## The Elements of Arithmetic |

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a b c d acres added alter annex ciphers Answer arithmetic arithmetical series called cent column common denominator contains 18 cube cubic foot decimal fraction decimal places decimal point divided dividend and divisor division drams equal example EXERCISES farthings fingers following rule four numbers given gives greater greatest common measure Hence hund hundreds last article last figure least common multiple length less means method metical miles multiple-part multiplicand number of ciphers number of combinations number of decimal number of figures number of permutations number of terms numerator and denominator obtained parallelopiped pebbles pence places of decimals pound proceed proportion pupil quantity question quotient reduced result shew shewn sides specific gravity square number square root subtract Suppose it required taken ten-thous tens thing third thousand twice whole number write written ΙΟ

### Popular passages

Page 164 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 33 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.

Page 58 - 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 vi - Since the publication of the first edition of this work, though its sale has sufficiently convinced me that there exists a disposition to introduce the principles of arithmetic into schools, as well as the practice, I have often heard it remarked that it was a hard book for children. I never dared to suppose it would be otherwise. All who have been engaged in the education of youth are aware that it is a hard thing to make them think...

Page vii - ... numbers proposed by the master, which should be as simple as possible. The very words of the book may be used, the figures being changed, and it will rarely be found that a learner is capable of making the proper alterations, without understanding the reason. The experience of the master will suggest to him various methods of trying this point. When the principle has been thus discussed, let the rule be distinctly stated by the master, or some of the more intelligent of the pupils; and let some...

Page 76 - When a decimal number is to be divided by 10, 100, 1000, &c., remove the decimal point as many places to the left as there are ciphers in the divisor, and if there be not figures enough in the number, prefix ciphers.

Page 19 - Find the diiference between 430172 and 189567. THE DIFFERENCE BETWEEN TWO NUMBERS WILL NOT BE ALTERED IF THE SAME QUANTITY IS ADDED TO BOTH OF THEM. Illustrations : " Conceive two baskets with pebbles in them, in the first of which are 100 pebbles more than in the second. If I put 50 more pebbles into each of them, there are still only 100 more in the first than in the second.

Page vii - ... them think; so hard, indeed, that masters had, within the last few years, almost universally abandoned the attempt, and taught them rules instead of principles; by authority, instead of demonstration. This system is now passing away; and many preceptors may be found who are of opinion that, whatever may be the additional trouble to themselves, their pupils should always be induced to reflect upon, and know the reason of, what they are doing. Such I would advise not to be discouraged by the failure...

Page 75 - To multiply a decimal by 10, 100, 1000, &c., remove the decimal point as many places to the right as there are ciphers in the multiplier ; and if there be not places enough in the number, annex ciphers.