11.9137 1726 41.5451 11.9953 1727 41.5571 11.9976 1692 41.1339 To find the Root of a Number, consisting of Integers and Decimals. RULE.-Multiply the difference between the root of the integer part of the given number, and the root of the next higher integer number, by the decimal part of the given number, and add the product to the root of the integer number given; the sum will be the root of the number required, correct in all cases of the square root to 3 places of decimals, and in the cube root to 7. EXAMPLE 1.-Required the square root of 60.2. √61 √60 7.7459 ✓60.2 = 7.75876 as required, correct to 3 places of decimals. EXAMPLE 2.-Required the cube root of 843.75. 3/844 9.4503 3843 9.4466 If the square root is required correct to more places of decimals, the following rule is correct to 7 places. Multiply the root of the nearest integer number by twice the difference between that and the given number, and divide the product by 3 times the integer number added to the given number; and the quotient added to the root of the integer number will be the root of the given number nearly. Then, the root of 60.2 will stand thus, 60×3 180+60.2 240.2) 3.09836 (.01289+7.7459 7.75889 the If the number consist wholly of decimals, the root will be decimals also. PRACTICAL GEOMETRY. Practical Geometry is the art of describing mathematical figures by a ruler and compasses, or other instruments proper for the purpose. PROBLEM I. To divide a given Line into two equal parts. From A and B as centres, with any distance greater than half the length of the line, describe arcs cutting each other in m and n; then a line drawn through the points m and n will divide the line into two equal parts, as required. A -B im PROBLEM II. To divide a given Angle into two equal parts. |