historical view of the

194

theorems, renders it worthy of notice ; especially asprinciples not dissimilar were afterwards broached inreference to a different subject, and have given riseto great discussion. To find the relative places in theinterpolation which must be occupied by the numberand by the index or logarithm, he adopted the suppo-sition of two points describing two different lines, theone with a constant velocity, and the other with a velo-city always increasing in the ratio of the space whichthe point had already gone over. The first of thesewould generate magnitudes in arithmetical, and thesecond, magnitudes in geometrical, progression. On thisprinciple he demonstrated liis rule for finding the loga-rithms of numbers. '

This, however, is not the sole monument of Na-pier’s profound mathematical talent. The two theorems,or rules, which go by his name, absolutely involve allthe most important cases of the solution of sphericaltriangles. They were published at the same time withhis “ System of Logarithms ; ” though before commu-nicated in manuscript to Cavalieri, who mentions themwith high commendation.

The intellectual character of Napier exhibits an in-stance of one of those singular inequalities which notunfrequently characterise high genius. Exact and com-prehensive as were his views of mathematical truth, hecould not discriminate other kinds; and engaged withall the sober assurance of certainty in a puerile com-mentary, in which he imagined he had decyphered allthe mysteries of the Apocalypse. He died in 1622.

Among those who contributed greatly to tbe advance-ment of mathematical learning in this period, we mustnot omit to mention sir Henry Savile . He becamedistinguished in the university of Oxford for his know-ledge of mathematics; and, about the year 1575, vo-luntarily read public lectures on that science. Heafterwards attained several preferments, and becamedeservedly esteemed as a man of universal attainments.In 1619, he founded at Oxford two professorships, for