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Example 7. To draw the quoins of a house in fig. 7. Produce in the-copy the external line/to meet the base-line ag produced in e; next, on" the paper on the board draw any lines ac;ab at right angles to each other; then the point of intersection 'will correspond to the point a in the copy. Measure the distance ag from the copy, and transfer it to the board; do the same with a e. From these points draw lines parallel to aft. The line ab will represent the corner line of house, the line gh the internal line of quoins, and ef the external. Suppose aft to be the height on which the quoins are to be disposed, make aft on the* board equal to aft in the copy; and on the supposition that there are to be twelve quoins in aft, divide aft into twelve equal portions, and through the points thus obtained draw lines-parallel to a c, as bhjfcL Finish as in the copy. Another method is as ' follows:—Draw lines ac, ab as before; measure from a to g, and draw from this a line parallel to aft / measure from a to 1, and draw through the point'1 a line 1*; measure Is, transfer it; measure st, and draw it at right angles' to at; join t2 by a line parallel to ae. The first quoin la, t2 will then be drawn, and afford datum points from which to finish the others;1 thus the line st produced towards /will give the external line of all the others; and the distance al, transferred in succession to the line aft, will mark the horizontal distances. /

Example 8. To draw the figure in fig. 8, which represents the plan of the roof of an outbuilding, or external addition, projecting from the main waJI/rcs. The dotted line cd must be first drawn in the copy, dividing aft into two parts at o ; next, on the board draw any tfro lines at right angles corresponding to those in the copy, as cd,fdns. To avoid unnecessary repetition, we wish the reader to understand that, when we give directions to xqeasure any part or distance, as " measure from c to ft and a," we mean, that the distance c b is first to be taken from the xsopy, and transferred from the corresponding point on the board; thus ascertaining the position of the points by a corresponding to those in the copy. The copy is, in all instances, the only source from which measurements are to be taken: nothing in this species of drawing is to be left to the eye,—all must be tested by the instruments. Inaccuracy of measurement in any one point will inevitably result in throwing the whole drawing wrong. Thus, for instance, supposing the distance al, in fig. 7, was taken with the smallest possible error in measurement—say too much—it would be found that the distance would not go twelve times between ah, but would go beyond ft to a much greater distance than would be supposed. Where an erroneous measurement is to be transferred from one point to another in succession, the original error increases in a remarkably quick ratio. But to proceed with the consideration of the construction of figure 8, after this, we hope not useless, digression. Measure from c to b and a, and draw acbd, from ab parallel to cd draw lines to / and e; measure from c to h; through h draw a line parallel to ab; from h measure torn, m. Or these points may be obtained by measuring from the lines af, be. From m, m draw lines parallel to cd to In; from n measure to o, and parallel to 13 draw a line to p. Measure from n to join 8p. From c measure to g; draw the lines gd, and join gm, gm. A line from 3 parallel to sp, joining a line from e parallel to op, will complete the figure.

Example 9. To draw the plan of part of roof in fig. 9. Bisect in the copy the line between cc in the point ft, and draw ab. On the board draw any line ab corresponding to aft in the copy, and at right angles to it another representing the line cd. At c, c drop the perpendiculars, as in the copy, and join them by a line parallel to cd. From c measure to d, and parallel to aft draw lines dh; measure from d to h. From c measure to e, and parallel to aft draw eg; measure from e to g, and draw a line gg parallel to cd. On eg measure to m, m; draw mm parallel to cd. From ft measure to o, and put in the lines oo, 11; join ol, ol: this represents the cistern in the roof for rain water. Join g 1, mo, mo, these representing the sloping lines of roof. From m measure to 2, and put in the plan of chimney flues.

Example 10. To draw the window in fig. 10. Bisect ab in c. and draw a line cf; draw corresponding lines on the board to ab, c/. From c measure to a and b, and draw lines ae, be. From c measure to n, d, m, 8, h, and /, and through all these points draw lines parallel to ab,—that drawn through d meeting the lines ee from the termination of ab. At n measure to an, a distance equal to half nn in the copy. Do the same at the points f and m to mm, gg. Parallel to fc from f»y n draw to «, t, and join hi, hi. From g, g parallel to cf draw to m, m. From d lay off to oo, and from these draw lines to mm, parallel to cf; join these with the point 8 by lines parallel to hi, hi. From i measure to h', and make tik at right angles to ou At right angles to k'k make kp; from p measure to r, and draw rt parallel to k'k. Measure tx, and put in the line 11. Example 11. To draw the window in fig» 11. Bisect ab in c, and draw cd. On the board draw any two lines corresponding to ab,cd in the copy; measure from c to a, b, and draw at these points to gg lines parallel to cd; measure to gg, and join ggg. From c measure to e and d and f; through these draw lines parallel to ab. From/measure to ff and from e to e, e; join fe,fe by lines parallel to cd. From e measure to h, h and to «, n; from ¿measure to m, m, and join mn, mn. From hh parallel to cd draw lines to oo; measure ho, and parallel to hh draw lines from oo meeting mn. Draw the parallelogram within eeff, and from c measure to \$ and t, and through these draw lines parallel to ab: these represent the divisions of the glass. Put in the lines 11 parallel to erf,.joiiung </</, hh: the drawing is complete.

Example 12. To draw the form of window in fig. 12. . Put the centreline cc as before. Corresponding to the lines ab, cc draw two on the board.

