the diameter is equal to twice the diameter of the generating circle. And: If the radius of any circle be taken to represent the longer of the two sides of a right-angled triangle, adjacent to the right angle, and of which right-angled triangle, the two sides adjacent to the right angle, are in the ratio of 3 to 4. Then, if squares be described on the sides of such right-angled triangle, the superficial area of the squares, are together exactly equal to the superficial area of the circle. With these illustrations I shall conclude our long correspondence. I think I have made it as obvious and evident, as that two and two make four, to anyone who will candidly and carefully examine my facts and arguments: That for every linear unit contained in the diameter of a circle, there are three and one-eighth linear units contained in the circumference. In conclusion, I respectfully submit, that in our correspondence, you have utterly failed to shake this proposition; and I shall be glad to find you are possessed of the moral courage to admit: That the problem of "The Quadrature of the Circle" has at length been satisfactorily solved. I am, Sir, Yours very respectfully, JAMES SMITH. |