## A Treatise on Algebra |

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### Contents

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### Common terms and phrases

added addition alike approach argument base coefficients combinations commensurable common constant continued convergents d₁ D₂ denominator derivative direction divide dividend division divisor equal equation error example exponent expression factors figures finite four fraction function given gives greater h. c. msr increasing infinite infinitesimal integers larger less letters limit logarithm measure multiplied negative NOTE operation opposite partial permutations places polynomial positive positive value possible prime PROB quotient rational reader reduced remainder represented result reversals root signs simple smaller solve sought stand subtract successive surds taken THEOR theorem things third true unit unknown elements variable vector wherein write

### Popular passages

Page 334 - 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 47 - 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 45 - 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 354 - Three numbers may be in proportion when the first is to the second as the second is to the third.

Page 49 - 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 39 - If both terms of a fraction be multiplied by the same number, the value of the fraction will remain unchanged.

Page 158 - 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 179 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.

Page 159 - Jesus was the author and finisher of the faith; to which nothing can be added, and from which nothing can be taken...

Page 57 - 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.