Page:The Construction of the Wonderful Canon of Logarithms.djvu/112

88 Notes. God) in a second Edition, to set out such Logarithmes as shal make those numbers aboue written to fall upon decimal numbers, such as 100,000,000, 200,000,000, 300,000,000, &c., which are easie to bee added or abated to or from any other number,

Most Illustrious Sir, I have always endeavoured 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. We have now also found out a better kind of logarithms, and have determined (if God grant a continuance of life and health) to make known their method of construction and use; but, owing to our bodily weakness, we leave the actual computation of the new canon to others skilled in this kind of work, more particularly to that very learned scholar, my very dear friend, Henry Briggs, public Professor of Geometry in London.

In the actual work of computing the Canon of Logarithms, Napier would continually make use of numbers extending to a great many places, and it was then no doubt that the simple device occurred to him of using a point to separate their integral and fractional parts, It would thus appear that in the working out of his great invention of Logarithms, he was led to devise the system of notation for decimal fractions which has never been improved upon, and which enables us to use fractions with the same facility as whole numbers, thereby immensely increasing the power of arithmetic. A full explanation of the notation is given in sections 4, 5, and 47, but the following extract, translated from ‘Rabdologiæ,’ Bk. I. chap. iv., is interesting as being his first published reference to the subject, though the above sections from the Constructio must have been written long before that date, and the point had actually been made use of in the Canon of Logarithms printed at the end of Wright’s translation of the Descriptio in 1616.

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