Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry |
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Page 22
... whence в - b being less than в , it is evident that the part , which is to be taken away must be less than aв ; and con- sequently since the first part of this product is aв , the second part must be ab ; for if it were -ab , a greater ...
... whence в - b being less than в , it is evident that the part , which is to be taken away must be less than aв ; and con- sequently since the first part of this product is aв , the second part must be ab ; for if it were -ab , a greater ...
Page 32
... whence I conclude that the fraction is already in its lowest terms . † In finding the greatest common measure of two quantities , either of them may be multiplied , or divided , by any quantity , which is not a divisor of the other , or ...
... whence I conclude that the fraction is already in its lowest terms . † In finding the greatest common measure of two quantities , either of them may be multiplied , or divided , by any quantity , which is not a divisor of the other , or ...
Page 33
... Whence x2 + 1 is the greatest common measure required . 2. Required the greatest common measure of the fraction x3- b2x x2 + 2bx + b2 ° x2 + 2bx + b2 ) x3 — b3x ( x x2 + 2bx2 + b2x * 2bx2 - 2b2x or x + b x2 + 2bx + b2 ( x + b x2 + bx bx ...
... Whence x2 + 1 is the greatest common measure required . 2. Required the greatest common measure of the fraction x3- b2x x2 + 2bx + b2 ° x2 + 2bx + b2 ) x3 — b3x ( x x2 + 2bx2 + b2x * 2bx2 - 2b2x or x + b x2 + 2bx + b2 ( x + b x2 + bx bx ...
Page 35
... Whence c + x is the greatest common measure ; and c + x cx + x2 00 the fraction required . a2c + a2x a2 to a single dimension only , I divide the same into the parts x2 + 2ax , and - bx - 2ab ; which , by inspection , appear to be equal ...
... Whence c + x is the greatest common measure ; and c + x cx + x2 00 the fraction required . a2c + a2x a2 to a single dimension only , I divide the same into the parts x2 + 2ax , and - bx - 2ab ; which , by inspection , appear to be equal ...
Page 39
... Whence and b = - с ac the new numerators . 2 b2 3 bc the common denominator . b ас с bc b C 2x ba and the fractions required . bc 2. Reduce and to equivalent fractions having a com- α mon denominator . 2cx ab Ans . and ac ac a a + b 3 ...
... Whence and b = - с ac the new numerators . 2 b2 3 bc the common denominator . b ас с bc b C 2x ba and the fractions required . bc 2. Reduce and to equivalent fractions having a com- α mon denominator . 2cx ab Ans . and ac ac a a + b 3 ...
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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...