Note. The Circle is the most capacious of all Figures; for if the Sides of a Triangle, Square, Pentagon, Hexagon, or any other regular Polygon, be equal to the Circumference of a Circle, it will not contain so great an Area as the Circle does. For, suppose the Circumference of a Circle be 75.4 Inches, its Area will be 452.4 Inches. Now, the fourth Part of the Circumference is 18.85, which squared gives only 355.3225 Inches, consequently is 97.3775 Inches less than the true Area of the Circle. Hence, we fee the Ground and Foundation of the Error of measuring round Timber, by taking of the Girth for the Side of the Square equal; which false Way ought, I think, no longer to take Place, but be finally banished from the Recommendation and Practice of all thinking Men, who have any Connection with such Kind of Menfurations. Again, if the Circumference of a Circle be 1, the Side of a Square of equal Area to that Circle is .2821; whereas by the false Method of the Girth it is but .25. 2 Problem 28. To raise the Earth according to the Proposal of the great Geometrician Archimedes of Syracufe. The celebrated Archimedes affirmed, that he could move the Earth, if he had a Place at a Distance from it to stand upon to manage his Machinery. * This he proposed to do, perhaps, with a long Lever in the following Manner. C B A Thus, suppose A to represent the Earth; B the Place, Prop, or Center of Motion; and C the Place where the moving Power is to be applied. Then, suppose a Man to pull or press the End of the long Arm with the Force of 200 Pound Weight, and that the Earth contains, in round Numbers, 4,০০০,০০০,০০০,০০০,০০০,000,000, or 4000 Trillions of Cubic Feet, each at a mean Rate weighing 100 Pound; and that the Prop or Center of Motion of the Lever is 6000 Miles from the Earth's Center: In this Cafe, the Length of the Lever from the Prop to the moving Power or Weight ought to be 12,000,000,০০০,০০০,০০০,০০০,০০০,০০০, or 12 Quadrillions of Miles; and fo many Miles must the Power move in order to raise the Earth but one Mile. Whence, it is easy to compute, that if Archimedes, or the Power applied, could move as swift as a Cannon-Ball, it would take 27,000,000,000,000, or 27 Billions of Years, to raise the Earth one Inch. * ωὸς ῶὲ τω, καί τὸν κοσμὸν κινήσω. Give me a Place to stand on, and I will move the Earth. Note. If any other Machine, such as a Combination of Wheels, Pullies, or Screws, was proposed to move the Earth, the Time it would require, and the Space gone through by the Hand that turned the Machine, would be the fame as above. Hence we learn, that however boundless our Imagination and Theory may be, the actual Operations of Man are confined within narrower Bounds, and more adapted to our real Wants, than to our Defires. With this Reflection, we close the present Work, wishing the Reader may receive that Benefit and Advantage from it, which was designed by the Author. To Note. The following Problem should have been added at Page 150. To measure the Middle Zone of a Sphere or Globe. Rule. To the Squares of the Radius, or Semidiameter of each End, add (one third) of the Square of their Distance, or the Height of the Zone. This Sum multiplied by the faid Height or Distance, and that Product again by 1.5708, will give the Solid Content. FINIS. |