A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side vi
... necessary modifi- cation of their meaning : but at the same time that the primitive assumption of such signs and operations is thus carefully limited in the extent of their signification , there is + no such limitation imposed upon the ...
... necessary modifi- cation of their meaning : but at the same time that the primitive assumption of such signs and operations is thus carefully limited in the extent of their signification , there is + no such limitation imposed upon the ...
Side vii
... necessary by the primitive meaning of those operations , has led to the independent existence of the signs and , as an assumption which is also necessary in order to preserve the assumed univer- sality of the values of the symbols and ...
... necessary by the primitive meaning of those operations , has led to the independent existence of the signs and , as an assumption which is also necessary in order to preserve the assumed univer- sality of the values of the symbols and ...
Side viii
... necessary but conventional , and that Arithmetic can only be considered as a Science of Suggestion , to which the principles and operations of Algebra are adapted , but by which they are neither limited nor determined . In our first ...
... necessary but conventional , and that Arithmetic can only be considered as a Science of Suggestion , to which the principles and operations of Algebra are adapted , but by which they are neither limited nor determined . In our first ...
Side ix
... necessary to establish the principles of this science upon a basis of their own : for the assumption in question can result from no process of reasoning from the principles or operations of Arithmetic , and if considered as a generaliza ...
... necessary to establish the principles of this science upon a basis of their own : for the assumption in question can result from no process of reasoning from the principles or operations of Arithmetic , and if considered as a generaliza ...
Side xii
... necessary identity of the results of arithmetical and symbolical Algebra , as far as this agreement can extend without violating the necessary limitations of the first of these sciences , we may legiti mately assume the operations ...
... necessary identity of the results of arithmetical and symbolical Algebra , as far as this agreement can extend without violating the necessary limitations of the first of these sciences , we may legiti mately assume the operations ...
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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...