dimensions of all magnitudes or quantities be determined by a measure of length, whose division corresponds with that of the coin, in which the value of the quantities produced by a regular involution of the length, is given, and all ratios, between which there is any connexion, be correspondent, we shall be perpetually embarrassed with innumer. able tedious reductions and intricate proportions. For this ratio, none can be compared with the decimal, to which are adapted, the characters by which we compute, all numbers from unity upward, and the American coin, which is (with others similarly divided) the best in the world; and which has, in our best American productions, been very much neglected, while the devoted labor of thousands has been be stowed on that, which is, only by pride and prepossession withheld from oblivion; and which will, with all others, and the hundreds of different and ill divided weights and measures, be lost in the aggrandize. ment of one complete standard of decimal coin, weight and measure; which will lessen the labor of acquirement in this science more than any other improvement it has ever received: the method of placing the decimal point being the only knowledge necessary, separate from that of performing operations in whole numbers.

A system as above mentioned of decimal division of quantity, which was calculated to explain the various operations of decimals, to show the propriety of corresponding divisions, &c. a sketch of arithmetical trigonometry, a demonstration of rules, and a few other subjects, have been omitted, as the size of the volume already exceeds what was designed, and as the task of publishing has been unexpectedly lengthy and tedious, owing to the difficulty of correcting a work of this kind, and to the copy being better calculated for an octavo page, and therefore comprises more than usual in the same space; which may by some be thought an error, if so, it is hoped it will be a profitable one, and that the size, price or contents of the volume will not be dissatisfactory to its purchasers.

From a conviction of the inadequate knowledge contained in our present systems of arithmetic, and of the many disadvantages experienced therefrom, the author was prompted to the undertaking of the arduous task, which has been executed with a fidelity suited to its impor tance. And how far it may be deserving of that patronage and encour agement to which it is so liberally recommended by those gentlemen who have honored it with their names, for which the highest expressions of gratitude are tendered, and what part, it may contain, of that. merit, which with unremitted diligence has been sought, is left to the candid decision of a liberal and impartial public.

Haverhill, Feb. 1811.

Use and Explanation of Characters.

THE characters or figns used, for fake of brevity, in the following treatise, and those used by others, fignify the fame that the phrases or words do which are here annexed to them.

O cipher; 1 one; 2 two; 3 three; 4 four; 5 five; 6 fix; 7 feven; 8 eight; 9 nine;

Signs,

fignifications,

explanations.

is equal to, or make; as, 1 = 100 cents, i.e. 1 $ is e

+ added to, or add;

qual to 100 cents.

as, 55=10, i.e. 5 added to 5 is equal to 10.

— or — subtracted from,or take;

Xorx multiplied by, or times;

divided by:

or 2)6( divifion ;

as, 3-5 = 2, i.e. 3 subtracted

from 5= 2. from 5-3=2. as, 3 x 2, or, 2 x 3=6, ie. 3 times 2 or 3 multiplied by 2= 6. as, 623, i.e. 6 divided by 2 3. 24,5 or 2.

as,

::::or :::: geometrical proportion;

..::.. arithmetical proportion; as, 2..4::3..5, ie. 2 is to 4 as 3 to

5 arithmetically.

42 or 42 Square (of 4) required; as, 4(4 x 4) 16. 24.·

23 or 23 cube (of 2) required; as,

2

82. 8 x 8.

23 — (2x2x2 =) 8.4}|3= 64. 33. 3 x 3 x 3 or 27.

22 x 2, 22 x 2 x 2, or 242 x 2 x 2 x 2, &c.

2

24, v 1/4, 1/4 or square root(of 4)required; as, 42. v/9

3

3. 164. 125-5.

3

38,8 or 8 cube root (of 8) required; as, '8=2. 82.

m

273.

V

*8, 1/8 or 8m any root (of 8) required; as, 28, or '8, or 48,800

B