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.

A Little more than three hundred years ago Napier announced to the world his discovery of Logarithms in the Mirifici Logarithmorum Canonis Description “ I have always endeavoured,” we read in one of his works, “ according to my strength and the measure of my ability to do away with the difficulty and tediousness of calculations, the irksomeness of which is wont to deter very many from the study of mathematics. With this aim before me, I undertook the publication of the Canon of Logarithms which I had worked at for a long time in former years; this canon rejected the natural numbers and the more difficult operations performed by them, substituting others which bring out the same results by easy additions, subtractions and divisions by two and by three.” Soon after the publication of the Canon, what he calls “another and better kind of logarithms “occurred to him, practically logarithms to the base 10, as we now know them, and a similar change in his system also suggested itself to Briggs, then Gresham Professor of Geometry in London, one of the first to recognise the immense value of Napier’s discovery In the interval between 1614 and Napier’s death in 1617, they had devised several methods for the construction of the new Tables; but owing to Napier’s failing health he had decided to leave the actual computation to Briggs. As early as 1617 Briggs was able to publish the logarithms of the numbers from 1 to 1000 to eight places. In 1624 he followed this with the numbers from 1 to 20,000 and 90,000 to 100,000 to fourteen places. In 1628 Vlacq, a Dutchman, published the logarithms of all numbers from 1 to 100,000 to ten places, along with a Table of the Logarithms of the Trigonometrical Ratios for every minute, to the same number of places. These Tables of Briggs and Vlacq have never been superseded—their work was done for all time. They contain errors which have gradually been discovered and corrected, but all the Tables that have been published since their time, with one single exception, have been copied, directly or indirectly, from their work.