CONTENTS

Introduction .

Pngr.

The construction of the tables...«... i

Application and use of the tables for finding the square, cube, square

root, &e. of numbers...... xiii.

To find the higher powers of numbers by tables II. and III. .... xxiii.

The solution of the irreducible case in cubic equations .. xxiv.

General approximation to the roots of equations and their several pro-perties ..5.*. xxxi.

Newton ’s approximation .... xxxiv.

Eaphson’s method..... • • .. xxxv.

Approximation by position... .. xxxvi,

Lagrange’s approximation........ xxxvii.

Observations relating to the principles of Newton ’s method.... xlv.

New method of approximation ..... H-

' Table of prime numbers.... lv.

Tables of hyperbolic logarithms, &c*«...... Ivii.

Tables .

Table L Containing the factors, squares, cubes, square rftots, cube

roots, and reciprocal of all numbers from 1 to 10000 .. 1

Table II. Containing the first ten powers of all numbers under 100 170

Table III. Containing the 4th and Sth powers of all numbers from

100 to 1000 . 1 76

Table IV. For the solution of the irreducible case in cubic equations 186Table V. Of all prime numbers under 100000 .................. 194

Table VI. Of hyperbolic logarithms for all numbers under 10000 .. 212

Table VII. Of differential coefficients ... 254

Table VUI. Containing various algebraical formula?, relating to the

-doctrines of equations, series, fluxions, fluents, See. .... 25?

Table IX. Of English and foreign weights and measures. 318

Table X. Of the specific gravities of different bodies.... .. 334