The Elements of Algebra: Designed for the Use of Students in the UniversityJohn William Parker ; sold by Deightons, 1837 - 539 σελίδες |
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Σελίδα 16
... obtained by taking the excess of the sum of those with one of the signs , above the sum of those with the other : and by prefixing the sign of the greater sum , agreeably to the views of common arithmetic . ( 4 ) 4ax ( 5 ) 3by ( 6 16 ...
... obtained by taking the excess of the sum of those with one of the signs , above the sum of those with the other : and by prefixing the sign of the greater sum , agreeably to the views of common arithmetic . ( 4 ) 4ax ( 5 ) 3by ( 6 16 ...
Σελίδα 30
... obtained by reversing the last operation conformably to the principles already explained . In this process , the ... obtain = b . - a 33. When the divisor is a simple quantity , the division is indicated according to article ( 9 ) , and ...
... obtained by reversing the last operation conformably to the principles already explained . In this process , the ... obtain = b . - a 33. When the divisor is a simple quantity , the division is indicated according to article ( 9 ) , and ...
Σελίδα 33
... that the sum of the indices in every term is always equal to m : whence we shall at length obtain a " for a remainder and continuing the division from this as before , we have a -2x2 - : E am - 2x2 am am - 2x2 am m - DIVISION . 33.
... that the sum of the indices in every term is always equal to m : whence we shall at length obtain a " for a remainder and continuing the division from this as before , we have a -2x2 - : E am - 2x2 am am - 2x2 am m - DIVISION . 33.
Σελίδα 38
... a2b + b3 + bc2 + 2 ( ab2 + abc + b2c ) a2c + b2c + c3 + 2 ( abc + ac2 + bc2 ) .. the cube of a + b + c = a3 + b3 + c3 + 3 ( a2 b + a2c + ab2 + ac2 + b2c + bc2 ) + 6abc . The same results might have been obtained however by a 38 INVOLUTION .
... a2b + b3 + bc2 + 2 ( ab2 + abc + b2c ) a2c + b2c + c3 + 2 ( abc + ac2 + bc2 ) .. the cube of a + b + c = a3 + b3 + c3 + 3 ( a2 b + a2c + ab2 + ac2 + b2c + bc2 ) + 6abc . The same results might have been obtained however by a 38 INVOLUTION .
Σελίδα 39
... obtained however by a somewhat shorter process , by first considering b + c as one quantity : thus , ( a + b + c ) 2 = { a + ( b + c ) } 2 = a2 + 2a ( b + c ) + ( b + c ) 2 = a2 + 2ab + 2ac + b2 + 2bc + c2 = a2 + b2 + c2 + 2 ( ab + ac + ...
... obtained however by a somewhat shorter process , by first considering b + c as one quantity : thus , ( a + b + c ) 2 = { a + ( b + c ) } 2 = a2 + 2a ( b + c ) + ( b + c ) 2 = a2 + 2ab + 2ac + b2 + 2bc + c2 = a2 + b2 + c2 + 2 ( ab + ac + ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a²b a²x² ab² according algebraical quantity Answer arithmetical progression assumed ax² B₁ binomial coefficients common factor continued fraction converging fractions cube root cx² decimal denominator denote difference digits divided divisible divisor equal equation equivalent expansion expressed find the number Find the sum formula geometrical progression given greater greatest common measure Hence infinitum integral last article least common multiple less magnitudes manifestly means n₁ negative nth term number of combinations number of terms obtained operation parallelopiped prime number prove quadratic quotient radix ratio remainder represent result shew similarly solution square root subtraction surd symbols Theorem vulgar fraction whence
Δημοφιλή αποσπάσματα
Σελίδα 349 - From half the sum of the three sides, subtract each side separately. Multiply the half sum and the three remainders together, and the square root of the product is the area.
Σελίδα 107 - A and B can do a piece of work in m days, B and C in n days, and C and A in p days. In what time can each alone jjerform the work ? 39.
Σελίδα 373 - The coefficient of the second term of an equation, with its proper sign, is the sum of the roots, with their signs changed ; the coefficient of the third term is the sum of the products of...
Σελίδα 138 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.
Σελίδα 146 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Σελίδα 145 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Σελίδα 115 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 35 - If the proposed quantity consists of more terms, it is evident that we have only to consider a-\-b in the place of a, and then by the same process another term of the root will be obtained, and so on ; and hence we have the following GENERAL RULE. 'Arrange the terms in the order of the magnitudes of the indices of some one quantity. Find the square root of the first term, and subtract its square from the proposed quantity. Bring down the next two terms, and find the next term of the root by dividing...
Σελίδα 137 - Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part, or parts, one quantity is of the other.
Σελίδα 132 - Find two numbers whose product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.