The Method of Quarter Squares


I OMITTED any reference to Leslie in my review of Mr. Blater's table (NATURE, vol. xl. p. 573), as I have never supposed that he was an independent discoverer of the method, or an independent calculator of a table, of quarter squares. I have eferred to his table in my Report on Mathematical Tables Brit. Assoc. Report, 1873, p. 23); and the passage quoted by Prof. Carey Foster (p. 593) is given in full in the preface to Mr. Blater's table. It seems to me that the words in question— “This application of a table of quarter squares, as it is derived from the simplest principles, might have readily occurred to a mathematician; yet I have nowhere seen it brought into practical use till, last summer, I met with, at Paris, a small book by Antoine Voisin, printed in 1817”—do not indicate an independent discovery; and this view is confirmed by the fact that, in the first edition of the “Philosophy of Arithmetic” (1817), Leslie makes no mention of quarter square. It was only in the second edition (1820), after having seen Voisin's work in the previous year, that he added, at the end of the volume, an account of the method, and a table extending to 2000. The table was copied, I presume, from Voisin, as Leslie does not claim it as the result of his own calculation. In the British Association Report I have described it as “reprinted from Voisin,” and have pointed out that it did not appear in the first edition. In the preface to Mr. Blater's letter it is described as “an extract from Voisin's table.” Although we may, I think, infer, almost with certainty, that the table is only a reprint,1 it is to be regretted that Leslie did not say so explicitly.

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GLAISHER, J. The Method of Quarter Squares. Nature 41, 9 (1889).

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