# An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

Hezekiah Howe, 1831 - 332 СЕКъДЕР

### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 introductory Observations on the Mathematics ingeneral 1 Notation Positive and Negative Quantities Axioms c 21 Subtraction 27 Multiplication 31 Division 41 WI Algebraic Fractions 49 Reduction of Equations by Transposition Multiplication and Division Solution of Problems 65 Involution Notation Addition Subtraction Multiplication and 83
 Ratio and Proportion 173 Variation or General Proportion 206 Arithmetical and Geometrical Progression 213 Mathematical Infinity 227 Division by Compound Divisors 233 Involution of Compound Quantitles by the Binomial Theorem 242 Evolution of Compound Quantities 253 Infinite Series 259

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 290 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
сЕКъДА 72 - ... in geometrical proportion, the product of the two extremes is equal to the product of the two means :" a principle which is at the foundation of the Rule of Three in arithmetic.
сЕКъДА 163 - 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 148 - A gentleman bought a number of pieces of cloth for 675 dollars, which he sold again at 48 dollars by the piece, and gained by the bargain as much as one piece cost him. What was the number of pieces ? Ans. 15.
сЕКъДА 186 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
сЕКъДА 20 - If the same quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered. 6. If a quantity be both multiplied and divided by another, the value of the former...
сЕКъДА 149 - Prob. 18. A gentleman bought two pieces of cloth, the finer of which cost 4 shillings a yard more than the other. The finer piece cost ё18 ; but the coarser one, which was 2 yards longer than the finer, cost only ё16. How many yards were there in each piece, and what was the price of a yard of each 1 Ans.
сЕКъДА 185 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
сЕКъДА 31 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
сЕКъДА 251 - Then divide the first term of the remainder by the first term of the divisor...