## A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the Higher Parts Usually Taught in Colleges : Containing Moreover, the New Method of Cubic and Higher Equations, as Well as the Development and Application of the More Recently Discovered Theorem of Sturm |

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### Common terms and phrases

A₁ algebraic annuity arithmetical progression assume becomes BINOMIAL THEOREM cleared of fractions common logarithms consequently cube root cubic equation D₁ degree denote dividend equa Equating the coefficients exponent expression Extracting the square factors figure Find a root find the value formula four quantities fourth geometrical progression given gives greatest common divisor greatest common measure Hence imaginary roots infinite series left-hand member m₂ method multinomial theorem multiply Napierian Nlog nth root nth term number of terms numerator and denominator obtain OPERATION polynomial proportion quadratic equation quotient real roots recurring equation Reduce remainder Required the sum result right-hand member root of equation Rule under Art scale of relation second term square root STURM'S THEOREM Subtracting suppose surd Taking the logarithm third three roots tion transposing and uniting uniting terms unknown quantity values substituted

### Popular passages

Page 199 - If we have a : c : : a' : c', a : c : : a" : c", a : c : : a'

Page 34 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.

Page 67 - A farmer had two flocks of sheep, each containing the same number. Having sold from one of these 39, and from the other 93, he finds twice as many remaining in the one as in the other. How many did each flock originally contain 1 Prob.

Page 195 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.

Page 116 - Divide it by twice the root just found, and add the quotient both to the root and to the divisor. Multiply the divisor thus increased, into the term last placed in the root, and subtract the product from the dividend.

Page 48 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...

Page 176 - A person being asked his age, answered, " My mother was 20 years old when I was born, and her age multiplied by mine, exceeds our united ages by 2500.

Page 95 - Substitution. water. How much gold, and how much silver, did this crown contain ? Ans. 14,77... Ibs. of gold, and 5,22.. .Ibs. of silver. 151. Problem. To solve any number of equations of the...

Page 205 - Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then...

Page 61 - Any term may be transposed from one side of an equation to the other by changing its sign.