734
THEORY AND PRACTICE OF ENGINEERING.
Hook II.
estimate of quantity, or the contents of either surfaces orsolids.
Tangent point is that at F, where the straightline V X touches the curve of the circle N, at a part ofits circumference G O F, or at G, where two circles toucheach other, without cutting; N is the central point ofthe circle: right lines drawn from this point to the cir-cumference are its radii; the two points which boundeach being the centre, and a dot on the circumference.The diameter passes through the centre, comprises twicethe radius, and may be defined as bounded by two points,situated somewhere on the outline of the circle. Thiscircumference may be also supposed to be divided bypoints into a number of degrees, and the divisionsbetween by others od infinitum, until the entire figure iscomposed of points, or forming a polygon with an in-finite number of sides.
Station point is the place from whence an observationis made, and the spot immediately beneath the centreof the instrument used ; R is such a point.
Distance point is a stone or hole in an object, re-marked in taking an observation; V in the tower servesfor such a point of sight, and is used to denote the hori-zontal or level line by which the height of the tower Tmay be ascertained.
Inaccessible point is one that cannot be approached, asS, the water which surrounds the tower not permittingan easy access to it.
Lines have length only, and are the boundaries ofall figures; they may be considered to pass from onebody to another, without being visible; CD is an ima-ginary line from the point of the pyramid to the stone.
A right line, as that of G H, is straight, and liesevenly between two points, neither ascending nor de-scending, but is the shortest distance between the ob-jects.
A curved line has no portion of a right line, but isconcave on one side and convex on the other.
GH is a perpendicular line standing on KL, theangles formed on each side being equal; GH L andGHK both being right angles. The plummet makes,when it is dropped, a perpendicular line, as at N.
The column L is a perpendicular line standing on itsbase M, or rather it diverges or tends to the centre ofthe earth, the line with which it is perpendicular beinga tangent to the earth’s circumference: falling bodiestend towards a point at its centre, and our ideas of aperpendicular line must always be with reference to alimited base, or it must be considered a diverging line;for the sides of buildings continued to a great height,and maintained perpendicularly, would, according to ourusual notions, require that the area of the upper flooror top should be larger than the one below ; the walls orlines that bound them, to be upright, must be radii, andconsequently diverge from each other as they are con-tinued upwards; in practice it is not necessary to haveany other guide than the plummet, which dropped froma height falls to the centre, and any material disposedwithin such a line gravitates to the same point. Spiresof churches are rarely found to have the point at theirapex directly over the centre of the area of their base;that at Salisbury is nearly 2 feet inclined beyond it; itis extremely difficult to ascertain one point by theplummet that is directly over another, when the heightis considerable. Columns are rarely found placed trulyperpendicular; their internal faces, as those towards thecell of a temple, are sometimes less inclined or diminished
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