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 |
Inni boken
Resultat 1-5 av 20
Side 40
... expanded . Thus ( a + b ) x ( c + d ) becomes when expanded ac + ad + bc + bd . 112. With a given multiplicand , the less the multiplier , the less will be the product . If then the multiplier be reduced to nothing , the product will be ...
... expanded . Thus ( a + b ) x ( c + d ) becomes when expanded ac + ad + bc + bd . 112. With a given multiplicand , the less the multiplier , the less will be the product . If then the multiplier be reduced to nothing , the product will be ...
Side 90
... expanded . Thus ( a + b ) , when expanded , becomes a2 + 2ab + b2 . And ( a + b + h ) , becomes a2 + 2ab + 2ah + b2 + 2bh + h2 . 218. With respect to the SIGN which is to be prefixed to quantities involved , it is important to observe ...
... expanded . Thus ( a + b ) , when expanded , becomes a2 + 2ab + b2 . And ( a + b + h ) , becomes a2 + 2ab + 2ah + b2 + 2bh + h2 . 218. With respect to the SIGN which is to be prefixed to quantities involved , it is important to observe ...
Side 150
... Expanding ( x + 3 ) 3 ( Art . 217. ) 9x2 + 27x = 117-27 = 90 x = 3 The two numbers , therefore , are 2 and 5 . - • Prob . 6. To find two numbers , whose difference shall be 12 , and the sum of their square 1424 . Ans . The numbers are ...
... Expanding ( x + 3 ) 3 ( Art . 217. ) 9x2 + 27x = 117-27 = 90 x = 3 The two numbers , therefore , are 2 and 5 . - • Prob . 6. To find two numbers , whose difference shall be 12 , and the sum of their square 1424 . Ans . The numbers are ...
Side 204
... y = 21 xy = 24 ) x = 6 , and y = 4 . 8. It is required to prove that a : x :: √2a - y : √y ( a + x ) 2 : ( α − x ) 2 : ; x + y : x − y . * on supposition that * Bridge's Algebra . - 1. Expanding , a2 + 2ax + x2 : a2 204 ALGEBRA .
... y = 21 xy = 24 ) x = 6 , and y = 4 . 8. It is required to prove that a : x :: √2a - y : √y ( a + x ) 2 : ( α − x ) 2 : ; x + y : x − y . * on supposition that * Bridge's Algebra . - 1. Expanding , a2 + 2ax + x2 : a2 204 ALGEBRA .
Side 205
... Expanding , a2 + 2ax + x2 : a2 - 2ax + x2 :: x + y : x - y 2. Adding and subtracting terms , 2a2 + 2x2 : 4ax :: 2x : 2y 3. Dividing terms , a2 + x2 : 2αx :: : y 4. Transf . the factor x , ( Art . 374. cor . ) a2 + x2 : 2a : x2 : y 5 ...
... Expanding , a2 + 2ax + x2 : a2 - 2ax + x2 :: x + y : x - y 2. Adding and subtracting terms , 2a2 + 2x2 : 4ax :: 2x : 2y 3. Dividing terms , a2 + x2 : 2αx :: : y 4. Transf . the factor x , ( Art . 374. cor . ) a2 + x2 : 2a : x2 : y 5 ...
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.