# HIGHER ARITHMETIC; OR THE SCIENCE AND APPLICATION OF NUMBERS; COMBINING THE ANALYTIC AND SYTHERIC MODES OF INSTRUCTION.

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### Contenido

 NoTjriON 20 Formation of different systems of Notation 29 Countingroom Exercises 37 SECTION XI 41 General Rule for Subtraction 44 General Rule for Multiplication 53 SECTION V 66 Different methods of Proving Division 72
 Compound Numbers reduced to Decimals 215 Addition of Circulating Decimals 222 Addition of Federal Money 229 Countingroom Exercises Contractions c 237 Applications of Percentage 244 General method for computing Interest 252 To compute Interest by the number of days 258 Vermont Rule 264

 General principles in Division 81 SECTION VI 89 Numbers changed from the decimal to other scales of Notation 95 Least Common Multiple three methods 102 General principles pertaining to Fractions 109 Addition of Fractions 119 Multiplication of Fractions by Cancelation 130 Division of Fractions common method 133 Complex Fractions reduced to Simple ones 139 Federal Money 236 144 Th Standard for Gold and Silver Coin of the United States 145 The Standard Unit of Liquid Measure of the United States 154 French Money Weights and Measures 161 Applications of Reduction 169 Compound Numbers reduced to Fractions 176 Compound Subtraction 183 Compound Division 189 Addition of Decimals 196 Division of Decimals 206
 Compound Interest 270 To find what sum must be discounted to produce a given amount 277 Profit and Loss four Cases 283 Duties Specific and Advalorem 289 To find what sum must be assessed to raise a given net amount 295 Analytic solutions t questions in Compound Proportion 307 SECTION XIV 313 Simple Proportion 321 Compound Proportion 328 SECTION XV 334 Partnership 340 Foreign Coins and Moneys of Account 348 Arbitration of Exchange 355 Properties of Squares and Cubes 365 Extraction of the Cube Root Horners Method 374 SECTION XVIII 381 Permutations and Combinations 388 Mechanical Powers 394

### Pasajes populares

Página 371 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 76 - Cut off as many figures from the right hand of the dividend as there are ciphers in the divisor. The remaining figures of the dividend will be the quotient, and those cut off the remainder.
Página 66 - The number to be divided is called the dividend. The number by which we divide is called the divisor.
Página 99 - The greatest common divisor of two or more numbers, is the greatest number which will divide them without a remainder. Thus 6 is the greatest common divisor of 12, 18, 24, and 30.
Página 17 - It shows that the numbers between which it is placed are to be multiplied together ; thus, the expression 7 x 5 = 35 is read, 7 multiplied by 5 is equal to 35.
Página 149 - Weight is used by apothecaries and physicians in compounding dry medicines. TABLE. 20 Grains (gr.} = 1 Scruple, . . sc., or 3. 3 Scruples = 1 Dram, . . dr., or 3 . 8 Drams = 1 Ounce, . . oz., or § . 12 Ounces = 1 Pound, . . Ib., or ft,.
Página 206 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.
Página 44 - PROOF.—Add the remainder to the smaller number ; and if the sum is equal to the larger number, the work is right. OBS. This method of proof depends upon the principle, that the difference between two numbers being added to the less, the sum must be equal to the greater.
Página 368 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 369 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.