Elements of Arithmetic, Theoretical and Practical: Adapted to the Use of Schools, and to Private Study |
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Page 14
... fourth the opposite of the third ; and such must be the case in any system of combination of quantity that can be devised . In all arithmetic , it is always necessary , that both the direct and inverse operation 14 NOTATIONS OF THE FOUR.
... fourth the opposite of the third ; and such must be the case in any system of combination of quantity that can be devised . In all arithmetic , it is always necessary , that both the direct and inverse operation 14 NOTATIONS OF THE FOUR.
Page 42
... third proposition will evidently furnish us the means to reduce fractions from one denomina- tor to certain other ones , in order to obtain the fractional parts expressed so as to be adapted to cer- tain purposes in the operations of ...
... third proposition will evidently furnish us the means to reduce fractions from one denomina- tor to certain other ones , in order to obtain the fractional parts expressed so as to be adapted to cer- tain purposes in the operations of ...
Page 43
... third of the forego- ing propositions , we have obtained means to make such changes , without altering the value of the frac- tions . The aim of such a change , must evidently be to obtain the same denomination for both , or all the ...
... third of the forego- ing propositions , we have obtained means to make such changes , without altering the value of the frac- tions . The aim of such a change , must evidently be to obtain the same denomination for both , or all the ...
Page 44
... third : ; ; ; 6 X 5 6 X 5 6 x 5 15 X 8 from these and the last , or , - 15 20 18 - 30 30 30 20 X 8 18 X 8 30 X 7 ; ; ; ; 30 X 8 30 X 8 30 X 8 30 x 8 120 160 144 210 or , ; ; ; 240 240 240 240 Here quantities of the same kind , are ...
... third : ; ; ; 6 X 5 6 X 5 6 x 5 15 X 8 from these and the last , or , - 15 20 18 - 30 30 30 20 X 8 18 X 8 30 X 7 ; ; ; ; 30 X 8 30 X 8 30 X 8 30 x 8 120 160 144 210 or , ; ; ; 240 240 240 240 Here quantities of the same kind , are ...
Page 46
... third line of numbers is obtained , this line is reduced by the divisor 5 , and the fourth row of figures is obtained , and the opera- tion is continued in the same way , until no common divisor is found ; as in the fifth line of the ...
... third line of numbers is obtained , this line is reduced by the divisor 5 , and the fourth row of figures is obtained , and the opera- tion is continued in the same way , until no common divisor is found ; as in the fifth line of the ...
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Common terms and phrases
acres added addition amount antecedent applied arithmetical proportion arithmetical series borrowing calculation called capital carried cattle cent ciple common difference compound interest consequents contained continued cube cubic decimal fractions decimal mark decimal system deno denominate fractions determined divided dividend division divisor equation evidently exactly executed expressed factors feet long following example following numbers four rules frac Francs geometric proportion geometric series geometrical ratio given numbers gives improper fraction indicated kind manner mean terms merator metic miles mination mode multiplied mutations nator nature number of terms obtain ounces payments pieces places of figures pounds preceding principles proper fraction quotient reduced remainder result rule of three rules of arithmetic scholar share shown side sign of equality simple smaller square root subdivision subtraction successive things third tion unit unknown quantity vulgar fraction whole numbers write yards
Popular passages
Page ii - In conformity to the act of Congress of the United States. entitled, " an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the time therein mentioned." And also to an act, entitled, " an act, supplementary to an act, entitled, an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned...
Page ii - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Page 42 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change. This is because a fraction b/b, b being any number, is equal to the multiplicative identity, 1 . Therefore, Hx8.= 88 _5_x!
Page 111 - A ratio is formed by two numbers, each of which is called a term, and both together, a couplet. Thus, 2 and 6 together form a couplet of which 2 is the first term, and 6 the second. The first term of a ratio is called the antecedent; -the second, the consequent.
Page 197 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Page 118 - PROPORTION THE PRODUCT OF THE TWO EXTREME TERMS IS EQUAL TO THE PRODUCT OF THE TWO MEAN TERMS.
Page ii - Answers, 6d. Each subject is also accompanied by an example fully worked out and minutely explained. The Exercises are numerous and practical. A Complete System of Arithmetic, Theoretical and Practical; adapted to the Use of Schools and Private Students; containing the Fundamental Rules, and their application to Mercantile Computations ; Vulgar and Decimal Fractions ; Involution and Evolution ; Series ; Annuities, Certain and Contingent. By JAMES TBOTTEB.
Page 53 - The reason for this rule is the same, in reality, as that for the preceding one. 37. |i'or, multiplying the numerator of the dividend by the denominator of the divisor multiplies the dividend by that number.
Page 169 - That is, the first term of an increasing arithmetical series is equal to the last term diminished by the product of the common difference into the number of terms less one. From the same formula...
Page 197 - The sides of two square pieces of ground are as 3 to 5, and the sum of their superficial contents is 30600 square feet. What is the length of a side of each piece ? Ans.