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Now whatever number EG represents, G1 will be the tenth of it, and the subdivisions in the vertical direction GB will be each 100th part. For example, if EG be a unit, the small divisions in EG, viz. G1, 1 2, &c., will be 10ths, and the divisions in the altitude will be the 100th parts of a unit.

To take any number off the scale, say 247, i.e. 2:47 ; place one foot of the compasses at F, and extend the other to the division marked 4 (on ); then move the compasses upward, keeping one foot on the line FD, and the other on the line 45; till the seventh interval is reached, and the extent on the compasses will be that required.

Scale of Chords.—A scale of chords is a scale by means of which, instead of a protractor or geometrical construction, angles of any number of degrees can be measured or constructed. When marked on a flat protractor, it is usually indicated by the sign C, or CHO.

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Its construction is as follows :—Any quadrant ABC is taken, and its arc AB is divided into 9 equal parts of 10° each ; thus, with the radius of the arc as radius, points 30° and 60° are marked off on the arc AB. Then each portion is divided into three equal parts by trial, and each point of division is numbered in tens of degrees from 0 to 90. The chord of the arc AB is then drawn, and from A as centre, with the points of division as radii in succession, arcs are described cutting the chord AB in points numbered similarly to the arc; thus transferring the degrees in the arc to a straight line, from either of which the same measurements may be taken.

50

B

Thus, at the point A, in AB to make any angle with AB, say 50°, we take the distance from 0 to 60° as radius, and from A as centre with AB as radius, we describe the arc BC.

We then take the distance from 0 to 50°, and mark it off from B to D. Draw DA, then angle DAB = 50°.

Note 1.-Under all circumstances, describe the arc BC with the distance from 0 to 60° as radius.

NOTE 2.- In the scale of chords, the divisions diminish from 0 to 90.

END OF PLANE GEOMETRY.

PRACTICAL SOLID GEOMETRY.

A COURSE OF PROBLEMS

IN

PRACTICAL SOLID GEOMETRY.

Section 1.--DEFINITIONS, &c.

1. The preceding portion of this work consists of drawing plane figures. We now come to the consideration of drawing solid objects geometrically. Hitherto the various figures drawn have had only length and breadth, but a solid object has another dimension, viz., thickness or solidity.

2. It must here be noted that a solid may be represented in two distinct ways, viz., perspectively and geometrically. When an ohject is drawn perspectively, it is drawn as it appears to one from any given point of view; but when it is drawn geometrically, it is drawn as it actually is, its true proportions and size being represented according to scale.

3. It follows that, in drawing a solid object geometrically, three dimensions have to be delineated upon a plane surface. To this end, we make two distinct drawings, one which represents the exact space it covers, as it would be seen when looked at from above, and another which represents its vertical appearance, as it would be seen when looked at in front. The former of these is called the plan, and shows the length and breadth ; the latter is termed the elevation, and shows the length and height.

4. From a consideration of the following illustrations, it will be

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