An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesH. Howe, 1827 - 332 sider |
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Resultat 6-10 av 20
Side 210
... Expanding , adding , and subtracting terms . ( Arts . 217 , and 389 , 7. ) 2A2 + 2B 4AB :: 2a2 + 262 : 4ab . Or , ( Art . 382. ) : 2 A2 + B2 : AB :: a2 + b2 : ab , that is , A2 + B2 AB . 416. The terms of one general proportion may be ...
... Expanding , adding , and subtracting terms . ( Arts . 217 , and 389 , 7. ) 2A2 + 2B 4AB :: 2a2 + 262 : 4ab . Or , ( Art . 382. ) : 2 A2 + B2 : AB :: a2 + b2 : ab , that is , A2 + B2 AB . 416. The terms of one general proportion may be ...
Side 242
... EXPANSION OF BINOMIALS . * ART . 467. THE manner in which a binomial , as well as any other compound quantity , may be involved by repeated multiplications , has been shown in the section on powers . ( Art . 213. ) But when a high power ...
... EXPANSION OF BINOMIALS . * ART . 467. THE manner in which a binomial , as well as any other compound quantity , may be involved by repeated multiplications , has been shown in the section on powers . ( Art . 213. ) But when a high power ...
Side 248
... expanding the factor ( 1 + 2 ) " , X n we have 3 ( @ + x ) " = a " × ( 1+ = ) " = a * × ( 1 × 4 + B + C22 ) & c α x × ( 1 × 12 & c . x2 a2 α 479. When the index of the power to which any ... Expand into a series 1 ( a + sired . 248 ALGEBRA .
... expanding the factor ( 1 + 2 ) " , X n we have 3 ( @ + x ) " = a " × ( 1+ = ) " = a * × ( 1 × 4 + B + C22 ) & c α x × ( 1 × 12 & c . x2 a2 α 479. When the index of the power to which any ... Expand into a series 1 ( a + sired . 248 ALGEBRA .
Side 249
... Expand into a series 1 ( a + y ) == ( a + y ) -2 . The terms without the co - efficients , are a - a , Quy , a- * y ... expanded by the binomial theorem , the series will never terminate . A series produced in this way terminates , only ...
... Expand into a series 1 ( a + y ) == ( a + y ) -2 . The terms without the co - efficients , are a - a , Quy , a- * y ... expanded by the binomial theorem , the series will never terminate . A series produced in this way terminates , only ...
Side 250
... Expand into a series ( 1 + x ) 3 . JC x2 3x3 3.5x4 Ans . 1 + 2.42.4.6 2.4.6.8 3. Expand √2 , or ( 1 + 1 ) 1⁄23 . Ans . 1+ 3 + & c . " 3.5 3.5.7 + 2 2.4 2.4.6 2.4.6.8 2.4.6.8.10 ' & c . 4. Expand ( a + x ) * , or a3 × ( 1+ ) . See art ...
... Expand into a series ( 1 + x ) 3 . JC x2 3x3 3.5x4 Ans . 1 + 2.42.4.6 2.4.6.8 3. Expand √2 , or ( 1 + 1 ) 1⁄23 . Ans . 1+ 3 + & c . " 3.5 3.5.7 + 2 2.4 2.4.6 2.4.6.8 2.4.6.8.10 ' & c . 4. Expand ( a + x ) * , or a3 × ( 1+ ) . See art ...
Vanlige uttrykk og setninger
12 rods abscissa added algebraic antecedent applied arithmetical become binomial calculation called co-efficients common difference Completing the square compound quantity consequent contained cube root cubic equation curve diminished Divide the number dividend division divisor dollars equa Euclid exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multiplicand multiplied or divided negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tities Transposing triangle twice unit unknown quantity varies
Populære avsnitt
Side 190 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Side 124 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Side 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Side 188 - : b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities...
Side 87 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.
Side 137 - In the same manner, it may be proved, that the last term of the square of any binomial quantity, is equal to the square of half the co-elficient of the root of the first term.
Side 295 - The operation consists in repeating the multiplicand, as many times as there are units in the multiplier.
Side 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 49 - As the value of a fraction is the quotient of the numerator divided by the denominator, it is evident, from Art.
Side 233 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.