An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry |
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Page 54
... Resolve the given number , or quantity , into two fac- tors , one of which shall be the greatest power contained in it , and set the root of this power before the remaining part , with the proper radical sign between them . ( r ) ...
... Resolve the given number , or quantity , into two fac- tors , one of which shall be the greatest power contained in it , and set the root of this power before the remaining part , with the proper radical sign between them . ( r ) ...
Page 94
... resolved as before . EXAMPLES . 1. Given 3x + 5 = 14 to find the values of and y . { x First , multiply the second equation by 3 , and it will give 3x + 6y = 42 . Then , subtract the first equation from this , and it will give 6y5y = 42 ...
... resolved as before . EXAMPLES . 1. Given 3x + 5 = 14 to find the values of and y . { x First , multiply the second equation by 3 , and it will give 3x + 6y = 42 . Then , subtract the first equation from this , and it will give 6y5y = 42 ...
Page 96
... equations , which may be resolved by the former rules . And in nearly the same way may four , five , & c . un- known quantities bé exterminated from the same num- ber of independent simple equations ; but , in cases 96 SIMPLE EQUATIONS .
... equations , which may be resolved by the former rules . And in nearly the same way may four , five , & c . un- known quantities bé exterminated from the same num- ber of independent simple equations ; but , in cases 96 SIMPLE EQUATIONS .
Page 109
... resolved by means of the following rule : RULE . Transpose all the terms that involve the unknown quantity to one side of the equation , and the known terms to the other ; observing to arrange them so , that the term which contains the ...
... resolved by means of the following rule : RULE . Transpose all the terms that involve the unknown quantity to one side of the equation , and the known terms to the other ; observing to arrange them so , that the term which contains the ...
Page 110
... resolved like quadratics , by first finding the value of the square root of the first term , according to the method used in the above rule , and then taking such a root , or power of the result , as is denoted by the re- duced index of ...
... resolved like quadratics , by first finding the value of the square root of the first term , according to the method used in the above rule , and then taking such a root , or power of the result , as is denoted by the re- duced index of ...
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An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle No preview available - 2017 |
Common terms and phrases
Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α
Popular passages
Page 10 - 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 20 - 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 27 - 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 173 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
Page 77 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 93 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Page 93 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Page 94 - 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 30 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.