Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |
From inside the book
Results 1-5 of 87
Page 11
... operations of Algebra are conducted by means of figures , letters , and signs . The letters and signs are often called symbols . ART . 6. Known quantities are generally represented by the first letters of the alphabet , as a , b , c ...
... operations of Algebra are conducted by means of figures , letters , and signs . The letters and signs are often called symbols . ART . 6. Known quantities are generally represented by the first letters of the alphabet , as a , b , c ...
Page 15
... operations indicated . Thus , in the algebraic expression 4a - 3c , if a 5 and c = 6 , the numerical value is 4X5-3 × 6 = 20-18 = 2 . ART . 28. The value of a polynomial is not affected by chang- ing the order of the terms , provided ...
... operations indicated . Thus , in the algebraic expression 4a - 3c , if a 5 and c = 6 , the numerical value is 4X5-3 × 6 = 20-18 = 2 . ART . 28. The value of a polynomial is not affected by chang- ing the order of the terms , provided ...
Page 18
... cannot change their charac- ter , and since each term is positive , therefore their sum is positive . OPERATION . + 3x2y + 5x2y + 7x2y + 15x2y Next , let it be required to find the sum 18 RAY'S ALGEBRA , PART SECOND .
... cannot change their charac- ter , and since each term is positive , therefore their sum is positive . OPERATION . + 3x2y + 5x2y + 7x2y + 15x2y Next , let it be required to find the sum 18 RAY'S ALGEBRA , PART SECOND .
Page 19
... OPERATION . + 9a -5a + 4a -2a + 6a OPERATION . -9a + 5a -4a + 2a -6a ART . 40. THIRD CASE . Let it be required to find the sum of 5a2 — 8b + c , + b — a2 , and 5b + 3a2 . - OPERATION . 5a2 - 8b + c a2 + b 3a2 + 5b 7a2-2b + c In writing ...
... OPERATION . + 9a -5a + 4a -2a + 6a OPERATION . -9a + 5a -4a + 2a -6a ART . 40. THIRD CASE . Let it be required to find the sum of 5a2 — 8b + c , + b — a2 , and 5b + 3a2 . - OPERATION . 5a2 - 8b + c a2 + b 3a2 + 5b 7a2-2b + c In writing ...
Page 21
... OPERATION . 7a Minuend 4a Subtrahend It is evident that 7 times any quantity , less 4 times that quantity , is equal to 3 times the quantity ; therefore , 7a less 4a is equal to 3a . Hence , to find the difference between two similar ...
... OPERATION . 7a Minuend 4a Subtrahend It is evident that 7 times any quantity , less 4 times that quantity , is equal to 3 times the quantity ; therefore , 7a less 4a is equal to 3a . Hence , to find the difference between two similar ...
Contents
| 67 | |
| 74 | |
| 80 | |
| 88 | |
| 95 | |
| 105 | |
| 112 | |
| 121 | |
| 123 | |
| 130 | |
| 137 | |
| 148 | |
| 155 | |
| 205 | |
| 211 | |
| 217 | |
| 224 | |
| 227 | |
| 287 | |
| 292 | |
| 293 | |
| 300 | |
| 302 | |
| 316 | |
| 322 | |
| 331 | |
| 337 | |
| 349 | |
| 355 | |
| 362 | |
| 368 | |
| 374 | |
| 384 | |
| 385 | |
| 394 | |
Other editions - View all
Common terms and phrases
algebraic algebraic quantity arithmetical progression Binomial Theorem coėfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Popular passages
Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 42 - 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 39 - 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 128 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 43 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Page 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.