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On Interpolation; an Essay containing a simple Exposition of the Theory in its most useful and practical applications, together with a general and complete Demonstration of the Methods of Quintisection of Briggs and Mouton for equal intervals; and of the process explained by Newton in his “Principia,” for intervals of any magnitude whatever*
Published online by Cambridge University Press: 18 August 2016
Extract
The calculation of extensive tables of logarithms could not fail to give rise to the method of interpolation; and such indeed was its origin. After Napier had made his memorable discovery, and he and Briggs had recognized the advantages that would result from the adoption of 10 as the base of a system of logarithms, it was Briggs who courageously undertook the immense labour required for calculating those famous tables, published in London in 1624, which have not been surpassed in extent and accuracy by any subsequent work. It is well known, however, that Briggs left a great hiatus in those tables, and that the logarithms of numbers between 20,000 and 90,000 are not to be found in them; but scarcely were the first tables printed, when Briggs undertook with fresh energy the computation of the Logarithms of the Trigonometrical Lines, and he was on the point of terminating this vast enterprise when arrested by death. It was his friend Gellibrand who completed the work, and gave it to the world in 1633.
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- Copyright © Institute and Faculty of Actuaries 1869
References
page 17 note * M. Maurice's demonstration fails to exhibit the general law of this formula for δ4ug . This defect we hope to supply in our next number.–ED. J. I. A.
page 17 note † It appears to us that M. Maurice does not do full justice to Briggs's method in consequence of his not observing that the differences δ4u8 , δ6u7 , δ8u6 , δ10u5 are all "central differences" opposite the same value, u10.–ED. J. I. A.