# An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry

Evert Duyckinck, Daniel D. Smith and George Long, 1818 - 260 СЕКъДЕР

### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 Addition 8 Nº 18 Algebraic Fractions 24 Involution or the raising of Powers 40 Of irrational Quantities or Sº 50 Of arithmetical Proportion and ression 72 Of Equations 81
 Of the Resolution of simple Equations 96 Of quadratic Equations 108 Questions producing quadratic Equations 116 Of cubic Equations 123 Of the Resolution of biquadratic Equations 130 To find the roots of s 140

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 16 - 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.
сЕКъДА 26 - 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.
сЕКъДА 33 - 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.
сЕКъДА 187 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
сЕКъДА 91 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
сЕКъДА 39 - ... and the quotient will be the next term of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before ; and proceed in this manner till the whole is finished*.
сЕКъДА 107 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
сЕКъДА 107 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
сЕКъДА 108 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
сЕКъДА 36 - 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.