In this department the lessons which we shall first consider are those which require for their construction nothing but the arrangement and combination of right or straight lines. It is scarcely necessary here to state, that the instruments requisite for the various operations are the same as those re-* quired for the constructions described in the Illustrated Practical Geometry, the 6drawing-board,' ' square,' and 'triangle,' being absolutely indispensable. As tiie work above noticed is strictly designed to be introductory to the present, we beg to refer the reader thereto for a description of these, and the readiest methods of using them.
Example 1. To draw the portion of1 hipped roof shewn in fig. 1. Sup
pose the figure to be that of which it is desired to make an exact copy. On the drawing-paper, properly fastened to the board, mark any point a; parallel to the side of the drawing-board, draw from this point any line, and make it equal to ab. Bisect this in the point m; at right angles to ab draw from this point a line to e7 and make this equal to me in the copy. Join ea, eb. At right angles to ab, from these points draw to c, d, making the length of t^ese equal to be in the copy. Draw the lines.ee, dd, parallel to ab. The example given in fig. 1 will thus be copied. The pupil should be very careful to take the measurements in his * compasses/ or ' dividers,' equal to those in the copy.
Example 2. To draw the part plan of the wall of a house, shewing the projection of one side of fireplace, with the internal flue, in Jig. 2. Divide the thickness of the wall g' g by the centre line ah, bisect fe, and draw at right angles to ab a line cmn. These lines are to be drawn on the copy in light pencil lines, as also the line g produced to d and h. On the paper on the drawing-board on which the copy is to be made, draw any lines aft, cn, corresponding to those made on the copy in fig. 2. From the point c of intersection, with the measurement cn taken from copy, lay off from c to n'; with distance rif from copy, lay off on a line drawn through n' at right angles to cn', to the points e and f; from e draw a line at right angles to ef to the point g, and make it equal to eg; do the same at f, and make the line equal to fv. Lines drawn from g and v, parallel to aft, will represent the internal line of wall; the external, or external line ^1, will be put in by measuring its distance on the copy from the centre line ab, and transferring it to the paper on the board, and thus drawing the line g 1 parallel to aft. The next portion to be copied is the internal fiue. Take the measurement dn from the copy and transfer it to the corresponding line on the board; in like manner put the measurement nm; with no or ms, on lines drawn at right angles to cn', measure to s, o, and join the points so, so; the. example is completed. Another method of copying this figure may be adopted, as follows::—Assume on the paper on which the drawing is to be made any point e; parallel to the side of the board draw a line ge, and make it equal to the line ge in the copy. At right angles to this draw ef, and make it equal to ef; from /, parallel to eg, draw fv; from g and v draw lines as in the copy parallel to fe\ ' parallel to these, and at the proper distance, put the line g 1. With the distance nn from e lay on die line eg, and through this point draw a line ono, parallel to fe. At the point m, the distance of which from the point n is easily obtained from the copy, draw another line sms; from the line ge measure to the line so, and transfer it to the board; parallel to ge draw so, meeting the lines ms, no. Measure the breadth of the fiue from otoo, transfer it to- the board, and join the upper ends of the lines through win by a line so. We have here shewn two methods, chiefly to enable the pupil, by a ready exercise of his reasoning powers, to decide as to the quickest method of copying any figure presented to him.
Example 3. To draw one jamb with two internal flues. Let aft, fig. 3, be the internal line of wall, abed the outline of jamb. Produce the sides h hf to meet the line ed, and mg, nf, to meet be, ad at the points o, o. Having fastened the paper properly on the board, and proceeded with the copy as directed above, the produced lines being marked in light pencil lines, the first operation is to draw any line, as ab, on the most convenient part of the paper on the board. From a measure to b; and from these points, at right angles to ab, draw lines to c and d; make be, ad, equal to the corresponding lines in the copy; join rfc. Next take from the copy the measurement from d to e (the point found by producing hf), and Lay it from the point d in the board on the line dc. Do the same from c to e; parallel to be draw lines eh, eh; measure next the distance from d to o, and transfer it to ad, be, to 0,0; parallel to aft draw a line 00. From g and f measure to h h; transfer these, and from the points obtained draw a line hh parallel to 00. With distance hs, or nf measure from h to 8, from g to m, from n to yj and from t to h; join the points. In inking the lines, the points be, da, hg, sm, tn, hf will be the terminations of the lines. In the examples given the lines not dotted shew the complete design.
Example 4. To draw the outline» of an ordinary sash window. Make any line ed equal to the corresponding line in the copy, fig. 4. At the points e, d draw lines perpendicular to cd of an indefinite length. With the measurement ea, from the copy, cut the lines ea, db, in a,b; join ab. Divide the line cd into three equal parts in the points n, n; parallel to ae, from these draw lines meeting ab. Divide the line ae into four equal parts in the points m, e, g; parallel to ab, from these draw lines meeting bd in m\f h. The parallelogram a bde is divided into twelve lesser ones, representing each a pane of glass.
Example 5. To draw the diagonal lines representing the panes in a rustic window, fig, 5. Draw cd, making it equal to erf in the copy; erf is the side of the square abdc, which describe. Divide the sides cd,ac, each into six equal parts; join the corresponding points, as 1, 2, 4, 5, 3, 6.
Example 6. To draw the central pilaster in fig. 6. Divide in the copy the line ab into two equal parts at e, and through this, at right angles to ab, draw the line cc; bisect the part 00 by a line sfs. On the paper on which the drawing is to be made, draw any line representing ee, and another at right angles to the first, representing ab in the copy, fig. 6. The intersection of these two lines will represent the point c. Take from the copy the measurement cf; transfer it from 6 to /; draw parallel to ab through this point a line, representing the line ifs in the copy. With* aej from c lay off on ab to a, b; draw indefinite lines from these points perpendicular to ab; measure ad, be equal to ad in the copy; join ed. With measurement ft, lay off from /to t and u, and on the line cc as many times as necessary; through these several points draw lines parallel to ab; these will be the centre lines of the parts corresponding to oo. With half of oo, from the points of intersection of these with the line cc, lay off equal to oo; through the points draw lines parallel to ab; produce ab to gg. The terminations of the parts oo will thus be formed, as represented in fig. 6. In the copy produce the internal lines h k, to meet the line ab in mn; from c, with cm lay off on ab to m, n, and parallel to cc from these points, draw Knes mh,nh. These lines will terminate the internal alternate portions. Another method of copying this figure will be as followsDraw any line ab, and at right angles to it another, bg; the point where they meet will correspond to the point b in the copy, and thus a datum point will be obtained from which to take measurements. With b a from the copy, cut off a ¿parallel to de; from a draw dg ; make ad, be each equal to the corresponding lines in the copy; join de. From e measure to the line above it, and transfer it to the paper on the board; from the same point measure to the next line; and so on in succession. Transfer these measurements to the corresponding points on the paper on the board, and through the points obtained draw lines parallel to ab ; these will form the under and upper lines of the parts oo. The lines representing the boundary-lines of the alternate inner portions can be obtained by measuring from e or dto the lines in the copy, and transferring them; thereafter through the points ob-; tained drawing lines at the parts required parallel to bg.
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