An Elementary Treatise on Algebra: Theoretical and Practical ... |
From inside the book
Results 1-5 of 40
Page 12
... observe that a broad generality , a wide latitude must be given to the term addition . In algebra , it rather means uniting , condensing , or reducing terms , and in some cases , the sum may appear like difference , owing to the ...
... observe that a broad generality , a wide latitude must be given to the term addition . In algebra , it rather means uniting , condensing , or reducing terms , and in some cases , the sum may appear like difference , owing to the ...
Page 13
... observe that 2 ( a + b ) +3 ( a + b ) must be together 5 ( a + b ) , that is , 2 times any quantity whatever added to 3 times the same quantity must be 5 times that quantity . Therefore , 4√x + y + 3√x + y = 7√x + y , for √x + y ...
... observe that 2 ( a + b ) +3 ( a + b ) must be together 5 ( a + b ) , that is , 2 times any quantity whatever added to 3 times the same quantity must be 5 times that quantity . Therefore , 4√x + y + 3√x + y = 7√x + y , for √x + y ...
Page 16
... observe that the smaller when the subtrahend becomes minus , it must be added . the number we take away , the greater the remainder , and From 12a 12a 12a 12a 12a 12a Take 20a 16a 12a 9a 6a a Diff . -8a -4a 0 За 6a lla When a greater is ...
... observe that the smaller when the subtrahend becomes minus , it must be added . the number we take away , the greater the remainder , and From 12a 12a 12a 12a 12a 12a Take 20a 16a 12a 9a 6a a Diff . -8a -4a 0 За 6a lla When a greater is ...
Page 27
... Observe , that to divide is to subtract the exponents . 7bd 7 Divide 14ab2cd by 6a2bc2 . Ans . 3ac3bda - c . ( Art . 19. ) A compound term divided by a simple term , is effected by dividing each term of the compound quantity by the ...
... Observe , that to divide is to subtract the exponents . 7bd 7 Divide 14ab2cd by 6a2bc2 . Ans . 3ac3bda - c . ( Art . 19. ) A compound term divided by a simple term , is effected by dividing each term of the compound quantity by the ...
Page 30
... ( Observe Art . 21. ) Ans . 2a2 + 2a + 5 . 9. Divide x - y6 by x3 + 2x2y + 2xy2 + y3 . Ans . x2 - 2x - y + 2xy2 - y3 . 10. Divide ax3- ( a2 + b ) x2 + b2 by ax - b . Ans . x2 - ax - b . 11. Divide 1 by 1 - a . Ans . 1 + a + a2 + a3 , & c ...
... ( Observe Art . 21. ) Ans . 2a2 + 2a + 5 . 9. Divide x - y6 by x3 + 2x2y + 2xy2 + y3 . Ans . x2 - 2x - y + 2xy2 - y3 . 10. Divide ax3- ( a2 + b ) x2 + b2 by ax - b . Ans . x2 - ax - b . 11. Divide 1 by 1 - a . Ans . 1 + a + a2 + a3 , & c ...
Other editions - View all
An Elementary Treatise on Algebra: Theoretical and Practical Horatio Nelson Robinson No preview available - 2016 |
Common terms and phrases
2d power 3d term 4th power added algebraic arithmetical arithmetical mean arithmetical series assumed binomial square cent Clearing of fractions coefficients common difference Completing the square compound interest compound quantity cube root cubic equation distance Divide the number dividend division divisor dollars equa equal roots equation becomes EXAMPLES Expand exponents factors find the values following rule four numbers fourth fraction will produce geometrical progression geometrical series give greater greatest common measure Hence improper fraction last term least common multiple less letter logarithm lowest terms method miles mixed quantity moon number of terms numbers in geometrical Observe operation primitive equation principle problem produce the series quadratic equations quotient remainder represent Required resolved second power shillings simple equations solution square root substitute subtract suppose Theorem third three numbers tion Transpose unknown quantity unknown term whole numbers
Popular passages
Page 11 - If equal quantities be divided by the same, or by 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.
Page 33 - To reduce a mixed quantity to an improper fraction, multiply the integer by the denominator of...
Page 195 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means as 7 to 3. What are the numbers?
Page 184 - If the sum of an arithmetical series is 567, the first term 7, and the common difference 2; what is the number of terms?
Page 202 - There are two numbers, which are to each other, as 16' to 9, and 24 is a mean proportional between them. What are the numbers ? Ans. 32 and 18. 13. The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to the greater as 102 to 5. What are the numbers 1 Ans.
Page 145 - Prob. 9. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16.
Page 42 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 155 - Any trinomial can be separated into two binomial factors, when the extremes are squares and positive, and the middle term is twice the product of the square roots of the extremes.
Page 191 - When three magnitudes, a, b, c, have the relation of a: c: : a—b : b—c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 143 - A and B, set out to meet each other; A leaving the town C at the same time that B left D. They travelled the direct road...