## The Elements of Algebra: Designed for the Use of Students in the University |

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### Common terms and phrases

aČ-bČ abscissa algebraical algebraical quantities annuity arČ arithmetical progression assumed binomial biquadratic coefficient common denominator conic section cube root cubic equation curve divided dividend division divisor equa equal expressed extract the square factors find the sum former four quantities fraction geometrical progression greater greatest common measure greatest root hence impossible roots increment integral last term least common multiple less Let the roots limiting equation logarithm magnitudes manner multiplied negative roots nth root nth term numerator and denominator obtained odd number ordinates original equation parabola positive possible roots present value probability proportionals proposed equation quadratic surds quan quotient ratio reduced remainder represented result SCHOLIUM shillings simple equation square root substituted subtract suppose supposition taken tion tities unity unknown quantity vulgar fraction whole number

### Popular passages

Page 68 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.

Page 48 - Divide this quantity, omitting the last figure, by twice the part of the root already found, and annex the result to the root and also to the divisor, then multiply the divisor as it now stands by the part of the root last obtained for the subtrahend.

Page 56 - Find the value of one of the unknown quantities, in terms of the other and known quantities...

Page 3-17 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.

Page 77 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.

Page 48 - Divide the number thus formed, omitting the last figure, by twice the part of the root already obtained, and annex the result to the root and also to the divisor. Then multiply the divisor, as it now stands, by the part of the root last obtained, and subtract the product from the number formed, as above mentioned, by the first remainder and second period. If there be more periods- to be brought down, the operation must be repeated.

Page 21 - Multiply as in whole numbers, and point off as many decimal places in the product as there are in both multiplicand and multiplier. DIVISION. Divide as in whole numbers, and point off...

Page 79 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.

Page 81 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 54 - Let the equation first be cleared of fractions ; then transpose all the terms which involve the unknown quantity to one side of the equation, and the known quantities to the other...