The Elements of Algebra: Designed for the Use of Students in the University |
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abscissa algebraical quantities annuity arithmetical progression assumed binomial biquadratic coefficients common denominator conic section cube root cubic equation curve decimal Diff difference divided dividend division divisor equa equal expressed factors find the sum former 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 m.m+r m+r.m+2r manner multiplied negative roots 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 shillings signs simple equation square root substituted subtracted suppose supposition taken tion tities unity unknown quantity vulgar fraction whole number
Popular passages
Page 64 - 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 44 - 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 52 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 37 - 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 73 - 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 44 - 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 13 - 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 73 - 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 73 - 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 50 - 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...