Problem VIII. To form an octagon, or eight-sided figure.
Refer back to [Fig. 5]. Draw the radius I, E, till it meets the circumference at E. Join the points E, A, and E, B. Repeat this at each of the four sides, and the octagon is formed.
Problem IX. To form a decagon, or ten-sided figure.
Refer to [Fig. 6], and proceed as in the preceding problem.
Problem X. To construct a duo-decagon, or twelve-sided figure.
Refer to [Fig. 7], and duplicate the chords, as already shown.
We do not present 7, 9, or 11 sided figures, because they seldom or ever come into practice. Our object being to give what is useful and not overburden the memory unnecessarily.
The learner should go over and work out each of the foregoing problems several times. In fact, until they are soundly secured in his memory, so that on any emergency he can apply them to a required practice. They are the simplest rudiments, but as practically useful as they are simple. The Architect, the builder, as well as the several trades of carpenter, joiner, carver, stone-cutter, mason, and in fact, all in any way concerned in the practice of construction will at some time or other wish to recall one of these useful problems. Therefore do we dwell on the necessity for committing them, understandingly, to memory, and likewise the advantage required in being able to draw them neatly and perfectly on paper. In order to do this with satisfaction to one’s self, it is desirable that a fine point be constantly maintained on the pencil, and that uniform nicety be preserved with the curved lines, as well as the right or straight lines. For nothing looks worse than undue thickness in the one or the other. All should be alike.
In theoretical geometry a line, whether right or curved, is but imaginary, not having any thickness whatever, and therefore no palpable existence. In practical geometry the line must be visible, but ought to be so uniformly fine as to occupy scarcely any perceptible thickness. And herein lies the greatest beauty in geometrical draughting. By strict attention to this apparently trifling matter, its advantages will show wherever minute angles occur. They will be clear and distinct, and always satisfactory.