A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side viii
... successive transitions which are made from the principles and operations of Arithmetic to those of Algebra , in order to shew that their connection is not necessary but conventional , and that Arithmetic can only be considered as a ...
... successive transitions which are made from the principles and operations of Arithmetic to those of Algebra , in order to shew that their connection is not necessary but conventional , and that Arithmetic can only be considered as a ...
Side xix
... successive derivative ex- pressions be not definable in the general form which they are supposed to possess , and the law of their connection be determinable from the application of the principle of equi- valent forms only , then the ...
... successive derivative ex- pressions be not definable in the general form which they are supposed to possess , and the law of their connection be determinable from the application of the principle of equi- valent forms only , then the ...
Side xxx
... successively with each other : thus , if n = 4 , then ( 1 ) = 1 , or √1 , or -1 , or --1 , and a , 1.a , -a , -√1.a , √1.a , will denote four lines equal to a , of which a and -a are in opposite directions , and √ - 1.a and √ - 1.a ...
... successively with each other : thus , if n = 4 , then ( 1 ) = 1 , or √1 , or -1 , or --1 , and a , 1.a , -a , -√1.a , √1.a , will denote four lines equal to a , of which a and -a are in opposite directions , and √ - 1.a and √ - 1.a ...
Side 19
... successively beneath 3x - 7y , as in addition , their signs being previously changed . 3x - 7y xX- 2y - -4y + 7x 9 x -- This would be the answer 13 y to the following question : " It is required to subtract + 2y and 4y - 7x from 3x - 7y ...
... successively beneath 3x - 7y , as in addition , their signs being previously changed . 3x - 7y xX- 2y - -4y + 7x 9 x -- This would be the answer 13 y to the following question : " It is required to subtract + 2y and 4y - 7x from 3x - 7y ...
Side 20
... successively removed , the quantities external to th being previously reduced to their most simple form . 33. The method of denoting the operation of m tiplication has been explained in Art . 8 . It will be convenient to consider three ...
... successively removed , the quantities external to th being previously reduced to their most simple form . 33. The method of denoting the operation of m tiplication has been explained in Art . 8 . It will be convenient to consider three ...
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Vanlige uttrykk og setninger
a+b+c a₁ affected arith Arithmetical Algebra arithmetical values assumed b₁ binomial binomial theorem c₁ chance coefficients common connection consequently considered contravalent corresponding cosines cube cubic equation decimal deduced definition denoted determined digit divided dividend divisor equa equal equation equivalent form examples expression factors follows formula fraction geometrical greater identical inasmuch interpretation inverse involve least common multiple likewise logarithms magnitudes means metical multiplied necessary negative number of terms numerator and denominator operations P₁ partial fractions plane position powers primitive equation primitive line principle problem proportion proposition quadratic equation quotient ratio rectangle reduced remainder represent respect result right angles shew shewn sides signs similar manner sines solution square root Subtraction symbols tion triangle unknown quantities whole number zero
Populære avsnitt
Side 104 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Side 669 - But if the digits be inverted, and then divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient ? Required the number.
Side 27 - The product is a2+2a6-}-62; from which it appears, that 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.
Side 331 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 339 - If four quantities are in proportion, they will be in proportion by COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Side 332 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third...
Side 340 - 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.
Side 674 - A person bought some sheep for £. 72 ; and found that if he had bought 6 more for the same money, he would have paid £. 1 less for each. How many did he buy...
Side 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Side 435 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...