The Elements of Algebra |
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Results 1-5 of 25
Page 1
... taken away from the former : thus 24-19 , or 24 minus 19 , means that 19 is to be taken from 24 , and a - b expresses the excess of a over b . ( 3 ) × , the sign of multiplication , which is placed between two numbers ; thus 12 x 18 is ...
... taken away from the former : thus 24-19 , or 24 minus 19 , means that 19 is to be taken from 24 , and a - b expresses the excess of a over b . ( 3 ) × , the sign of multiplication , which is placed between two numbers ; thus 12 x 18 is ...
Page 2
... taken 7 times , has 7 for its coefficient . The coefficient therefore is a number written to the left hand of the quantity expressed by a letter or letters : and shews how many times the quantity expressed by the letter or letters ought ...
... taken 7 times , has 7 for its coefficient . The coefficient therefore is a number written to the left hand of the quantity expressed by a letter or letters : and shews how many times the quantity expressed by the letter or letters ought ...
Page 3
... taken 7 times we should prefix 7 ; and write 7a b3c , instead of repeating aaaabbbcc seven times . 4. The sign is ... taken as one sum . Thus 3a + b or 3 ( a + b ) , means that the sum of a and b is to be multiplied by 3 , and thus if 56 ...
... taken 7 times we should prefix 7 ; and write 7a b3c , instead of repeating aaaabbbcc seven times . 4. The sign is ... taken as one sum . Thus 3a + b or 3 ( a + b ) , means that the sum of a and b is to be multiplied by 3 , and thus if 56 ...
Page 9
... coefficients , and write after this difference , the literal quantity : but when the quantities are unlike , the sign - , is placed between them . Then if 5a is to be taken from 7a the 1-5 ADDITION OF LIKE AND UNLIKE QUANTITIES . 9.
... coefficients , and write after this difference , the literal quantity : but when the quantities are unlike , the sign - , is placed between them . Then if 5a is to be taken from 7a the 1-5 ADDITION OF LIKE AND UNLIKE QUANTITIES . 9.
Page 10
... taken from a , ought to be diminished by c , before the subtraction be effected : we have in fact subtracted a quantity too great by c , and therefore to obtain a true re- sult the difference a - b must be increased by c , or the dif ...
... taken from a , ought to be diminished by c , before the subtraction be effected : we have in fact subtracted a quantity too great by c , and therefore to obtain a true re- sult the difference a - b must be increased by c , or the dif ...
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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.