Having drawn the square at an angle of 45°, as shown in the previous figure, we find the length of one of its sides, dh, by drawing a line, SK, through h, one of its extremities, till it cuts the base line at K. Then, with the other extremity d for centre and dK for radius, describe a quarter of a circle Km; the chord thereof mK will be the geometrical length of dh. At d raise vertical dC equal to mK, which gives us the height of the cube, then raise verticals at a, h, &c., their height being found by drawing CD and CD´ to the two points of distance, and so completing the figure.
Fig. 72.
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Pavements Drawn by Means of Squares at 45°
| Fig. 75. |
The square at 45° will be found of great use in drawing pavements, roofs, ceilings, &c. In Figs. 73, 74 it is shown how
having set out one square it can be divided into four or more equal squares, and any figure or tile drawn therein. Begin by making a geometrical or ground plan of the required design, as at Figs. 73 and 74, where we have bricks placed at right angles to each other in rows, a common arrangement in brick floors, or tiles of an octagonal form as at Fig. 75.