Numbers Symbolized: An Elementary Algebra

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D. Appleton, 1889 - Algebra - 364 pages
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Page 40 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal. 6. Things which are double of the same thing, or of equal things, are equal to each other.
Page 160 - ... term is found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.
Page 74 - 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.
Page 278 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms.
Page 174 - At the left of the dividend write three times the square of the root already found, for a trial divisor ; divide the first term of the dividend by this divisor, and write the quotient for the next term of the root.
Page 260 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 169 - Tlie result will be the complete divisor. Multiply the complete divisor by the last term of the root found, and subtract this product from the dividend.
Page 153 - A and B can do a piece of work in 4 days, A and C in 6 days...
Page 271 - ... the sum of the terms. The first term and last term are called the extremes, and all the terms between the extremes are called arithmetical means.
Page 300 - The product of two binomials having a common term equals the square of the common term, plus the algebraic sum of the other two terms into the common term, and the product of the unlike terms.

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