# The National Arithmetic, on the Inductive System: Combining the Analytic and Synthetic Methods, Together with the Cancelling System; Forming a Complete Mercantile Arithmetic

R.S. Davis, 1849 - 360 pages

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### Contents

 ���� 7 Numeration 15 Addition 25 Contractions in Multiplication 37 Tables of Money Weights and Measures 44 Compound Addition 50 Reduction 64 Compound Multiplication 78
 Banking 193 Equation of Payments 199 Ratio 205 Proportion 215 Chain Rule 221 General Average 227 Duodecimals 234 Involution Evolution or the Extraction of Roots 239

 Compound Division 86 Addition of Vulgar Fractions 110 Multiplication of Vulgar Fractions 121 Questions to be performed by Analysis 129 Decimal Fractions Numeration of Decimal Fractions 135 135 Division of Decimals 141 Exchange of Currencies 147 Addition of Circulating Decimals 156 Questions to be performed by Analysis 162 Simple Interest 170 Partial Payments 173 Miscellaneous Problems in Interest 181 Discount 187
 Extraction of the Square Root 241 Extraction of the Cube Root 248 Arithmetical Progression 257 Infinite Series 267 Alligation 275 Life Insurance 282 Exchange 290 Value of Gold Coins 305 Gauging 327 Mechanical Powers 335 Strength of Materials 341 Miscellaneous Questions 347 APPENDIX Weights and Measures 355

### Popular passages

Page 92 - To reduce a mixed number to an improper fraction. RULE. � Multiply the whole number by the denominator of...
Page 243 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.
Page 239 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 176 - Compute the interest to the time of the first payment ; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and in like manner from one payment to another, til! all the payments are absorbed ; provided the time between one payment and another be one year or more.
Page 176 - But if any payments be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation, for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid, up to the end of the...
Page 124 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 248 - Raise the ratio to a power whose index is equal to the number of terms, from which subtract 1 ; divide the remainder by the ratio, less 1, and the quotient, multiplied by the first term, will be the answer.
Page 293 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 284 - Thirty days after sight of this first of exchange (second and third of the same tenor and date unpaid...
Page 33 - Cut off the ciphers from the divisor, and the same number of figures from the right of the dividend. Then divide the remaining figures of the dividend by the remaining figures of the divisor.