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algebraic quantities arithmetical binomial called coefficient Completing the square continued fraction decimal divide the number dividend division entire number enunciation equa equal equation whose roots equation x3 evident example exponent expression extract the root factors figure find the greatest find the number find the square find the values following rule formula Freeing from denominators geometrical progression given number gives greater greatest common divisor integral roots last term less logarithm manner monomial multiplied negative roots number of terms obtain operation perfect square polynomials positive roots preceding progression by quotient proportion proposed equation question radical sign ratio real roots reduced remainder Required the number resolve the equation result second degree second power second term shillings solution square root substitution subtract synthetic division third power third root tion transformed units unity unknown quantities values of x vulgar fraction whence
Σελίδα 117 - 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.
Σελίδα 19 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Σελίδα 282 - VARIATIONS of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of variations of the signs, p the number of permanences ; we shall have m=n+p. Moreover, let n' denote the number of positive roots, and p...
Σελίδα 100 - ... 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.
Σελίδα 9 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Σελίδα 98 - If both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed.
Σελίδα 217 - ... exponent of which is one less than the number, which marks the place of this term. Let L "designate any term whatever of the progression, and let n represent the number of this term; from what has been said, we have This is called the general term of the progression.
Σελίδα 67 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14ff days, B 17ff, and C 23J y . 21.