A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Resultat 1-5 av 52
Side xv
... reason that direct and inverse processes in Algebra are not co- extensive , and ambiguities which have no existence in the first will necessarily present themselves in the second : thus a - b may arise from a + ( − b ) or a− ( + b ) ...
... reason that direct and inverse processes in Algebra are not co- extensive , and ambiguities which have no existence in the first will necessarily present themselves in the second : thus a - b may arise from a + ( − b ) or a− ( + b ) ...
Side xx
... reason concerning hypothe- tical equivalent forms , as if they were really existing , with a view to discover some property in the forms themselves , or in others derived from them , by which their possible or necessary existence may be ...
... reason concerning hypothe- tical equivalent forms , as if they were really existing , with a view to discover some property in the forms themselves , or in others derived from them , by which their possible or necessary existence may be ...
Side 42
... reason - a = a b : for may be changed - without af- ( 4 ) b fecting the quotient . a ab ( Art . 10 ) : and X - - b = ō b a -a X - -b ⋅ b = - a , = — a ( Art . 10 ) : con- sequently and are equivalent expressions . b From these examples ...
... reason - a = a b : for may be changed - without af- ( 4 ) b fecting the quotient . a ab ( Art . 10 ) : and X - - b = ō b a -a X - -b ⋅ b = - a , = — a ( Art . 10 ) : con- sequently and are equivalent expressions . b From these examples ...
Side 85
... reasons for choosing a right angle in preference to any other . For in the first place , it is the mean between all ... reason that we speak of the quadratures of areas as equivalent to the determination of their values . Meaning of the ...
... reasons for choosing a right angle in preference to any other . For in the first place , it is the mean between all ... reason that we speak of the quadratures of areas as equivalent to the determination of their values . Meaning of the ...
Side 89
... reason , have the same sign : whilst those pairs of solids , which have one point only in common and all the three edges with different signs , such as ( 1 ) and ( 8 ) , ( 2 ) and ( 7 ) , ( 3 ) and ( 5 ) , ( 4 ) and ( 6 ) , will have ...
... reason , have the same sign : whilst those pairs of solids , which have one point only in common and all the three edges with different signs , such as ( 1 ) and ( 8 ) , ( 2 ) and ( 7 ) , ( 3 ) and ( 5 ) , ( 4 ) and ( 6 ) , will have ...
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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...