The Dissection of Rectilineal Figures

Extract

Another function of the pentagon dissection, Fig. 19, is to provide, by means of an additional cut in each pentagon, an eight-part type of dissection of a pair of quadrilaterals. This, which I will call the first type of eight-part dissection of quadrilaterals, is shown in Fig. 24. The dissection of the pair of quadrilaterals is shown in full lines, and dotted lines are added to show a pair of auxiliary pentagons, the lettering being the same as in the previous figures. A dissection of the pair of pentagons is shown, and there is an additional cut in the first pentagon joining T to the middle point X of the base AB, and an additional cut in the second pentagon joining W to the middle point Y of the base CD. The other new lines shown in the figure are merely consequential on the formation of a pair of quadrilaterals by means of these two cuts. There is no relation between the dimensions of the quadrilaterals except the equality of their areas. Each quadrilateral is divided by six lines, two or more of which are broken ; four of these lines are half sides of the other quadrilateral, and the other two are half diagonals, one of one quadrilateral and the other of the other quadrilateral.