A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side xiii
... 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 to all such cases like- wise it is ...
... 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 to all such cases like- wise it is ...
Side xxiii
... divisor of two alge- braical expressions , the necessity for whose separate and independent consideration we have had particular occasion to point out . The sixth Chapter is devoted to the complete develope- ment of the general ...
... divisor of two alge- braical expressions , the necessity for whose separate and independent consideration we have had particular occasion to point out . The sixth Chapter is devoted to the complete develope- ment of the general ...
Side 41
... divisor must produce the dividend : this is only another mode of expressing the principle just referred to : it ... divisor and the dividend are Case 1 . mononomials . RULE . Omit all the quantities which are common to the divisor and ...
... divisor must produce the dividend : this is only another mode of expressing the principle just referred to : it ... divisor and the dividend are Case 1 . mononomials . RULE . Omit all the quantities which are common to the divisor and ...
Side 42
... divisor given in Ex . 2 . = - a b a = : for the 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 ...
... divisor given in Ex . 2 . = - a b a = : for the 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 ...
Side 43
... divisor is under a frac- tional form which is , " To invert the divisor , and then proceed as in multiplication . " a3 a3 ÷ a === a2 : for a a1 ÷ a3 = = a ' : for ( 7 ) α ( 8 ) ( 9 ) 3 a3 - a = α χα = a2 . a απ α και - = = a1 . a3 a3 3 ...
... divisor is under a frac- tional form which is , " To invert the divisor , and then proceed as in multiplication . " a3 a3 ÷ a === a2 : for a a1 ÷ a3 = = a ' : for ( 7 ) α ( 8 ) ( 9 ) 3 a3 - a = α χα = a2 . a απ α και - = = a1 . a3 a3 3 ...
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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...