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This new integral of Lebesgue is proving itself a wonderful tool. I might compare it with a modern Krupp gun, so easily does it penetrate barriers which were impregnable.

Bulletin of the American Mathematical Society, vol. 23, 1916.

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# Mathematical Treasures

## Jonas Moore's Arithmetick in Four Books

This is the title page of Moore's Arithmetick in Four Books, by Jonas Moore (1627 - 1679). Moore served many years as a surveyor, and his work was necessary in the draining of the Fens, a marshland in eastern England near Cambridge. His Arithmetick first appeared in 1650, but this is a copy of the third edition, published nine years after his death. Moore's portrait is on the left. Note that, according to the title page, it is in algebra that "all difficult questions receive their analytical laws and resolutions."

On pp. 274-275, there is a mixture problem dealing with the composition of an ointment. Notice the ingredients.

Moore gives on p. 407 various Renaissance and 17th century names and notations for the powers of an unknown in a comprehensive table. Note that columns 7, 8, and 9 give Viète's, Harriot's, and Descartes' notation for powers, respectively. (The actual powers are below the central line; above the reciprocals of the powers.)

On pp. 454 - 457, Moore gives a careful treatment, with examples, of the procedure for turning a word problem into an algebraic equation. But he always aims at generality, if possible. Interestingly, Moore gives on p. 454 both Viète's and Descartes' procedure for choosing letters for knowns and unknowns.

Note Moore's final statement, which still applies today: "And note that of all the parts of equation, this only of the invention is most difficult." Students will probably agree with that statement.