## 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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abscissa according added addition algebraic altered antecedent applied arithmetic become calculation called changed co-efficients common Completing compound connected consequent considered contains continued cube curve demonstration denominator determine difference diminished divided dividend division divisor effect equal equation Euclid evident examples exponents expressed Extracting extremes factors figure four fourth fraction frequently geometrical give given greater half Hence inches increased infinite instances known length less letters manner mathematics means method Mult multiplied nature necessary negative notation Note obtain positive preceding principle Prob problem progression proportion proposition quotient radical ratio Reduce Reduce the equation remainder root rule shows sides simple square square root substituted subtracted supposed taken taking third tion Transp Transposing twice unit unknown quantity varies whole

### Popular passages

Page 214 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.

Page 188 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.

Page 227 - 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 189 - If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS OF BOTH COUPLETS, MAY BE INVERTED, WITHOUT DESTROYING THE PROPORTION.

Page 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.

Page 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.

Page 187 - When there is a 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.

Page 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.

Page 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...