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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...
Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2006
according added addition affected algebraic altered antecedent applied arithmetical becomes binomial called changed co-efficients combinations common measure Completing compound consequent considered consists containing continued cube denominator derived determine difference diminished divided dividend division divisor dollars equal equation Euclid evident example Expand exponents expression Extracting extremes factors figure four fourth fraction frequently geometrical give given greater greatest half Hence increased infinite integral known last term length less letters manner mathematics means method multiplied nature necessary negative observe obtain particular permutations positive preceding principle Prob problem progression proportion quadratic quotient radical ratio Reduce Reduce the equation remainder result root rule sets sides simple square square root substituted subtracted supposed taken taking third tion Transposing twice unit unknown quantity varies whole number
Σελίδα 47 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Σελίδα 36 - This, according to the definition (Art. 90.) is taking the multiplicand as many times, as there are units in the multiplier.
Σελίδα 215 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c. are all equal ; the quantities are said to be in continued proportion. The consequent of each preceding ratio is, then, the antecedent of the following one.
Σελίδα 220 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Σελίδα 378 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 35 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Σελίδα 146 - Art. 257, may be applied to every case in evolution. But when the quantity whose root is to be found, is composed of several factors, there will frequently be an advantage in taking the root of each of the factors separately. This is done upon the principle that the root of the product of several factors, is equal to the product of their roots.
Σελίδα 289 - After arranging the terms according to the powers of one of the letters, take the root of the first term, for the first term of the required root, and subtract the power from the given quantity.