An Elementary Treatise on Algebra: Theoretical and Practical |
Common terms and phrases
a₁ absolute magnitude algebra answer arithmetical arithmetical progression assume becomes compound interest compound quantity contain continued fraction converging fractions cube root denote difference dividend dividing division divisor eliminate employed equa equal Exam Exer Exercises factors find the numbers find the value foregoing fourth give given equation greater greatest common divisor greatest common measure Hence hypotenuse imaginary infinite number infinite series instances last term less means merator method mode multiplying nth power nth root number of terms numerator and denominator obtained operation plain positive principle quadratic equation quan question quotient radical remainder required number resolving the equation result rule second member second term sign changed solution solve square number square root substituting subtraction t₁ taken taking tion transposing transposition triangle unknown quantities vinculum whence whole number
Popular passages
Page 241 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Page 226 - It is required to find three numbers in arithmetical progression, such, that the sum of every two of them may be a square. Let x, x-\-y and х-^-Яу represent the numbers.
Page 271 - In applying the above general rule to any particular example it will be found that the algebraic sign of the result is the same as the sign of the original function.
Page 155 - ... the sum of all the products that can be formed by taking...
Page 274 - Hence, a root is divided by another root of the same letter or quantity, by subtracting the exponent of the divisor from that of the dividend. Ex. 1. Divide (abft by (abft. Ans. Ex. 2. Divide a3 by <A Ex. 3. Divide a$ by a*.
Page 102 - Now, boys, here is an arithmetical puzzle for you. A man offered to sell his horse (which was a valuable one,) by receiving so much a piece for the nails in his horse's shoes. He was to have a farthing for the first nail...
Page 15 - Divide 39 into four parts, such, that if the first he increased by 1, the second diminished by 2, the third multiplied by 3, and the fourth divided by 4, the results may be all equal.
Page 261 - Show that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines diminished by twice the rectangle contained by the lines.
Page 250 - CE is equal to the difference of the segments of the base made by the perpendicular.
Page 3 - Division is indicated by the sign of division -r-, or by writing the dividend over the divisor with a line between them. Thus, 42-r6 and 452 have the same meaning, and each is read : forty-two divided by six.