The Elements of Algebra: Designed for Beginners |
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A's share apples arithmetical means arithmetical progression bers binomial binomial theorem brandy cents coefficient College common denominator common difference complete equation Completing the square cube digits Divide the number dividend divisor dollars equal Examples exponent extract the square factor Find the square Find the sum find the values Find two numbers following RULE fourth power gallons geometrical progression Give the rule Given greater number Hence horse last term Let x represent letters lowest terms metical monomial multiplied number of terms obtain pears perfect square polynomial pounds preceding problem principles Prob Professor Loomis's QUEST.-Give the rule QUEST.-How QUEST.-What quotient radical quantities Reduce remainder represent the number Required the square required to find result second degree second power second term shillings solved square root subtract text-book tion Transposing Trigonometry twice unknown quantity values of x Whence worth yards
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Page 81 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 102 - To reduce fractions to a common denominator. RULE. Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 79 - 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 100 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Page 181 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 140 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 82 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 231 - Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.
Page 198 - Multiply the divisor thus increased by the last term of the root, and subtract the product from the last remainder.
Page 273 - ... be added to it, the digits will be inverted. What is the number ? Let the digits be equal to x — y, a;, and z-\-y, respectively.