The Elements of Algebra |
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Page 3
... result should be taken 7 times we should prefix 7 ; and write 7a b3c , instead of repeating aaaabbbcc seven times . 4. The sign is placed over a quantity when its root is to be extracted , the particular root being indicated by a small ...
... result should be taken 7 times we should prefix 7 ; and write 7a b3c , instead of repeating aaaabbbcc seven times . 4. The sign is placed over a quantity when its root is to be extracted , the particular root being indicated by a small ...
Page 8
... result is 2 a2 . The usual method of proceeding in addition is , to write the expressions whether simple or compound under each other , and add or subtract the coefficients of like terms as in the addition of numbers , thus , 5 a 7a a + ...
... result is 2 a2 . The usual method of proceeding in addition is , to write the expressions whether simple or compound under each other , and add or subtract the coefficients of like terms as in the addition of numbers , thus , 5 a 7a a + ...
Page 9
... result given above . SUBTRACTION . 11. In subtraction when the quantities are like we take the difference between the coefficients , and write after this difference , the literal quantity : but when the quantities are unlike , the sign ...
... result given above . SUBTRACTION . 11. In subtraction when the quantities are like we take the difference between the coefficients , and write after this difference , the literal quantity : but when the quantities are unlike , the sign ...
Page 10
... result a - b + c , requires explanation . First , having to subtract b - c , if we only subtract b , the result ab , is obviously too little , for the quantity b , which has been taken from a , ought to be diminished by c , before the ...
... result a - b + c , requires explanation . First , having to subtract b - c , if we only subtract b , the result ab , is obviously too little , for the quantity b , which has been taken from a , ought to be diminished by c , before the ...
Page 12
... results , he may proceed to the fol- lowing examples in addition and subtraction . EXAMPLES - ADDITION . ( 1 ) The sum of 3a + 2b , 5a + 6b , a + 3b and b + a is 10a + 12b . ( 2 ) Of a + 2b + 3c , 2a + 3b + c , and 3a + b + 2c is 6 ( a ...
... results , he may proceed to the fol- lowing examples in addition and subtraction . EXAMPLES - ADDITION . ( 1 ) The sum of 3a + 2b , 5a + 6b , a + 3b and b + a is 10a + 12b . ( 2 ) Of a + 2b + 3c , 2a + 3b + c , and 3a + b + 2c is 6 ( a ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - 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 173 - 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.