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abscissa according added addition algebraic antecedent applied arithmetical become binomial calculation called changed co-efficients common Completing compound connected consequent considered consists contained continued cube curve demonstration denominator determined difference divided dividend division divisor dollars effect equal evident examples Expand expression extracting factors figure four fourth fraction frequently geometrical give given greater half Hence inches increased infinite instances involved known length less letters manner mathematics means measure method Mult multiplicand multiplied nature necessary negative Note obtain placed positive preceding principle Prob problem progression proportion quotient radical sign ratio Reduce the equation relations remainder rule shows sides simple square root substituted subtracted supposed taken taking third tion triangle twice unit unknown quantity varies whole
Página 190 - 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.
Página 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Página 188 - : b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities...
Página 87 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.
Página 137 - In the same manner, it may be proved, that the last term of the square of any binomial quantity, is equal to the square of half the co-elficient of the root of the first term.
Página 295 - The operation consists in repeating the multiplicand, as many times as there are units in the multiplier.
Página 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Página 49 - As the value of a fraction is the quotient of the numerator divided by the denominator, it is evident, from Art.