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added addition algebraic becomes binomial called cents changed Clearing coefficient common contains corresponding cost denominator difference direction distance divided dividend division divisor dollars equal equation EXAMPLE EXERCISES exponent expression Extracting factors feet figures Find two numbers four fourth fraction given gives greater half Hence increased indicated less logarithm means method multiply negative NOTE operations parentheses polynomial positive pound preceding problem progression Proof quadratic equation quotient ratio reduced remainder REMARK represent result rule share Solution Solve square root substitute subtract suppose surds symbol THEOREM third tion Transposing twice unit unity unknown quantity varies whence whole write
Page 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 152 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Page 247 - Л + 3, — 6, + 12, — 24, etc., is a progression in which the ratio is — 2. NOTE. A progression like the second one above, formed by dividing each term by the same divisor to obtain the next term, is included in the general definition, because dividing by any number is the same as multiplying by the reciprocal. Geometrical progressions may therefore be divided into two classes, increasing and decreasing. In the increasing progression the common ratio is greater than 1 and the terms go on increasing...
Page 95 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 267 - The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, AŤ = (10°)
Page 100 - 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.
Page 129 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 250 - A gentleman bought a horse, agreeing to pay what his shoes would amount to, at 1 cent for the first nail, 2 for the second, 4 for the third, and so on, doubling the price of each succeeding nail to the last.
Page 252 - I was using, while in the other case the author was using a quantity of debt by way of illustration, and in order to adapt the reasoning to my example it was necessary to change some of the words, but if I changed the reasoning in any sense it was done inadvertantly. The author said "For since the debt is halved at every payment, if there was any payment which discharged the whole remaining debt, the half of a thing would be equal to the whole of it, which is impossible.
Page 242 - Let us put a, the first term of a progression. d, the common difference. n, the number of terms. I, the last term. 2, the sum of all the terms. The series is then a, a + d, a + %d, ....?. Any three of the above five quantities being given, the other two may be found.