A Theoretical and Practical Treatise on Algebra: In which the Excellencies of the Demonstrative Methods of the French are Combined with the More Practical Operations of the English and Concise Solutions Pointed Out and Particularly Inculcated : Designed for Schools, Colleges and Private Students |
From inside the book
Results 1-5 of 16
Page 76
... four methods already explained . ( Art . 51. ) Another theoretical method , from the French , we present to the ... numbers , 76 ELEMENTS OF ALGEBRA .
... four methods already explained . ( Art . 51. ) Another theoretical method , from the French , we present to the ... numbers , 76 ELEMENTS OF ALGEBRA .
Page 77
... numbers , they can be so assumed that am + a'n - a " = 0 and bm + b'n - b " = 0 . Then am + a'n = a " ( 1 ) and⚫ bm ... four methods just explained . But we would not restrict the pupil to the very letter of the rule , for that in ...
... numbers , they can be so assumed that am + a'n - a " = 0 and bm + b'n - b " = 0 . Then am + a'n = a " ( 1 ) and⚫ bm ... four methods just explained . But we would not restrict the pupil to the very letter of the rule , for that in ...
Page 97
... 4 days , and son 3 days , and received $ 11.50 ; at another time he served 9 days , his wife 8 days , and his ... Four times the product of any two numbers , is equal to the square of their sum , diminished by the square of their ...
... 4 days , and son 3 days , and received $ 11.50 ; at another time he served 9 days , his wife 8 days , and his ... Four times the product of any two numbers , is equal to the square of their sum , diminished by the square of their ...
Page 122
... numbers the terms are mingled together , and b can only be found by trial . Again , the terms 3a2 + 3ab + b2 explain ... four times the third power for the fourth root , & c . , and the quotient will be the next term of the root ...
... numbers the terms are mingled together , and b can only be found by trial . Again , the terms 3a2 + 3ab + b2 explain ... four times the third power for the fourth root , & c . , and the quotient will be the next term of the root ...
Page 158
... four preceding equations , as follows : ( 1 ) x = −a ± √o + a2 ( 2 ) x = a ± √b + a2 ( 3 ) x = a ± √a2 — b ( 4 ) ... numbers , and at least a and b prime to each other . There- We now desire to find some method of making 158 ...
... four preceding equations , as follows : ( 1 ) x = −a ± √o + a2 ( 2 ) x = a ± √b + a2 ( 3 ) x = a ± √a2 — b ( 4 ) ... numbers , and at least a and b prime to each other . There- We now desire to find some method of making 158 ...
Common terms and phrases
2d power 3d term 4th power algebraic apply arithmetical mean arithmetical progression arithmetical series assumed binomial square binomial theorem cent Clearing of fractions coefficients common measure Completing the square cube root decimal denominator distance Divide the number dividend division dollars equa equal roots equation becomes evolution example Expand exponent expressed factors find the values four numbers fraction will produce geometrical progression geometrical series give greater Hence infinite series infinity last term least common multiple less letter logarithm method miles minus moon Multiply negative number of terms numbers in geometrical observe operation primitive equation problem produce the series quadratic equations quotient ratio rectangle Reduce remainder represent Required resolved result second term solution specific gravity square root substitute subtract suppose surd Theorem third three numbers tion Transpose unknown quantity whole number
Popular passages
Page 18 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 28 - 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.
Page 23 - 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 191 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Page 82 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to 1.
Page 196 - 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 ? Ans.
Page 191 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 198 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page vii - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal....
Page 55 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.