The Magician's Own Book, or, the Whole Art of Conjuring / Being a complete hand-book of parlor magic, and containing over one thousand optical, chemical, mechanical, magnetical, and magical experiments, amusing transmutations, astonishing sleights and subtleties, celebrated card deceptions, ingenious tricks with numbers, curious and entertaining puzzles, together with all the most noted tricks of modern performers.

by George Arnold; Frank Cahill

A bricklayer had to construct a wall, whose length in the direction A B C was twenty-four feet. The one half of this wall, namely from B to C, had to be built over a piece of rising ground, so that the base of this part of the wall would necessarily be more than twelve feet. In making out his account he charged more for this half of the wall than for that which was built on level ground from A to B. A geometrician assured him that the square contents of both portions of the wall were exactly alike; which may be proved in the following manner:—

Fig. 4.

Cut two pieces of cardboard, in the form shown in Figs. 2 and 3, to represent the two parts of the wall; lay the piece representing the straight wall on the curved piece, and it will be found that the angles which project at A and B will exactly fill up the spaces at E and F. The piece of board representing the straight wall may thus be found to be exactly sufficient to form a piece equal to that representing the curved wall. You may then lay the curved piece upon the straight one, and reversing the experiment prove that the curved piece is capable of forming a rectangular piece equal to the other.

TRIANGULAR PROBLEM.

Take four square pieces of pasteboard of the same dimensions, and divide them diagonally, that is, by drawing a line from two opposite angles, as in the figures, into eight triangles. Paint seven of these triangles with the prismatic colors, red, orange, yellow, green, blue, indigo, violet, and let the eighth be white. To find how many chequers or regular four-sided figures, different either in form or color, may be made out of these eight triangles.

First, by combining two of these triangles there may be formed, either the triangular square A, or the inclined square B, called a Rhomb. Secondly, by combining four of the triangles the large square C may be formed, or the long square D, called a parallelogram. Now the first two squares, consisting of two parts out of eight, may each of them by the eighth rank of the triangle be taken twenty-eight different ways, which makes fifty-six. And the last two squares, consisting of four parts, may each be taken by the same rank of the triangle seventy times, which makes 140.

TO FORM A SQUARE.