Graphic Algebra ; Or, Geometrical Interpretation of the Theory of Equations of One Unknown Quantity
Graphic Algebra ; Or, Geometrical Interpretation of the Theory of Equations of One Unknown Quantity
Andrew W Andrew Wheeler Phillips
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76. Find the value to six decimal places of one root of the equation x"^ — 8;r* + \/^ + 44r — 8 = O, the integral part of the root being 5. 82 GRAPHIC ALGEBRA. A B C D V 1-8 + 14 + 4 - 8 1 5.2360679 - 3 I - I - 5 + 2 + 9 + 44 = I8t divisor. — 13 = 1st dividend. 7 44 53.288 10.6576 13. a 46.44 63.072 = 2d divisor. — 2.3424 = 2d dividend. 12.4 48.92 51.44 64.626 66.193 747 068 = 3d div'r. 1.9388 oi24i 12.6 - .4035 9759 = 3d divid'd. 12.8 3 6 51.82 52.21 49 07 66.509 66.825 I 17736 633024 = 4th d'... .3990 54706416 12.8 r.- .0045 42883584 =4th d'd. 9 12.8 9 52-59 74 12.9 26 52.67 4956 12.9 32 52.75 2548 The above calculation is exhibited in an abbreviated form. Thus, in making the substitution, we multiply A by 5, add the product to jB, and set down simply the result, which is — 3. We do the same in each of the columns, thus dispensing with half the number of lines employed in pre- ceding examples. Again, when we wish to obtain a root correct to a limited number of places, we may omit much of the labor by cutting oflF all figures beyond a certain decimal ; that is, we need set down none of those figures on the right of each of the verti- cal lines drawn in the several columns.
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