## An Introduction to Algebra: With Notes and Observations: Designed for the Use of Schools and Places of Public Education |

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### Common terms and phrases

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

### Popular passages

Page 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.

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 50 - ... 4. Divide the dividend by the divisor, and the quotient will be the next term of the root. 5. Involve the whole root...