## The Collegiate Algebra: Adapted to Colleges and Universities |

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The Collegiate Algebra: Adapted to Colleges and Universities James Bates Thomson No preview available - 2019 |

The Collegiate Algebra: Adapted to Colleges and Universities James Bates Thomson No preview available - 2019 |

### Common terms and phrases

a₁ added algebraic apply assume base becomes binomial called chance changed coefficients common constant containing continued convergent cube denominator depends difference differential direction distance Divide dividend division divisor equal equation evident example exponent expressed factors figures formula fourth fraction function give given greater Hence illustrated imaginary increase indicated integral less letters logarithm manner means measure method miles multiplied negative NOTE OPERATION polynomial positive problem proportion quantity quotient ratio real roots Reduce remainder represent result roots rule solution square root student Substituting Subtracting successive taken Theorem third tion true unit unknown quantity variable whole write zero

### Popular passages

Page 305 - I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Page 47 - 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 157 - 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 226 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.

Page 196 - DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.

Page 157 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 226 - WHEN three numbers are such that the first is to the third, as the difference of the first and second is to the difference of the second and third, they are said to be in HARMONICAL PROPORTION, and a series of numbers in continued harmonical proportion, constitutes a HARMONICAL PROGRESSION.

Page 195 - Y, and x + y is the sum of their logarithms; from which it follows that the sum of the logarithms of two numbers is equal to the logarithm of their product. Hence, To multiply two or more numbers...

Page 39 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.

Page 197 - We have then this rule, 49. Add to the index, if necessary, such a negative number as will make it exactly divisible by the divisor, and prefix an equal positive number to the decimal part of the logarithm. 1. Required the 5th root of 0.009642.