A Theoretical and Practical Treatise on Algebra ...J. Ernst, 1848 - 320 σελίδες |
Συχνά εμφανιζόμενοι όροι και φράσεις
3d term algebraic annuity apply arithmetical mean arithmetical progression arithmetical series assumed binomial square binomial theorem cent Clearing of fractions coefficients Completing the square compound interest cube root denominator difference distance Divide the number dividend division dollars equa equation becomes EXAMPLES Expand exponent expressed factor find the values following rule four numbers fraction will produce geometrical progression geometrical series give greater Hence improper fraction infinity last term least common multiple less letter logarithm lowest terms method miles Multiply negative number of terms numbers in geometrical observe operation primitive equation problem Prod produce the series quadratic equations quotient Reduce remainder represent resolved result second term shillings simple equations solution square root substitute subtract suppose surd Theorem third three numbers tion Transpose unity unknown quantity values of x whole number
Δημοφιλή αποσπάσματα
Σελίδα 18 - ... 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 17 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Σελίδα 193 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Σελίδα 84 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to I.
Σελίδα 193 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 58 - Divide 48 into two such parts, that if the less be divided by 4, and the greater by 6, the sum of the quotients will be 9. Ans. 12 and 36.
Σελίδα 59 - Four places are situated in the order of the letters A, B, C, D. The distance from A to D is 34 miles. The distance from A to B is to the distance from C to D as 2 to 3. And ^ of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances'!
Σελίδα 55 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Σελίδα 96 - It will thus afford a direct solution to the following problems : 1. The hour and minute hands of a clock are together at 12 o'clock ; when are they next together ? The circumference of the dial-plate is divided into 12 spaces.
Σελίδα 5 - If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.