An Introduction to Algebra: Being the First Part of a Course of Mathematics : Adapted to the Method of Instruction in the American CollegesHowe & Spalding, 1820 - 332 sider |
Inni boken
Resultat 1-5 av 19
Side 40
... expanded . Thus ( a + b ) × ( 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 redu- ced to nothing , the product will ...
... expanded . Thus ( a + b ) × ( 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 redu- ced to nothing , the product will ...
Side 90
... expanded . Thus ( a + b ) , when expanded , becomes a2 + 2ab + b2 . And ( a + b + h ) 2 , 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 ) 2 , 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 And ( x + 3 ) 3 — x3 = 117 x = --聖=一肚 ㄢ ˇ The two numbers , therefore , are 2 and 5 . 347 Prob . 6. To find two numbers , whose difference shall be 12 , and the sum of ...
... Expanding ( x + 3 ) 3 ( Art . 217. ) 9x2 + 27x = 117—27 = 90 And ( x + 3 ) 3 — x3 = 117 x = --聖=一肚 ㄢ ˇ The two numbers , therefore , are 2 and 5 . 347 Prob . 6. To find two numbers , whose difference shall be 12 , and the sum of ...
Side 205
... Expanding , 2. Adding and subtracting terms , 3. Dividing terms , 2a2 + 2x2 : 4ax :: 2x : 2y a2 + x2 : 2αx : x : y 2 4. Transf . the factor x , ( Art . 374. cor . ) a2 + x2 : 2a :: x2 : y 5. Inverting the means , 6. Subtracting terms ...
... Expanding , 2. Adding and subtracting terms , 3. Dividing terms , 2a2 + 2x2 : 4ax :: 2x : 2y a2 + x2 : 2αx : x : y 2 4. Transf . the factor x , ( Art . 374. cor . ) a2 + x2 : 2a :: x2 : y 5. Inverting the means , 6. Subtracting terms ...
Side 210
... Expanding , adding , and subtracting terms , ( Arts . 217 and 389 , 7. ) 2A2 + 2B2 : 4AB :: 2a2 + 2b2 : 4ab . Or , ( Art . 382. ) A2 + B2 : AB :: a2 + b2 : ab ; that is , A + B ∞ AB . 416. The terms of one general proportion may be ...
... Expanding , adding , and subtracting terms , ( Arts . 217 and 389 , 7. ) 2A2 + 2B2 : 4AB :: 2a2 + 2b2 : 4ab . Or , ( Art . 382. ) A2 + B2 : AB :: a2 + b2 : ab ; that is , A + B ∞ AB . 416. The terms of one general proportion may be ...
Vanlige uttrykk og setninger
12 rods abscissa added algebraic antecedent applied arithmetical become binomial calculation co-efficients common difference Completing the square compound quantity consequent contain cube root cubic equation curve Divide the number dividend division divisor dollars equa errour 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 tity Transp Transposing triangle twice unit unknown quantity varies α α
Populære avsnitt
Side 298 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 186 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Side 199 - If three quantities are proportional, the first is to the third, as the square of the first, to the square of the second ; or as the square of the second, to the square of the third.
Side 231 - 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.
Side 203 - What two numbers are those, whose difference, sum, and product, are as the numbers 2, 3, and 5, respectively ? Ans.
Side 42 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factors a and Id will produce the dividend.
Side 215 - THE EXTREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES.
Side 81 - ... of this part. At the end of the third year, his original stock was doubled. What was that stock ? Ans.
Side 237 - Divide one of the quantities by the other, and the preceding divisor by the last remainder, till nothing remains ; the last divisor will be the greatest common measure.