Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies, Part 1 |
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Page 4
... contain a large number of examples for prac- tice . Should any instructor deem these too numerous , a portion of them may be omitted . To teach the subject successfully , the principles must be first clearly explained , and then the ...
... contain a large number of examples for prac- tice . Should any instructor deem these too numerous , a portion of them may be omitted . To teach the subject successfully , the principles must be first clearly explained , and then the ...
Page 6
... contain- ing two Unknown Quantities • 219 220-222 CHAPTER VIII - PROGRESSIONS AND PROPORTION . Arithmetical Progression • 220-225 222-227 Geometrical Progression 226-230 228--232 Ratio • • 231-239 232-234 Proportion 240-255 234-240 ...
... contain- ing two Unknown Quantities • 219 220-222 CHAPTER VIII - PROGRESSIONS AND PROPORTION . Arithmetical Progression • 220-225 222-227 Geometrical Progression 226-230 228--232 Ratio • • 231-239 232-234 Proportion 240-255 234-240 ...
Page 43
... contained in two or more expressions . The pupil has already learned , that these ex- pressions may be all positive , or all negative , or partly positive and partly negative . If they are either all positive , or all negative , the sum ...
... contained in two or more expressions . The pupil has already learned , that these ex- pressions may be all positive , or all negative , or partly positive and partly negative . If they are either all positive , or all negative , the sum ...
Page 54
... contained in the parentheses . 26. ( x - 3 ) ( x - 3 ) ( x - 3 ) .. 27. ( x - 4 ) ( x - 5 ) ( x + 4 ) ( x + 5 ) . 28. ( a + c ) ( a − c ) ( a + c ) ( a − c ) . . Ans . x3 - 9x2 + 27x - 27 . Ans . x - 41x2 + 400 • Ans . at - 2a2c2 + ca ...
... contained in the parentheses . 26. ( x - 3 ) ( x - 3 ) ( x - 3 ) .. 27. ( x - 4 ) ( x - 5 ) ( x + 4 ) ( x + 5 ) . 28. ( a + c ) ( a − c ) ( a + c ) ( a − c ) . . Ans . x3 - 9x2 + 27x - 27 . Ans . x - 41x2 + 400 • Ans . at - 2a2c2 + ca ...
Page 55
... contained in another . Or , it may be defined thus : Having the product of two factors , and one of them given , Division teaches the method of finding the other . The number by which we divide , is called the divisor ; the num- ber to ...
... contained in another . Or , it may be defined thus : Having the product of two factors , and one of them given , Division teaches the method of finding the other . The number by which we divide , is called the divisor ; the num- ber to ...
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Common terms and phrases
acre added algebraic quantities apples arithmetical progression arithmetical series binomial Binomial Theorem bought bushels coefficient common difference complete equation Completing the square cost Divide the number dividend division dollars entire quantity equal EQUATIONS CONTAINING exactly divide exponent expressed extract the square Find a number Find the cube Find the product Find the square Find the sum find the value following examples fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges perfect square polynomial positive quantity preceding principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result second degree second power solution solving square root three numbers tities Transposing twice unknown quantity whole number yards
Popular passages
Page 60 - 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 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 178 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 124 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 64 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.