Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry |
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Page 29
... continued is said to be equal to the 2 fraction Thus we say the vulgar fraction when reduced to 9 ' a • a + x a decimal , is 22222 , & c . , infinitely continued . The terms in the quotient are found by dividing the remainder by a , the ...
... continued is said to be equal to the 2 fraction Thus we say the vulgar fraction when reduced to 9 ' a • a + x a decimal , is 22222 , & c . , infinitely continued . The terms in the quotient are found by dividing the remainder by a , the ...
Page 30
... continued , is ; a singular conclusion , when it is perceived from the terms themselves , that their sum must necessarily be either 0 or +1 , to whatever extent the division is supposed to be continued . The real question , however ...
... continued , is ; a singular conclusion , when it is perceived from the terms themselves , that their sum must necessarily be either 0 or +1 , to whatever extent the division is supposed to be continued . The real question , however ...
Page 43
... continued product of 8122 4x 2 ' 5 ' 10x and 21 ° Here x X 4x X 10x 2 × 5 × 21 40x3 210 21 4x3 the product . х a + x 3. It is required to find the product of and α a x xx ( a + x ) x2 + ax Here α ax ( a — x ) a2 the product . ax 3x 5x 4 ...
... continued product of 8122 4x 2 ' 5 ' 10x and 21 ° Here x X 4x X 10x 2 × 5 × 21 40x3 210 21 4x3 the product . х a + x 3. It is required to find the product of and α a x xx ( a + x ) x2 + ax Here α ax ( a — x ) a2 the product . ax 3x 5x 4 ...
Page 44
... continued product of α and a + x Ans . 2x 4x2 3 ' 7 8αx3 21a + 21a 2x 3ab 7. It is required to find the continued product of α C and 5ac 26 . Ans . 15ax . bx b 8. It is required to find the product of 2a + and 3a a ax 26 b2 Ans . 6a2 + ...
... continued product of α and a + x Ans . 2x 4x2 3 ' 7 8αx3 21a + 21a 2x 3ab 7. It is required to find the continued product of α C and 5ac 26 . Ans . 15ax . bx b 8. It is required to find the product of 2a + and 3a a ax 26 b2 Ans . 6a2 + ...
Page 51
... continued . EXAMPLE . 1. It is required to extract the square root of 1 + x . OC 1 + x ) 1 + 2 1 ૭ + 1 ) αc x + 202 1 X2 203 5x4 + & c . 8 16 128 ' x2 2 + x 4 + 64 x2 2 + x 4 16 + 218000 ∞ol 8 00180 204 64 204 ევნ + + 16 64 256 5x4 ...
... continued . EXAMPLE . 1. It is required to extract the square root of 1 + x . OC 1 + x ) 1 + 2 1 ૭ + 1 ) αc x + 202 1 X2 203 5x4 + & c . 8 16 128 ' x2 2 + x 4 + 64 x2 2 + x 4 16 + 218000 ∞ol 8 00180 204 64 204 ევნ + + 16 64 256 5x4 ...
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Bonnycastle's Introduction to Algebra: Containing the ..., Pages 1-283 J. Bonnycastle,J. Ryan,J. F. Jenkins No preview available - 2017 |
Common terms and phrases
Algebra answer arise arithmetical arithmetical mean ax² ax³ binomial bx² coefficients consequently cube root cubic equation decimal denominator denoted divisor equal EXAMPLES FOR PRACTICE expression find a number find the square find the sum find the value find two numbers former formula fraction gallons geometrical give given number Given x² greater greatest common measure Hence infinite series last term less logarithms method multiplied negative nth root number of terms perpendicular PROBLEM proportion quadratic equation quadratic surd question quotient rational remain Required the number Required the sum required to divide required to find resolved result rule shillings side square number square root substituted subtracted surd third unknown quantity value of x Whence whole numbers yards
Popular passages
Page 43 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 45 - ... required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.
Page 27 - 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.
Page 111 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Page 29 - In the case here given, the operation of division may be considered as terminated, when the highest power of the letter, in the first, or leading term of the remainder, by which the process is regulated, is less than the...
Page 112 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the the same work alone ? Ans.
Page 12 - Q/~\—C = equal to, the sign of equality; signifying that the quantities between which it is placed are equal to each other. Thus...
Page 52 - ... and the quotient will be the next term of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before...
Page 126 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Page 109 - A labourer engaged to serve for 40 days, on condition that for every day he worked he should...