Excerpt from On the Arenarius of Archimedes Archimedes saw that by these means the myriad itself became consolidated into a unit, of which 100, 1000, or any multiple might be taken, until the system, as it were, limited itself by reaching a myriad of myriads. He conceived the idea there fore of going on by analogy, and, calling the first his wpe'rrm dptguoi, to consider the Jpn pvpm'des' of them as the monad of his detrre'pm eplflpoi, of which 10, 100, 1000, might again be taken, until they reached in amount to the myriad of myriads which would form the monad of Tpl'roz dpcepoi. In this manner, the myriad of myriads of each order became the monad of that which immediately followed it, until this enumeration arrived at the pupzdxw popcoa-rol spate}: of these the myriad of myriads might be taken, and here there would be a limit: it would, indeed, require an unit with 800 millions of our ciphers to express the value of it, but still it would be a termination, to provide against which Archimedes denominates all this vast accumulation the wpe'n-a wepw'boc of his system, and consolidates the highest of them into a monad of the wrroc dpcepoi of a dmepa wept'odos', in Which he goes on, till having reached the myriad of myriads of the pvptdxtc uvc'roi dpceuol, the last of them becomes the monad of the wpd'rrm dpteuol 769 7pz'1'as' wepcddou. Thus, he says, we may go on to the completion of the pvptdxw nvplmd wepc'odoc. He proceeds no fur ther in the detail; but it is evident that the last number in this enormous period might, in the same way, be taken for the monad of a new series, and so the system might be continued to any extent. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.