# A Practical System of Algebra: Designed for the Use of Schools and Private Students (Google eブックス)

Baldwin and Cradock, 1831 - 309 ページ

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### 目次

 Definitions and Notation 2 Subtraction 12 Division 22 Fractions 33 Addition of Fractions 46 Multiplication of Fractions 53 Involution 59 Of Equations 72
 Examples for Practice 143 Questions for Practice 152 Addition of Surds 160 Division of Surds 166 Geometrical Progression 181 Examples for Practice 250 Summation of Series 256 Examples for Practice 264

 Miscellaneous Examples 84 Expression of Questions 103 Questions for Practice 117 Quadratic Equations 124
 Indeterminate Analysis 270 Diophantine Analysis 276 Quadratic Equations 291 Cubic c Equations 297

### 人気のある引用

154 ページ - What two numbers are those, whose difference is to the greater as 2 to 9, and the difference of whose squares is 128 1 Prob.
iii ページ - For, if the wit be too dull, they sharpen it ; if too wandering, they fix it ; if too inherent in the sense, they abstract it.
68 ページ - ... the square of the two terms of the root already obtained, the remainder will be equal to twice the first two terms of the root multiplied by the third plus the square of the third. Dividing this remainder, therefore, by twice the terms of the root already found, or which is the same thing, dividing the first term of the remainder by twice the first term of the root, we shall obtain the third term sought. Subtracting from the first remainder twice the product of the first two terms of the root...
302 ページ - J of the first, \ of the second, and \ of the third, may be all equal to each other. Ans. 8, 12, and 16.
120 ページ - Two persons, A and B, lay out equal sums of money in trade ; A gains \$126, and B loses \$87, and A's money is now double of B's : what did each lay out ? Ans. \$300.
53 ページ - 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.
305 ページ - The sum of the first and second of four numbers in geometrical progression is 15, and the sum of the third and fourth is 60. Required the numbers.
33 ページ - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
308 ページ - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
307 ページ - Find four numbers in arithmetical progression such that the sum of the first and third shall be 22, and the sum of the second and fourth 36.