First Lessons in Algebra: Embracing the Elements of the Science

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A.S. Barnes and Company, 1840 - Algebra - 252 pages
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Page 138 - ... the entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root, and a remainder of 40, which shows that 665 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part of the root ? To prove this, we will first show that, the difference between the squares of two consecutive numbers, is equal to twice the less number augmented by unity.
Page 214 - B's journey in 15$ days, but B would have been 28 days in performing A's journey. What was the distance between C and D ? Ans.
Page 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 134 - ... one or two figures, will be found between two whole numbers differing from each other by unity. Thus 55, which is comprised between 49 and 64, has for its square root a number between 7 and 8. Also 91, which is com prised between 81 and 100, has for its square root a number between 9 and 10.
Page 231 - Quantities are said to be in proportion by inversion, or inversely, when the consequents are made the antecedents and the antecedents the consequents.
Page 155 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Page 116 - A person bought a chaise, horse, and harness, • for 60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each?
Page 135 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 137 - RULE. I. Separate the given number into periods 'of two figures each, beginning at the right hand: the period on the left will often contain but one figure. II. Find the greatest perfect square in...
Page 45 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.

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