On the Arenarius of Archimedes

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: degree resembles this plan; for a million of millions makes a billion, a million of billions a trillion, and so on; but these words have not been determined for any very high multiples, and even the billion, the first of them, is hardly ever used, while the rest are so seldom met with, that they hardly...
More Description

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: degree resembles this plan; for a million of millions makes a billion, a million of billions a trillion, and so on; but these words have not been determined for any very high multiples, and even the billion, the first of them, is hardly ever used, while the rest are so seldom met with, that they hardly belong to common language; and instead of constituting a regularly developed system, they seem rather to be mere examples of the manner in which such names might, if required, be constructed. Now a comparison of the suggestions of Archimedes with what later times have thus adopted, enables us to see the superiority of his mind. The monads in both cases go on in geometrical progression, in which our common ratio would be a million, but his myriad of myriads is 100 millions; so far he has the.advantage; but this, though not trifling, is nothing compared with his contrivance for continuing the numeration. In cases of this kind, the attainment of the end depends in great measure on arrangement, and the application of suitable notation and distinctions. Archimedes himself, for the quadrature of the spiral, introduces preliminary propositions, which are founded on the principles by which figures are supposed to be generated in the method of fluxions. Maclaurina has actually made use of them in his valuable treatise on that branch of science, with a particular acknowledgment of the author from whom they were taken; but Archimedes did not generalize the ideas, and adapt expressions to them, by which they might be conveniently brought into extended application. The consequence was, that this most prolific germ re- a Page 59. art. 16. chapter{{Section 4mained for centuries without its due expansion, and his method of reasoning, which under more favourable circumstances has been the basis...