A Treatise on Algebra |
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Common terms and phrases
algebraic arithmetic progression ax˛ B₁ base binomial coefficients complete quotient continued fraction convergent d₁ D₂ degree denominator divide dividend divisor entire numbers equal equations involving exponent expression factors finite number function geometric progression given equations h. c. msr imaginary incommensurable infinite infinitesimal integers integral power larger letters limit logarithm mantissa measure modulus monomial multiplicand multiplied n₁ NOTE nth root operand operation pair of equations partial products permutations plat polynomial positive integers positive value prime PROB quadratic QUADRATIC EQUATION quotient radius of convergence ratio remainder result signs simple equation simple fraction smaller square root subtraction surds THEOR theorem unit unknown elements V₁ variable vector wherein
Popular passages
Page 340 - The fore-wheel of a carriage makes 6 revolutions more than the hind- wheel in going 120 yards; but if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind-wheel in the same distance.
Page 51 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 183 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 362 - Quantities are said to be in continued proportion when the first is to the second, as the second is to the third, as the third to the fourth ; and so on.
Page 49 - If the first be the same multiple of the second, or the same part of it. that the third is of the fourth, the first is to the second as the third is to the fourth...
Page 162 - The circumference of a circle is the limit which the perimeters of regular inscribed and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons.
Page 53 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 43 - If both terms of a fraction be multiplied by the same number, the value of the fraction will remain unchanged.
Page 163 - It is the complete system of divine truth, to which nothing can be added, and from which nothing can be taken, f with impunity.
Page 61 - 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.