From c measure to a, b, and from same point to/ m, and c; through c draw a line parallel to ab, as ee, and through//f, and m, gg. Measure from/ to /,/, and from m to g, g; join gf. From c measure to x, and join gx, gx. Parallel to ab put in the lines dd, hv, hv. From v, h, parallel to gfy draw lines to meet g, g, and from the points o, o lines to meet them, parallel to gx. From e measure to n, and put in nt; put in the square ssss bylines parallel io mo, gx. Draw the external 4 dressings' by the method described in fig. 10. Example 13. To draw the chimney-shaft in fig. 13. Bisect the line ab, draw a line doc through this; draw corresponding lines to ab, cd on the board; measure from c to o, s, x, and hh; measure from o to gg, and put in the part gg, as well as those under it. Through s draw a dotted or occult line* ese, divide og, og into two parts at ppy with the half of op, from s lay off four times to ee, on both sides of the line cd, join ge, and from t, t lines meetingProduce the lines ept and s beyond the line hh ; measure from 1 to n, n, join nm, nm, vx, and put in the remaining portion as by preceding lessons.

Example 14. To draw the steps of a stairtase as in fig. 14. Let dg be the height from one line of floor to the other, represented by the upper and tinder lines ; and cd the distance in which the steps are to fall. The height, of each step is 7 inches, technically called a 'riser'; the breadth being tisually 9 inches; this part on which the foot rests is called the 'tread.1 The measurements in the figure are taken from a scale one-fourth of an inch to the foot. Suppose the width cd to be 6 feet, allowing 9 inches for the tread, this will give eight divisions; divide cd therefore into eight equal parts, and from these points draw lines perpendicular to cd. Taking the

* " * For definition of the various kinds oi lines see Illustrated Practical Geometry.

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6 V ds height;d<), from "one landing to another, to be 5 feet 3 inches, this will give, nine divisions of 7 inches each; divide dg therefore into nine equal parts, and from the points thus obtained draw lines par rallel to ccL From the intersection of tjiese lines 11 at a, draw to the intersection of 2 the line from 1, with that from 2 on dg ; from the point n, the intersection of the lines 2 2, draw a line meeting the intersection of the vertical line 2 with the horizontal 3. The intersection of the lines 33 gives the point qf next step, and so on, each time proceeding nearer the line ag.

Example 15. To delineate the plan of the stairs in the preceding lesson. The distance aft, fig. 15, corresponds to dg in fig. 14; the breadth aft being that between the side walls or balustrades; if a line be drawn, from the point 9, fig. 14, to the left-hand top corner of the front step at c, it will be found to touch the corners of all the steps ; this forms the foundation for another method of delineating the profile of the steps in a staircase as described in -

Example 16. Let 12, fig. 16, be the breadth, and 2ft the height from one landing to another as before; raise the step 13 and join ft 3. From ft on the perpendicular b2} mark off to c a distance equal to the height of one* riser equal to 7 inches. From c draw a line exactly parallel to a 2, or perpendicular to ft 2, meeting the diagonal line ft 3 in d; from d-dropa perpendicular de, equal 7 inches or be; from e draw parallel to cda line meeting ft 3 as before; from / drop a perpendicular to h, and proceed thus till finished. Great care must be taken to draw the lines truly parallel to the proper lines; also to drop the perpendiculars, as de, exactly from the point where the horizontal lines, as cd, join the diagonal ft 3. The least deviation from accuracy in the beginning will inevitably result in throwing - the operations towards the end fax wrong. The lines should be drawn very finely, so that the exact points of intersection will be easily observable. Th£ method shewn in fig. 14 will be least liable to error. We give the two methods, as affording opportunities of extended practice to the pupil) and as suggestive of plans he may himself adopt

Example 17. To delineate the' a plan of a staircase having 'returns* by which the direction is changed. Assume any point in fig. 17, draw n/ aft, perpendicular to it draw ac. Measure from a to s and g, draw from these points ef, g h parallel to ac ; from a measure to d, and draw dm parallel to aft; measure from d to c, and draw the line 1 ; divide dc into seven equal parts. From d measure to n, and from a to o; join sn, so. We give another lesson similar to this in

Example 18. Draw a ft, bd at right angles to one another ; from* ft measure to c and e, and draw eh, ch at right angles to bd, ba. Divide ed into two equal parts, and ca into seven. Measure from c to f, and from ft to g ; join hf, hg. Example 19 shews plan of cellarnsteps having a return at head which is entered from p, and one at foot entered from s. A party-wall is between the two houses, the steps of the adjoining house being shewn in dotted lines. Draw ac, aft at right angles; from a measure to c; draw cd, representing the inside line of external wall, parallel to aft. From ac measure off the thickness of party wall, dividing the two staircases, and draw a line db parallel to ac. From d and ft measure to e andf; from these points draw lines parallel to aft. From c measure to m, and from a to n; join em, nf. Measure from d to h, and from ft to g; join fg, eh. Divide the distance between ef into as many equal parts as in the drawing, from these points draw lines parallel to ab; these represent the steps in the stair parallel to the party-wall.

Example 20. In fig. 20 we give a sectional vertical sketch, shewing a flight of stairs c, reaching to the first landing-place d\ from the ground-floor aft, with return steps e, leading to the first floor f; the landing-place d, counts as one step, a step rising into the room of which d'd is the door; a a is the door of a room on the ground-floor, gg of one on the ground-floor. The ground-plan of this is shewn in

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