A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página iv
... given of its application . The entire work was composed , not exclusively for the best scholars , nor for such as are unwilling to study , but rather for the majority of our students ; and as such , it is commended to the attention of ...
... given of its application . The entire work was composed , not exclusively for the best scholars , nor for such as are unwilling to study , but rather for the majority of our students ; and as such , it is commended to the attention of ...
Página 10
... given the sum and difference of two quantities , we may obtain by means of Algebra a general expression for the quantities themselves . This result will always be found true , whatever may be the magnitude of the quantities . Hence ...
... given the sum and difference of two quantities , we may obtain by means of Algebra a general expression for the quantities themselves . This result will always be found true , whatever may be the magnitude of the quantities . Hence ...
Página 11
... given in Sections XII . XIV . etc. Thirdly , in Arithmetic all the different quantities which enter into a problem are blended together in the result , so as to leave no trace of the operations to which they have been subjected . From a ...
... given in Sections XII . XIV . etc. Thirdly , in Arithmetic all the different quantities which enter into a problem are blended together in the result , so as to leave no trace of the operations to which they have been subjected . From a ...
Página 16
... given quantity . The symbol✓ is called the radical sign , and when pre- fixed to a quantity denotes that its root is to be extracted . Thus , 29 , or simply ✓9 , denotes the square root of 9 , which is 3 . 364 denotes the cube root of ...
... given quantity . The symbol✓ is called the radical sign , and when pre- fixed to a quantity denotes that its root is to be extracted . Thus , 29 , or simply ✓9 , denotes the square root of 9 , which is 3 . 364 denotes the cube root of ...
Página 25
... given , we first subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 than the number which was required to be sub- tracted . Therefore , in order to correct this result , the 3 must be ...
... given , we first subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 than the number which was required to be sub- tracted . Therefore , in order to correct this result , the 3 must be ...
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Términos y frases comunes
according to Art algebraic arithmetical arithmetical progression binomial cents Charles Anthon coefficients Completing the square contrary sign cube root denotes derived polynomial Divide the number dividend divisible equal roots equation whose roots equation x³ example exponent expression Extract the square factors find the square find the values following RULE fourth power fourth root fraction geometrical geometrical progression given equation greater greatest common divisor Hence infinite series irreducible fraction last term less letters taken method miles monomial mth degree multiplied negative nth root number of permutations number of terms obtain order of differences preceding Prob problem proportion PROPOSITION quadratic equations quotient ratio real roots Reduce remainder represent Required the square Required the sum result second degree second term Sheep extra square root subtract suppose surd theorem unity unknown quantity variation whence whole number
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Página 189 - ... 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.
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Página 43 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.