...terminated both ways by the superficies of the sphere. Euclid, at the end of the twelfth book, shews that spheres are to one another in the triplicate ratio of their diameters, that is, their solidities are to one another as the cubes of their diameters. And Archimedes determines...

...terminated both ways by the superficies of the sphere. Euclid, at the end of the twelfth book, shews that spheres are to one another in the triplicate ratio of their diameters, that is, their solidities are to one another as the cubes of their diameters. And Archimedes determines...

...terminated both ways by the superficies of the sphere. Euclid, at the end of the twelfth book, shews that spheres are to one another in the triplicate ratio of their diameters, that is, their solidities are to one another as the cubes of their diameters. And Archimedes determines...

...water will be voided by a pipe 2 inches in diameter, Model Farm, than by a pipe 1 inch in diameter? 3. Spheres are to one another in the triplicate ratio of their diameters, how much more Hubstance is there in a turnip 6 inches in diameter, than in one 3 inches in diameter?...

...called the first octad: 108 to 1016 may be called the second octad and so on1. Using these numbers, and following the rule that spheres are to one another...less than a thousand myriads or ten millions of the 8th octad. This number would be expressed in our notation by 1063 or 1 with 63 ciphers annexed. 40....

...that they have shown that circles are to one another in the duplicate ratio of their diameters, and that spheres are to one another in the triplicate ratio of their diameters, and further that every pyramid is one third part of the prism having the same base with the pyramid...

...that they have shown that circles are to one another in the duplicate ratio of their diameters, and that spheres are to one another in the triplicate ratio of their diameters, and further that every pyramid is one third part of the prism which has the same base with the pyramid...

...number of the sand. By Assumption 5 [p. 227], (diam. of poppy-seed) ^ -^ (finger-breadth) ; and, since spheres are to one another in the triplicate ratio of their diameters, it follows that (sphere of diam. 1 finger-breadth) ^ 64,000 poppy-seeds 64,000 x 10,000 640,000,000...

...number of the sand. By Assumption 5 [p. 227], (diam. of poppy-seed) ^ ^ (finger-breadth); and, since spheres are to one another in the triplicate ratio of their diameters, it follows that (sphere of diam. 1 finger-breadth) ^ 64,000 poppy-seeds *• 64,000 x 10,000 $ 640,000,000...

...required in powers of 10. Since the diameter of a poppy-seed is not less than xffth of a dactylus, and spheres are to one another in the triplicate ratio of their diameters, a sphere of diameter 1 dactylus is not greater than 64,000 poppy-seeds, and, therefore, contains not...