Page 91. It is shown what the characteristic of whole numbers consisting of any number of digits will be, and it may be thence inferred what that of a decimal will be, but it had better be stated thus: 4, 04, 004, 0004, are represented by :-as any decimal numbers, 4 4 4 4 10' 10' 10' 104' their charac teristics will be (−1), (−2), (−3), (−4), according as the number of ciphers on the left hand side of the decimal are none, one, two, or three. 11) must be deducted that the one carried from the addition of (8 + 3 from the sum 5 of the negative characteristics. = In seeking the root of any decimal quantity by logarithms, since numerator and denominator must each be multiplied by 10. And by the reverse operation, to find the continued fraction equivalent to 17 It is required to find the value to six places of decimals of Page 179. Ex. 18. and 19. It ought to have been noticed in the text, that the areas of all similar plane figures are proportional to the squares, and the content of all similar solid figures, to the cubes of their homologous sides. Thus if it were required to know the radius of a circle that contains 4 acres, having given that the radius of the circle containing half an acre is 16 yds. If, however, in this example it were given to find a cylinder similar to the first, which should contain ten times as much, we should have then a proportional increase both in the area of the base and the height, and then 1 10 :: 73 : x3, .. x = 3430 = 15.085 feet. A sphere, whose radius is 6, and an equilateral cone have the same solidity; what is the difference of the radii of the base of the one and of a great circle of the other? |