Elements of AlgebraHilliard, Gray, 1833 - 298 σελίδες |
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Σελίδα viii
... Whole numbers , except such as are perfect squares , admit of no assignable root , either among whole numbers or fractions What is meant by the term incommensurable or irrational How to denote by a radical sign , that a root is to be ...
... Whole numbers , except such as are perfect squares , admit of no assignable root , either among whole numbers or fractions What is meant by the term incommensurable or irrational How to denote by a radical sign , that a root is to be ...
Σελίδα x
... whole numbers To extract the cube root of fractions 161 162 163 - 164 ib . - ib . 168 169 · 170 172 173 175 Method of approximating the cube root of numbers which are not perfect cubes Extraction of the roots of higher degrees To ...
... whole numbers To extract the cube root of fractions 161 162 163 - 164 ib . - ib . 168 169 · 170 172 173 175 Method of approximating the cube root of numbers which are not perfect cubes Extraction of the roots of higher degrees To ...
Σελίδα 5
... whole of b , or two halves of b , which reduces itself to augmenting by the half of b , or by that α b - b It is evident then 2 a b + 2 ; and by translating this expres- + b becomes 2 2 sion we learn , that of the two parts sought the ...
... whole of b , or two halves of b , which reduces itself to augmenting by the half of b , or by that α b - b It is evident then 2 a b + 2 ; and by translating this expres- + b becomes 2 2 sion we learn , that of the two parts sought the ...
Σελίδα 15
... whole , that the unknown quantity x is taken so many times as there are units in the difference of the numbers a and b , augmented by the number c , that is to say , so many times as is denoted by the number a factors of the first ...
... whole , that the unknown quantity x is taken so many times as there are units in the difference of the numbers a and b , augmented by the number c , that is to say , so many times as is denoted by the number a factors of the first ...
Σελίδα 16
... whole numbers into fractions of a given kind . ( Arith . 79 , 69. ) Let all the terms of the pro- posed equation be transformed by these rules into fractions of the same denominator , beginning with the fractions , which are 2x 4 x 5x 3 ...
... whole numbers into fractions of a given kind . ( Arith . 79 , 69. ) Let all the terms of the pro- posed equation be transformed by these rules into fractions of the same denominator , beginning with the fractions , which are 2x 4 x 5x 3 ...
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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.