As the following treatise is not intended to lessen the merit of any preceding work of the kind, but principally to simplify the rules of the science, and furnish the pupil with familiar and suitable examples; if it should, in these respects, claim any preference to other systems, I flatter myself, that the public, and my fellow teachers particularly, will favor it with their patronage: and to their decision, I respectfully submit the work. The tables inserted in reduction, by some authors, are, in this treatise, omitted; as they swell the book to little purpose: The pupil being thoroughly acquainted with the tables in Compound Addition, would supersede the necessity for the tables in that rule. The three last cases in Vulgar Fractions, and Combination of Numbers, are also omitted; the uselessness of which, and a desire to make room for things of greater utility, without increasing the price of the book, being thought a sufficient apology for their suppression. Some useful information, therefore, respecting Carpenter and Mason's work, is added; which cannot fail of being acceptable to youth apprenticed to these callings. But as to these, and some other advantages, which I hope this treatise will be found to possess, and the mode adapted respecting federal money in the several rules, the public decision will be the best criterion. Besides the ordinary rules in books of this kind, I have inserted Policies of Insurance, taken principally from Pike' Arithmetic; I have also added, a concise Treatise or Gauging. This being an amusing, as well as necess art, and seldom introduced into books of this kind, cannot fail of being acceptable to teachers in general. Having said thus much, it may not be amiss to add, that there are, no doubt, errors of the pen and press; but the candid will pass a favorable construction upon what is almost impossible to avoid in a work of this nature. Such detections, however, or any hint of improvement, communicated to me, should a second impression be encouraged, will be gratefully received. J. P. EXPLANATIONS OF CHARACTERS. SIONS. SIGNIFICATIONS. more; as, 6+2=8 less; as, 8-2-6 into, with, er multiplied by; as, 6×2=12 by (i. e divided by) as, 6÷2=3; or 2)6(3 proportionality; as, 2:4::6:12 2 2 ARITHMETIC. ARITHMETIC is that science which treats of the properties, powers, and operations of numbers. It has five primary rules..........viz. Numeration...... Addition...... Subtraction...... Multiplication......and Division. NUMERATION. NUMERATION teaches how to read any number of figures which may be written; and also to express, by figures properly arranged, any number of figures which can be conceived. The characters used in calculations are 1 one.......2 two.......3 three......4 four......5 five......6 six ....... seven......8 eight......9 nine....... cipher. TABLE: Tens............ Hundreds............. ....... 1........One 2 1........Twenty-one 3 2 1........Three hundred twenty-one 3 2 1........ 4 thousand 321 3 2 1........54 thousand 321 3 2 1........654 thousand 321 3 2 1........7 million 654 thousand 321 3 2 1........87 mill. 654 thousand 321 3 2 1........987 mill. 654 thous. 789........ 123 mill. 456 thou 69 1........483 mill. 572 tho B The above table is thus briefly comprised and enlarged: Although the preceding table is sufficient in practice, yet the following may not be unnecessary : Nonillions. Octillions. Septillions. Sextillions. Quintillians. 654321 987654 321987 654321 987654 Quadrillions, Trillions. Billions. Millions. Units.. 98654 321987 654321 321987 654321 Billions are substituted for millions of millions.......Trillions for millions of millions of millions........Quadrillions for inillions of millions of millions of millions, &c. EXAMPLES: Set down in figures the following numbers: Nine hundred and five. Twelve thousand and ninety. Two hundred eighty thousand, seven hundred. eight hundred and seventy-two. Seven hundred sixty-four thousand millions, eight hundred ninety-five millions, two hundred thirty-one thousand, eight hundred and seventy-nine. In words express these numbers: Numbers are also thus denoted, and are called numeral 1....2.....3...45678910....... 500.....10001798......... A less numeral number, placed after a greater, augments VI 6...... IV 4XI 11. IX 9. CX 110.......XC 90 ADDITION of integers is the collecting of several Place the numbers so, that units be under units, tens under tens, &c. Then add the right-hand column, setting down the units of the result, carrying the left-hand figure |