Elements of AlgebraHilliard, Gray, 1833 - 298 σελίδες |
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Σελίδα viii
... tion , the terms of which are not squares Resolution of equations , involving only the second power of the 119 120 unknown quantity ib . The square root of a quantity may have the sign + or The square root of a negative quantity is ...
... tion , the terms of which are not squares Resolution of equations , involving only the second power of the 119 120 unknown quantity ib . The square root of a quantity may have the sign + or The square root of a negative quantity is ...
Σελίδα ix
... tion of their Roots 148 Table of the first seven powers of numbers from 1 to 9 To obtain any power whatever of a simple quantity ib . · 149 To extract the root of any power whatever of a simple quantity To simplify radical expressions ...
... tion of their Roots 148 Table of the first seven powers of numbers from 1 to 9 To obtain any power whatever of a simple quantity ib . · 149 To extract the root of any power whatever of a simple quantity To simplify radical expressions ...
Σελίδα xii
... tion depends Note on the changes of the value of polynomials - - ib . 232 234 - 237 To assign a number which shall render the first term greater than the sum of all the others Every equation denoted by an odd number has necessarily a ...
... tion depends Note on the changes of the value of polynomials - - ib . 232 234 - 237 To assign a number which shall render the first term greater than the sum of all the others Every equation denoted by an odd number has necessarily a ...
Σελίδα 5
... tion of the question proposed ; but Algebra does more ; it furnishes a rule for calculating the greater part without the aid of the less as follows ; α b being the value of this , augmenting it by the excess b , we - 2 2 b α b 2 + b ...
... tion of the question proposed ; but Algebra does more ; it furnishes a rule for calculating the greater part without the aid of the less as follows ; α b being the value of this , augmenting it by the excess b , we - 2 2 b α b 2 + b ...
Σελίδα 11
... tion supposes equal , there are regular steps for deducing from this expression the value of the unknown quantity , which is the object of the second part of the solution . Before treating of these I shall explain the use of some terms ...
... tion supposes equal , there are regular steps for deducing from this expression the value of the unknown quantity , which is the object of the second part of the solution . Before treating of these I shall explain the use of some terms ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ac² algebraic algebraic quantities Arith arithmetic becomes binomial changing the signs coefficient consequently contains courier cube root deduce denominator denoted divided dividend and divisor division enunciation equa equal to zero evident example exponent extract the root factors fifth power figures follows formula fraction given in art given number gives greatest common divisor letters logarithm manner method multiplicand multiplied negative number of arrangements observed obtain operation polynomials proposed equation proposed number proposed quantity quan question quotient radical quantities radical sign reduced remainder represented resolved result rule given second degree second member second term simple quantities square root subtract suppose tens third tion tities units unity unknown quantity whence whole numbers
Δημοφιλή αποσπάσματα
Σελίδα ii - District Clerk's Office. BE IT REMEMBERED, That on the seventh day of May, AD 1828, in the fifty-second year of the Independence of the UNITED STATES OF AMERICA, SG Goodrich, of the said District, has deposited in this office the...
Σελίδα 249 - If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean.
Σελίδα 33 - 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 ii - CLERK'S OFFIcE. BE it remembered, that on the eleventh day of November, AD 1830, in the fiftyfifth year of the Independence of the United States of America, Gray & Bowen, of the said district, have deposited in this office the title of a book, the right whereof...
Σελίδα 296 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Σελίδα 30 - ... by itself as many times less one as there are units in the exponent of this power.
Σελίδα 116 - On the contrary, the square root of a number, which is not a perfect square, is...
Σελίδα 165 - Therefore, the cube of a number containing two figures, consists of, The cube of the tens, three times the square of the tens multiplied by the units, three times the tens multiplied by the square of the units, and the cube of the units.
Σελίδα 296 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Σελίδα 271 - From what has preceded, we perceive that the value of a fraction is the quotient arising from the division of the numerator by the denominator, or from the expression of this division.