The Dissection of Rectilineal Figures

Extract

When my previous paper on the “Dissection of Rectilineal Figures” was published (Mathematical Gazette, October, 1914, vol. vii. p. 381), I had not seen Mr. H. M. Taylor’s paper in the Messenger of Mathematics, 1905, vol. xxxv p. 81. He gives the four-part dissection of a pair of triangles, and two varieties of this; the three dissections being all of one type. He also gives the three-part and other dissections of a pair of parallelograms. He also gives a four-part dissection of a triangle and a parallelogram (equivalent, by projection, to that of a triangle and a square) which, for the case of an equilateral triangle and a square, was published in 1905 by Mr. H. E. Dudeney, This dissection, which I did not know before, is also applied by Mr. Taylor to the case of a quadrilateral and a triangle with a side equal to a diagonal of the quadrilateral. As I have already given two types of dissection of a triangle and a square, with four parts in their fundamental case, which I have called the first and second types, I will call this, which is shown in Fig. 17, the third type.