A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side vi
... operations of Addition and Subtraction in their simple arithmetical sense , are assumed to be denoted by the signs + and - , and to be used in connecting such symbols with each other : Multi- plication and Division , two inverse operations ...
... operations of Addition and Subtraction in their simple arithmetical sense , are assumed to be denoted by the signs + and - , and to be used in connecting such symbols with each other : Multi- plication and Division , two inverse operations ...
Side vii
... operations of Addition and Subtraction should be confined to quan- tities of the same kind , or that the quantities ... operations , has led to the independent existence of the signs and , as an assumption which is also necessary in ...
... operations of Addition and Subtraction should be confined to quan- tities of the same kind , or that the quantities ... operations , has led to the independent existence of the signs and , as an assumption which is also necessary in ...
Side viii
... operation and other modes of combining them as designating operations with arithmetical names and arithmetical meanings : but in the very first appli- cations of such operations , the mere use of general symbols renders the proper ...
... operation and other modes of combining them as designating operations with arithmetical names and arithmetical meanings : but in the very first appli- cations of such operations , the mere use of general symbols renders the proper ...
Side ix
... operations of Arithmetic , and if considered as a generaliza- tion of them , it is not the last result of a series of propo- sitions connected with them : it must be considered therefore as an independent principle , which is suggested ...
... operations of Arithmetic , and if considered as a generaliza- tion of them , it is not the last result of a series of propo- sitions connected with them : it must be considered therefore as an independent principle , which is suggested ...
Side xiii
... operations , when the multiplier or divisor is a number or numerical fraction , which are equally applicable to all quantities whatever be their nature , we may legitimately extend this interpretation of the meaning of such operations ...
... operations , when the multiplier or divisor is a number or numerical fraction , which are equally applicable to all quantities whatever be their nature , we may legitimately extend this interpretation of the meaning of such 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...