In an appendix of forty-one pages he gives his third method, "local arithmetic," which is performed on a chess-board, and depends, in principle, on the expression of numbers in the scale of **radix** 2.

He uses "radicatum" for power (for root, power, exponent, his words are **radix**, radicatum, index).

- It should be observed that the **radix** of the scale is exactly the same thing as the root mentioned under (ii.) above; and it is better to use the term " root " throughout.

It was first formally proposed as an independent method, with great improvements, by Robert Flower in The **Radix**, a new way of making Logarithms, which was published in 1771; and Leonelli, in his Supplement logarithmique (1802-1803), already noticed, referred to Flower and reproduced some of his tables.