## A Treatise on Surveying and Civil Engineering, Wherein Everything that is Useful and Curious is Demonstrated from Its First Principles |

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Page 5

SECTION I. The area of any plain

SECTION I. The area of any plain

**figure**, is the measure of the space contained within its bounds , without any regard to thickness . This area is estimated by the number of small squares that may be contained in it . Page 6

( The truth of this rule is manifest , as the

( The truth of this rule is manifest , as the

**figure**may be divided into two right - angled triangles . ) . Ex . Required the contents of a lot of land in the form of a trapezoid , whose base is 41. 10 perches and ulars 10. 12 and 6. Page 7

Let ABC

Let ABC

**figure**1 , be the given triangle . Draw the parallels CP and BX , meeting the two sides CA , AB , and making AX = CX , and AC = AP . Also , draw the perpendicular AN bisecting BX and PC in N and R ; and NOS parallel to the side ... Page 8

Let ABC

Let ABC

**figure**2 , be the proposed triangle . Let fall the perpendicular AP , and bisect BC in O. Take AC = b , AB = c , and BC = a . Now , we get b2 - c2 = 2a . PO , and a sides a2 + ba - c2 2a 2 and you get -PC . b2 - c2 2 a a 2 b2 ... Page 9

Look to the last

Look to the last

**figure**. Now , CA. = the area . And sine A : BC : : sine B : CA. ( 16 . 6. ) sine A. CA. = BC . sine B. , and BC . area . MN . 2 S.A.CA. Take b this value of BC . into the first equation and it will give , AC2.### What people are saying - Write a review

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### Common terms and phrases

abutments adjustment allow angle appears arch base bearing breadth bridge called canal centre chain connected consequently construction contained correct cross crown curve depression depth determine diameter difference direction distance divided division draw earth east effect engineer equal error evident fall feet figure find the area give given greater ground half height Hence horizontal inches inclination land latitude length limb lower manner mean measure meridian method middle miles move multiplied natural nearly necessary object observed parallel pass perpendicular pieces plane plate position possible practice Prob quantity radius railway refraction right angles river road rule screws side sight slope square staff station stone straight stream suppose surface survey taken telescope theodolite thickness triangle true turn upper velocity vernier vertical wedge whole

### Popular passages

Page 7 - ... and 48° 15'? Ans. 6 A. 3 R. 18 P. PROBLEM V. To find the area of a triangle when the three sides are given. RULE. From half the sum of the three sides...

Page 23 - ... perfect in both positions of the telescope, the line of collimation in altitude or depression is correct, but if not, the operation must be repeated carefully, until the adjustment is satisfactory. A similar proceeding will also put the vertical line correct, or rather, the point of intersection, when there are two oblique lines instead of a vertical one. The second adjustment is that which puts the level attached to the telescope parallel to the rectified line of collimation. The clips...

Page 54 - The middle 18 feet of pavement is to be coated with hard stones to the depth of 6 inches. Four of these 6 iuches to be first put on and worked in by carriages and horses, care being taken to rake in the ruts until the surface becomes firm and consolidated, after which the remaining 2 inches are to be put on.

Page 54 - All the irregularities of the upper part of the said pavement are to be broken off by the hammer, and all the interstices to be filled with stone chips firmly wedged or packed by hand with a light hammer, so that when the whole pavement is finished there shall be a convexity of four inches in the breadth of fifteen feet from the centre.

Page 54 - Upon the level bed prepared for the road materials, a bottom course, or layer of stones, is to be set by hand, in form of a close firm pavement ; the stones set in the middle of the road are to be 7 inches in depth ; at 9 feet from the centre, 5 inches ; at 12 feet from the centre, 4 inches ; and at 15 feet, 3 inches.

Page 68 - RULE.* To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by £ of the height will give the solidity.

Page 84 - ... the practical architect to adopt his visions, raised another system, which is said to secure a perfectly equilibrated structure, by making an equality at every point of the curve. The deduction from this theory consists in making the height of the wall incumbent on any point of the intrados, directly as the cube of the secant of the curve's inclination to the horizon at that point, or inversely as the radius of curvature there. It must be added, that this theory expects the joints of the voissoirs...

Page 23 - First, make the centre of the horizontal wire coincide with some well-defined part of a distant object; then turn the telescope half round in its Y's till the level lies above it, and observe if the same point is again cut by the centre of the wire ; if not, move the wire...

Page 24 - P; which done, reverse the telescope in its Y's, that is, turn it end for end, which must be done carefully, that it may not disturb the vertical arc, and if the bubble resume its former situation in the middle of the tube, all is right; but if it retires to one end, bring it back one half, by the screw...

Page 25 - ... determined by repeating the observation of an altitude or depression in the reversed positions, both of the telescope and the vernier plate : the two readings will have equal and opposite errors, one half of their difference being the index error.