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

J. Smith, 1815 - 305 Seiten

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### Inhalt

 Quadratic Equations 79 On Ratios 91 On Variation 103 On Arithmetical Progression 109 On Permutations and Combinations 115 On Surds 123 The Nature of Equations 135 The Transformation of Equations 142
 On Continued Fractions 209 The cube root of atv b² 217 On the Sunnmation of Series 227 On Chances 259 On Life Annuities 272 On the Construction of Equations 292 General Properties of Curve Lines 298

### Beliebte Passagen

Seite 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.
Seite 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.
Seite 52 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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...