An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

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Durrie & Peck, 1847 - 332 páginas
 

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Página 59 - FRACTIONS, MULTIPLY THE NUMERATORS TOGETHER, FOR A NEW NUMERATOR, AND THE DENOMINATORS TOGETHER, FOR A NEW DENOMINATOR.
Página 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Página 188 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Página 231 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 290 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Página 134 - Two travellers A and B set out to meet each other, A leaving the town C, at the same time that B left D.
Página 216 - If the first term of an increasing arithmetical series is 3, the common difference 2, and the number of terms 20 ; what is the sum of the series 1 Ans.
Página 185 - When there ka series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c. are all equal ; the quantities are said to be in continued proportion.
Página 42 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the 'dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factor a and bd .will produce the dividend. The first of these, being a divisor, maybe set aside.
Página 224 - There are three numbers in geometrical progression, the greatest of which exceeds the least by 15; and the difference of the squares of the greatest and the least,. is to the sum of the squares of all the three numbers as 5 to 7. What are the numbers 1 Ans.

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