An Introduction to Algebra: With Notes and Observations: Designed for the Use of Schools and Places of Public EducationKimber and Conrad, and Joseph Crukshank; T. & G. Palmer, printers, 1811 - 220 sider |
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Resultat 1-5 av 5
Side 46
... involved to the fifth power . The terms without the co - efficients will be a5 , a1x , a3x2 , a2x3 , ax4 , x5 , and the co - efficients will de 5X4 10X3 10x2 5X1 1 , 5 , " , 2 3 5 And therefore the fifth power is a5 + 5a4x + 10a3x2 + ...
... involved to the fifth power . The terms without the co - efficients will be a5 , a1x , a3x2 , a2x3 , ax4 , x5 , and the co - efficients will de 5X4 10X3 10x2 5X1 1 , 5 , " , 2 3 5 And therefore the fifth power is a5 + 5a4x + 10a3x2 + ...
Side 82
... involved , and find its value in each of the equ tions , by the methods already explained . 2. Let the two values thus found be made equal each other , and there will arise a new equation wit only one unknown quantity in it , whose ...
... involved , and find its value in each of the equ tions , by the methods already explained . 2. Let the two values thus found be made equal each other , and there will arise a new equation wit only one unknown quantity in it , whose ...
Side 84
... involved . 2. Substitute the value , thus found , for its equal in the other equation , and there will arise a new equation , with only one unknown quantity , whose value may be found as before . 1. Given { EXAMPLES . x + 2y = 172 84 ...
... involved . 2. Substitute the value , thus found , for its equal in the other equation , and there will arise a new equation , with only one unknown quantity , whose value may be found as before . 1. Given { EXAMPLES . x + 2y = 172 84 ...
Side 133
... involved , will give x4 + ax3 + 2Ax2 + ‡ a2x2 + a ^ x + a2С = xa + ax3 + bx2 -B2x2-2B Cx - c2 + cx + d : from whence , by equating the homologous terms , we shall have 1. 2A + a2 -B2 — b , or 2A + ‡ a2 — b = B2 ; 2. аA - 2BC 3. A2 - C2 ...
... involved , will give x4 + ax3 + 2Ax2 + ‡ a2x2 + a ^ x + a2С = xa + ax3 + bx2 -B2x2-2B Cx - c2 + cx + d : from whence , by equating the homologous terms , we shall have 1. 2A + a2 -B2 — b , or 2A + ‡ a2 — b = B2 ; 2. аA - 2BC 3. A2 - C2 ...
Side 154
... involved , either the given number , or the highest power of the unknown quantity , may vanish from the equation ; and then , if the unknown quantity be but of one dimension , the problem will be solved by reducing the equation . 2. But ...
... involved , either the given number , or the highest power of the unknown quantity , may vanish from the equation ; and then , if the unknown quantity be but of one dimension , the problem will be solved by reducing the equation . 2. But ...
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An Introduction to Algebra: With Notes and Observations, Designed for the ... John Bonnycastle Uten tilgangsbegrensning - 1822 |
Vanlige uttrykk og setninger
affirmative algebra arithmetical mean arithmetical series co-efficient common denominator common difference common index completing the square consequently cube numbers cube root cubic equation decimal diff Diophantus dividend divisor equa equal extracting the root find the roots find the square find the sum find the value find three numbers find two numbers find x four numbers geometrical progression geometrical series give given equation given number greater greatest common improper fraction infinite series last term Let the number loga method moidores multiplied natural numbers nth power nth root number answering number of terms number required orders of differences quadratic equation question Reduce remainder Required the difference Required the product Required the square Required the sum required to find rithm root required RULE second term simple equations simple terms square root substituted subtracted sum required surd tion unknown quantity Whence whole numbers
Populære avsnitt
Side 26 - 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 ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Side 98 - 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 61 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.
Side 164 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of differences.
Side 97 - 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.
Side 28 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Side 192 - For the same reason, if the logarithm of any number be multiplied by the index of its power, the product will be equal to the logarithm of that power.
Side 39 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Side 50 - ... 4. Divide the dividend by the divisor, and the quotient will be the next term of the root. 5. Involve the whole root...