First Principles of Algebra: Complete Course

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Allyn and Bacon, 1912 - Algebra - 481 pages
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Page 176 - The Square Root of a number is one of its two equal factors. Thus, the square root of 25 is 5, since 5x5 are 25.
Page 172 - If squares are constructed on the two sides, and also on the hypotenuse of a right-angled triangle, then the sum of the squares on the sides is equal to the square on the hypotenuse.
Page 279 - Axioms (1) If equal numbers are added to equal numbers, the sums are equal.
Page 456 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 238 - In any proportion, the product of the means equals the product of the extremes.
Page 423 - The weight of a body above the earth's surface varies inversely as the square of its distance from the earth's center. If an object weighs 2000 pounds at the earth's surface, what would be its weight if it were 12,000 miles above the center of the earth, the radius of the earth being 4000 miles ? CHAPTER XI POWERS AND ROOTS 150.
Page 56 - ... expression composed of parts connected by the signs + and — is called a polynomial. Each of the parts thus connected, together with the sign preceding it, is called a term.
Page 74 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 463 - A geometric progression is a series of numbers in which any term after the first is obtained by multiplying the preceding term by a fixed number, called the common ratio. The...
Page 421 - ... second and third the means of the proportion. The first and third are the antecedents of the ratios, the second and fourth the consequents. If a, b, c, x are proportional, x is called the fourth proportional to a, b, c. If a, x, x, b are proportional, x is called a mean proportional to a and b, and ba third proportional to a and x. 173. If four numbers are proportional when taken in a given order, there are other orders in which they are also proportional. Eg If a, 6, c, d are proportional in...

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