Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry |
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Page 7
... obtained with difficulty is usually re- membered with ease ; and what is purchased with pain is often pos- sessed with pleasure . The seeds of knowledge are sown in every soil , but it is by proper culture alone that they are cherished ...
... obtained with difficulty is usually re- membered with ease ; and what is purchased with pain is often pos- sessed with pleasure . The seeds of knowledge are sown in every soil , but it is by proper culture alone that they are cherished ...
Page 8
... obtaining it ; the active principles are immediately put into motion , and the certainty of the conquest is en- sured ... obtained and proper data can be established . To trace this science to its birth , and to point out the various ...
... obtaining it ; the active principles are immediately put into motion , and the certainty of the conquest is en- sured ... obtained and proper data can be established . To trace this science to its birth , and to point out the various ...
Page 9
... obtained from the best authors , and a judicious use of their instructions . To direct the student in his choice of books , and to prepare him properly for the ad- vantages he may receive from them , is therefore , the business of every ...
... obtained from the best authors , and a judicious use of their instructions . To direct the student in his choice of books , and to prepare him properly for the ad- vantages he may receive from them , is therefore , the business of every ...
Page 71
... obtained by this method , Q will either be unity , or some power of 2 less than 2c . If the residual A - B be given , it is evident from its genesis by invo- lution , that the same rule gives its root -- y . See Universal Arith- metic ...
... obtained by this method , Q will either be unity , or some power of 2 less than 2c . If the residual A - B be given , it is evident from its genesis by invo- lution , that the same rule gives its root -- y . See Universal Arith- metic ...
Page 73
... obtained by barely changing the sign of b in the former . EXAMPLE . It is required to find the cube root of 106 √ 3 ... obtain an equation , in which the value of x , as before mentioned , is irrational , when the extraction required is ...
... obtained by barely changing the sign of b in the former . EXAMPLE . It is required to find the cube root of 106 √ 3 ... obtain an equation , in which the value of x , as before mentioned , is irrational , when the extraction required is ...
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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...