . 15 . 41. Acute Plate I. 41. Acute and obtuse angled triangles are in GEOMETRY . 21.
... . fig . 13 . 39. Or obtuse angled , having one obtuse angle , as E. fig . 14 . 40. Or acute angled , having all the angles acute , as F. fig . 15 . 41. Acute Plate I. 41. Acute and obtuse angled triangles are in GEOMETRY . 21.
Page 22
... triangles , in all which any side may be called the base , and the other two the sides . 42. The perpendicular height of a triangle is a line drawn from the vertex to the base perpen- dicularly thus if the triangle ABC , be propos- ed ...
... triangles , in all which any side may be called the base , and the other two the sides . 42. The perpendicular height of a triangle is a line drawn from the vertex to the base perpen- dicularly thus if the triangle ABC , be propos- ed ...
Page 28
... triangle ABC , one of its legs , as BC , being produced towards D , it will make the external angle ACD equal to the two internal opposite angles taken fogether . Viz . to B and A. fig . 3 . . Plate I. Thro ' C , let CE be Thro ' 28 ...
... triangle ABC , one of its legs , as BC , being produced towards D , it will make the external angle ACD equal to the two internal opposite angles taken fogether . Viz . to B and A. fig . 3 . . Plate I. Thro ' C , let CE be Thro ' 28 ...
Page 29
... triangle be known , the sum of the other two is also known : for since the three angles of every triangle con- tain two right ones , or 180 degrees , therefore 180 -the given angle will be equal to the sum of the other two ; or 180 ...
... triangle be known , the sum of the other two is also known : for since the three angles of every triangle con- tain two right ones , or 180 degrees , therefore 180 -the given angle will be equal to the sum of the other two ; or 180 ...
Page 30
... triangle ABC be supposed to be laid on the triangle DEF , so as to make the points A and B coincide with D and E , which they will do , because ABDE ( by the hypothesis ) ; and since the angle AD , the line AC will fall along DF , and ...
... triangle ABC be supposed to be laid on the triangle DEF , so as to make the points A and B coincide with D and E , which they will do , because ABDE ( by the hypothesis ) ; and since the angle AD , the line AC will fall along DF , and ...
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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.