An introduction to algebra. To which is added an appendix containing a synopsis on variable quantities by S. Maynard1836 - 80 pages |
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Page 3
... value , or greater than any quantity that can be assigned . The coefficient of a quantity is the number or letter ... x in the quan- tity ax . A quantity without any coefficient prefixed to it is supposed to have 1 , or unity ; and when ...
... value , or greater than any quantity that can be assigned . The coefficient of a quantity is the number or letter ... x in the quan- tity ax . A quantity without any coefficient prefixed to it is supposed to have 1 , or unity ; and when ...
Page 29
... x + a - x x3 - y3 to a 5. It is required to reduce the fraction whole quantity . X- y Ans . x2 + xy + y3 . 10x - 5x ... value will not be altered thus , 2 2X3 6 = " 3 3-3 1 = and 33X3 9 12 12 ÷ 34 a ac ab a or ; = and b bc bc C which ...
... x + a - x x3 - y3 to a 5. It is required to reduce the fraction whole quantity . X- y Ans . x2 + xy + y3 . 10x - 5x ... value will not be altered thus , 2 2X3 6 = " 3 3-3 1 = and 33X3 9 12 12 ÷ 34 a ac ab a or ; = and b bc bc C which ...
Page 81
... value of a , is either +3 or 5 and in the cubic equa- tion ra 9x2 + 26x = 24 , the roots are 2 , 3 , and 4 , as will be found by substituting each of these numbers for x . - In an equation of an odd number of dimensions , one of its ...
... value of a , is either +3 or 5 and in the cubic equa- tion ra 9x2 + 26x = 24 , the roots are 2 , 3 , and 4 , as will be found by substituting each of these numbers for x . - In an equation of an odd number of dimensions , one of its ...
Page 83
... value . - Thus , if x + 5 = 7 + 5 ; then , by cancelling , x = 7 . - And , if abc ; then , by changing the signs , x - a - c - b , or x = a + c - b . : CASE II . If the unknown quantity , in any equation , be multiplied by any number ...
... value . - Thus , if x + 5 = 7 + 5 ; then , by cancelling , x = 7 . - And , if abc ; then , by changing the signs , x - a - c - b , or x = a + c - b . : CASE II . If the unknown quantity , in any equation , be multiplied by any number ...
Page 85
... x = 27 , then x = 3 / 27 3 . Also , if 3x - 9 = 24 ; then 3r2 = 24 + 9 = 33 , or x2 = 33 11 , and consequently x ... value of x . Here 5x - 2x = 6 + 15 , or 3x = 6 + 15 = 21 ; and there- 21 fore , by division , we shall have x === 3 = 7 ...
... x = 27 , then x = 3 / 27 3 . Also , if 3x - 9 = 24 ; then 3r2 = 24 + 9 = 33 , or x2 = 33 11 , and consequently x ... value of x . Here 5x - 2x = 6 + 15 , or 3x = 6 + 15 = 21 ; and there- 21 fore , by division , we shall have x === 3 = 7 ...
Common terms and phrases
Algebra arithmetical arithmetical mean arithmetical series binomial coefficient common denominator consequently constant quantity cube root cubic equation decimal Defi denoted determine diff dividend division divisor equal EXAMPLES FOR PRACTICE expression find the difference find the square find the sum find the value find three find two numbers fraction geometrical mean geometrical series give given number greatest common measure Hence improper fraction infinite series last term latter logarithms method multiplied natural numbers negative nth root number of terms orders of differences perpendicular plane triangle PROBLEM proportion quadratic equation question quotient rational remaining Required the sum required to convert required to divide required to find required to reduce result rule second term simple form square number square root substituted subtract surd third tion unknown quantity Whence whole numbers
Popular passages
Page 36 - 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 18 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 40 - ... required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.
Page 117 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Page 26 - 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.
Page 48 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before; and proceed in this manner till the whole is finished.* EXAMPLES.
Page 116 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Page 76 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 82 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 2 - It denotes that the quantities between which it is placed are equal to each other. Thus, o=3, denotes that the quantity represented by a is equal to 3.