A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and CollegesHarper & Brothers, 1846 - 503 sider |
Inni boken
Resultat 1-5 av 100
Side viii
... given Quantity . · Numbers between the Roots substituted for the unknown Quantity give results alter- nately Positive and Negative . 315 319 • 320 . 321 NUMBER OF REAL AND IMAGINARY ROOTS IN AN EQUATION . Equation whose Roots separate ...
... given Quantity . · Numbers between the Roots substituted for the unknown Quantity give results alter- nately Positive and Negative . 315 319 • 320 . 321 NUMBER OF REAL AND IMAGINARY ROOTS IN AN EQUATION . Equation whose Roots separate ...
Side xiii
... given ones must fulfill , which conditions are indicated by the question itself . The solution has for its object to determine such required quantities as will verify these conditions . It is necessary , therefore , to endeavor first to ...
... given ones must fulfill , which conditions are indicated by the question itself . The solution has for its object to determine such required quantities as will verify these conditions . It is necessary , therefore , to endeavor first to ...
Side 20
... given product , the other factor being given ; and as multiplication is divided into three cases , so , in like manner , is division . ( 1 ) When both dividend and divisor are monomials . ( 2 ) When the dividend is a polynomial , and ...
... given product , the other factor being given ; and as multiplication is divided into three cases , so , in like manner , is division . ( 1 ) When both dividend and divisor are monomials . ( 2 ) When the dividend is a polynomial , and ...
Side 24
... given dividend , and the first step will be the same as before . Similar reasoning will apply to the rest of the process . Note . - The arrangement of the terms is for convenience . The term having the highest or lowest exponent of some ...
... given dividend , and the first step will be the same as before . Similar reasoning will apply to the rest of the process . Note . - The arrangement of the terms is for convenience . The term having the highest or lowest exponent of some ...
Side 32
... given for Synthetic Division is due to the late W. G. Horner , Esq . , of Bath , whose researches in science have issued in several elegant and useful processes , especially in the higher branches of algebra , and in the evolution of ...
... given for Synthetic Division is due to the late W. G. Horner , Esq . , of Bath , whose researches in science have issued in several elegant and useful processes , especially in the higher branches of algebra , and in the evolution of ...
Innhold
100 | |
119 | |
128 | |
134 | |
142 | |
144 | |
155 | |
160 | |
284 | |
291 | |
302 | |
312 | |
343 | |
349 | |
350 | |
356 | |
173 | |
181 | |
190 | |
191 | |
199 | |
205 | |
218 | |
224 | |
232 | |
239 | |
245 | |
246 | |
252 | |
255 | |
261 | |
270 | |
272 | |
278 | |
362 | |
364 | |
369 | |
370 | |
372 | |
410 | |
416 | |
422 | |
430 | |
433 | |
444 | |
478 | |
479 | |
486 | |
493 | |
501 | |
Andre utgaver - Vis alle
A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ... Charles William Hackley Uten tilgangsbegrensning - 1846 |
A Treatise on Algebra, Containing the Latest Improvements Charles William Hackley Uten tilgangsbegrensning - 1850 |
A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ... Charles William Hackley Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
a₁ algebraic becomes binomial binomial theorem coefficients column common divisor consequently contain continued fraction contrary signs cube cubic equation denominator derived functions determine difference divide divisible elimination equa equal roots equation whose roots EXAMPLE exponent expression extract final equation formula fraction 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 terms number of variations obtain odd number permutations polynomial positive roots prime number problem proposed equation quadratic equation 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 Transposing unity unknown quantity V₁ vanish whence whole number
Populære avsnitt
Side 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Side 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.
Side 107 - There will be as many figures in the root as there are periods in the given number.
Side 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.
Side 23 - 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.
Side 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Side 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.
Side 128 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c.
Side 48 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.
Side 237 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.