A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the Higher Parts Usually Taught in Colleges : Containing Moreover, the New Method of Cubic and Higher Equations, as Well as the Development and Application of the More Recently Discovered Theorem of SturmO. Hutchinson, 1842 - 360 σελίδες |
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Σελίδα 14
... become , when a = 2 , and b = 1 ( 2 + 1 ) " = 4 + 4 + 1 = 9 ( 1 ) ( 2-1 ) 2 = 4-4 + 1 = 1 ( 2 ) ( 2 + 1 ) 2+ ( 2-1 ) ... becomes familiar with the nature of algebraic expressions . 2 ( 4 ) 2 ADDITION . ( 23. ) ADDITION , in Algebra , 14 ...
... become , when a = 2 , and b = 1 ( 2 + 1 ) " = 4 + 4 + 1 = 9 ( 1 ) ( 2-1 ) 2 = 4-4 + 1 = 1 ( 2 ) ( 2 + 1 ) 2+ ( 2-1 ) ... becomes familiar with the nature of algebraic expressions . 2 ( 4 ) 2 ADDITION . ( 23. ) ADDITION , in Algebra , 14 ...
Σελίδα 24
... . Subtracting this last result from the former , we have ac - bc- ( ad - bd ) , which , by ( Art . 28 ) , becomes ac - bc - ad + bd for the product of a - b by c - d . a2 ÷ a = a2-1 = a1 = a a1a 24 MULTIPLICATION . Multiplication,
... . Subtracting this last result from the former , we have ac - bc- ( ad - bd ) , which , by ( Art . 28 ) , becomes ac - bc - ad + bd for the product of a - b by c - d . a2 ÷ a = a2-1 = a1 = a a1a 24 MULTIPLICATION . Multiplication,
Σελίδα 31
... becomes 0 its value is reduced to 1 . ( 42. ) That whenever it is negative it is the reciprocal of what it would be were it positive . ( 43. ) Hence , changing the sign of the exponent of a quantity is the same as taking its reciprocal ...
... becomes 0 its value is reduced to 1 . ( 42. ) That whenever it is negative it is the reciprocal of what it would be were it positive . ( 43. ) Hence , changing the sign of the exponent of a quantity is the same as taking its reciprocal ...
Σελίδα 39
... becomes 25a2 = 25a2b − 1y — 2 by 2 42ax3yz5 2. Reduce to its lowest terms . 35xyz 3 3 In this example , the greatest common measure of the nu- merator and denominator is 7xyz3 , hence , dividing both nu- merator and denominator of our ...
... becomes 25a2 = 25a2b − 1y — 2 by 2 42ax3yz5 2. Reduce to its lowest terms . 35xyz 3 3 In this example , the greatest common measure of the nu- merator and denominator is 7xyz3 , hence , dividing both nu- merator and denominator of our ...
Σελίδα 41
... become N = qın + q372 ( 4. ) n = 929372 + r2 ( 5. ) The right - hand member of ( 5 ) will divide by ra , and therefore its left - hand member must also be divisible by ra , that is , n is divisible by r2 . The value of n , ( 5 ) , being ...
... become N = qın + q372 ( 4. ) n = 929372 + r2 ( 5. ) The right - hand member of ( 5 ) will divide by ra , and therefore its left - hand member must also be divisible by ra , that is , n is divisible by r2 . The value of n , ( 5 ) , being ...
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A₁ algebraic annuity arithmetical progression assume becomes BINOMIAL THEOREM cleared of fractions common logarithms consequently cube root cubic equation D₁ degree denote dividend equa Equating the coefficients exponent expression Extracting the square factors figure Find a root find the value formula four quantities fourth geometrical progression given gives greatest common divisor greatest common measure Hence imaginary roots infinite series left-hand member m₂ method multinomial theorem multiply Napierian Nlog nth root nth term number of terms numerator and denominator obtain OPERATION polynomial proportion quadratic equation quotient real roots recurring equation Reduce remainder Required the sum result right-hand member root of equation Rule under Art scale of relation second term square root STURM'S THEOREM Subtracting suppose surd Taking the logarithm third three roots tion transposing and uniting uniting terms unknown quantity values substituted
Δημοφιλή αποσπάσματα
Σελίδα 199 - If we have a : c : : a' : c', a : c : : a" : c", a : c : : a'
Σελίδα 34 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
Σελίδα 67 - A farmer had two flocks of sheep, each containing the same number. Having sold from one of these 39, and from the other 93, he finds twice as many remaining in the one as in the other. How many did each flock originally contain 1 Prob.
Σελίδα 195 - 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.
Σελίδα 116 - Divide it by twice the root just found, and add the quotient both to the root and to the divisor. Multiply the divisor thus increased, into the term last placed in the root, and subtract the product from the dividend.
Σελίδα 48 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Σελίδα 176 - A person being asked his age, answered, " My mother was 20 years old when I was born, and her age multiplied by mine, exceeds our united ages by 2500.
Σελίδα 95 - Substitution. water. How much gold, and how much silver, did this crown contain ? Ans. 14,77... Ibs. of gold, and 5,22.. .Ibs. of silver. 151. Problem. To solve any number of equations of the...
Σελίδα 205 - Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then...
Σελίδα 61 - Any term may be transposed from one side of an equation to the other by changing its sign.