## Elements of algebra, by A. Ingram and J. Trotter1844 |

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added annuity arithmetical progression Assume ax³ bound bx² coefficient Complete the square consequently containing continued fraction converging fractions cube root cubic equation cx² denominator digits divisible divisors Edinburgh Academy Edition equal exponent expression find a number find such values find the least find the values find three numbers find two numbers formula fourth geometrical progression given equation given number greater hence integer joint lives last term least positive less Let the equation Let x² logarithm minus multiplied mx² number of permutations number of terms numbers in arithmetical obtain partial quotients present value prime number PROP proportionals quadratic QUADRATIC EQUATIONS ratio Reduce remainder Required simple solution square numbers square root substituting subtract taken third tion trial unknown quantity values of x whence whole number

### Popular passages

Page 29 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.

Page 19 - 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 3 - A DICTIONARY OF THE ENGLISH LANGUAGE; containing the Pronunciation, Etymology, and Explanation of all Words authorized by eminent writers ; to which are added a Vocabulary of the Roots of English Words, and an accented list of Greek, Latin, and Scripture Proper Names. By Alexander Reid, AM, Rector of the Circus School, Edinburgh.

Page 70 - The sum of any number of terms is equal to the sum of the extremes multiplied by half the number of terms.

Page 13 - Melrose's Concise System of Practical Arithmetic; containing the Fundamental Rules and their Application to Mercantile Calculations ; Vulgar and Decimal Fractions ; Exchanges ; Involution and. Evolution ; Progressions ; Annuities, Certain and Contingent, etc.

Page 1 - ... by means of lessons on useful and interesting subjects is steadily kept in view. Directions are given relative to the mode of teaching, as well as tables and lists calculated to assist in the process of instruction. On this point the Spectator newspaper, when reviewing the series, remarked : — "In recommending these books, it must not be conceived that we recommend them as likely to save trouble to the teacher, or to operate by witchcraft on the pupil. At their first introduction they will...

Page 70 - In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2.

Page 50 - A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After 'A' has been working at it for 5 days and B for 7 days, C finishes it in 13 days.

Page 1 - ... to profit by the lessons. But this once done, their foundation is sound, and their progress sure. And let both parents and teachers bear in mind that these are the only means to acquire real knowledge.

Page 16 - Latin Delectus "and "Greek Extracts " the sentences have been arranged strictly on the progressive principle, increasing in difficulty with the advancement of the Pupil's knowledge; while the Vocabularies contain an explanation not only of every word, but also of every difficult expression which is found in the works,— thus rendering the acquisition of the Latin and Greek languages both easy and agreeable. The Selections from Cicero embrace the portions of his works which are best adapted for Scholastic...