Page:A History of Mathematics (1893).djvu/184

 Napier and Briggs, Adrian Vlacq of Gouda in Holland. He published in 1628 a table of logarithms from 1 to 100,000, of which 70,000 were calculated by himself. The first publication of Briggian logarithms of trigonometric functions was made in 1620 by Gunter, a colleague of Briggs, who found the logarithmic sines and tangents for every minute to seven places. Gunter was the inventor of the words cosine and cotangent. Briggs devoted the last years of his life to calculating more extensive Briggian logarithms of trigonometric functions, but he died in 1631, leaving his work unfinished. It was carried on by the English Henry Gellibrand, and then published by Vlacq at his own expense. Briggs divided a degree into 100 parts, but owing to the publication by Vlacq of trigonometrical tables constructed on the old sexagesimal division, Briggs' innovation remained unrecognised. Briggs and Vlacq published four fundamental works, the results of which "have never been superseded by any subsequent calculations."

The first logarithms upon the natural base e were published by John Speidell in his New Logarithmes (London, 1619), which contains the natural logarithms of sines, tangents, and secants.

The only possible rival of John Napier in the invention of logarithms was the Swiss Justus Byrgius (Joost Bürgi). He published a rude table of logarithms six years after the appearance of the Canon Mirificus, but it appears that he conceived the idea and constructed that table as early, if not earlier, than Napier did his. But he neglected to have the results published until Napier's logarithms were known and admired throughout Europe.

Among the various inventions of Napier to assist the memory of the student or calculator, is "Napier's rule of circular parts" for the solution of spherical right triangles. It is, perhaps, "the happiest example of artificial memory that is known."