78 EQUAL AND SYMMETRICAL FIGURES

often, tne outlines are pierced by some pointed instru-ment, at short and equal distances, in their whole length ;then, with a little bag, containing finely powdered char-coal, we strike on the model, as it lies over the other sur-face, MNPQ, and the fine charcoal dust passing throughthe small holes, traces, very accurately, the outline of thefigure to be made.

When the model cannot, or must not be perforated, asheet of transparent paper is laid over it, and its exactform, or the parts to be made, are drawn or copied onthe paper. The paper may be transferred to anothersurface, and pierced, or the figure may be cut out, orotherwise copied, as is most convenient.

Symmetry of figures. —Two figures, abed, a'b'c'd', fig. 1,repeated, pi. 5, are symmetrical when their correspondingpoints a and a', b and b', c and c', &c. are placed onparallel lines, all of which are accurately divided in themiddle by a perpendicular line MN. If we were to dou-ble the frame MNPQ, on MNP'Q', it is plain that a willfall on a', b on b', &c.—so that the figure abed, could it beimpressed on the surface MNP'Q', would produce thefigure a'b'c'd', which is symmetrical to the former. Bymeans of parallels, therefore, and a perpendicular, dividingthem in the middle, we can always make a figure, a'b'c'd’,symmetrical with another, abed.

Production of equal or symmetrical figures, by engrav-ing, printing, lithography, Sfc. —The object of these artsis to form, on a surface of wood, metal, or stone, or onany other substance, certain figures, of which the impres-sion may be afterwards transferred exactly to some othersurfaces. It must be observed, that the figure producedis reversed, in regard to the plate by which it is made,for the right of the plate is imprinted on the left, andthe left on the right of the paper, or other material, em-ployed to receive the impression; we must, therefore, writeor draw the figure reversed, on the plate, if we wish thatthe impression shall represent an object in its natural po-sition. For this reason, types are cast reversed, and pla-