A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and CollegesHarper & Brothers, 1846 - 503 Seiten |
Inhalt
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45 cents algebraic becomes binomial binomial theorem coefficients column common divisor consequently contain continued fraction contrary signs cubic equation denominator derived functions determine difference divide dividend divisible elimination equa equation whose roots EXAMPLE exponent expression extract final equation Find two numbers formula give given equation given number greatest common divisor Hence imaginary roots indeterminate last term least common multiple letters logarithm method modulus monomial multiplied negative roots nth root number of variations obtain odd number polynomial positive roots preceding prime number problem proposed equation PROPOSITION quotient radical ratio real roots reduced remainder represent result second degree second term solution square number square root substituting subtract successive suppose symmetric functions theorem third tion transformed equation unity unknown quantity V₁ vanish whence whole number
Beliebte Passagen
Seite 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Seite 172 - 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 would it take each person to perform the same work alone ? Ans.
Seite 278 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Seite 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.
Seite 184 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Seite 239 - ... digit ; but if the digits be inverted, and the resulting number be divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient : find the number.
Seite 236 - A's journey. How far did each travel ? A 72 miles. B 54 miles. 9. A company at a tavern had £8 15s. to pay for their reckoning ; but before the bill was settled, two of them left the room, and then those who remained had 10s. apiece more to pay than before : how many were there in the company ? Ans. 7.
Seite 314 - Every equation of an odd degree has at least one real root ; and if there be but one, that root must necessarily have a contrary sign to that of the last term. - 4".
Seite 145 - Elimination by Substitution consists in finding the value of one of the unknown quantities in one of the equations, in terms of the other unknown quantity and known terms, and substituting this, instead of the quantity, in the other equation.
Seite 170 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together.