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P. 132. What the Archimedean and, in general, the Greek method of root- extraction really was, has "been a favourite subject of conjecture. See for example, H. WEISSENBOEN'S Berechnung des JKreisumfanges bei Archi medes und Leonardo Pisano, Berlin, 1894. ject, For bibliography of this sub see S. GtJNTHEE, Gesch. d. antiken Naturwissenschaft u. Philosophic, p. 16. GREECE whose radius extends from the earth of grains in a sphere the fixed A counterpart stars. 29 to of this interesting speculation, " called the " sand-counter (arenarius), is found in a calcula tion attributed to Buddha, the Hindu reformer, of the number of primary atoms in a line one mile in length, when the atoms are placed one against another.
A'l mm no theorems, and In most cases the It contains Its. hardly any general rules of procedure. writer treats in succession several problems of the same kind. From them rules, it but this would be easy, by induction, to obtain general not done. When we remember that only one is hundred years ago it was the practice of many English arith metical writers to postpone the discussion of fractions to the end of their books, it is surprising to find that this hand-book of 4000 years ago begins with exercises in fractions, and pays but little attention to whole numbers.
If the signs used in the latter were, but by the study of ancient statuary, bas-reliefs, and paintings this secret may yet be unravelled. Of the abacus there existed many forms at different times and among the various nations. In all cases a plane was divided into regions and a pebble or other We object represented a different value in different regions. possess no detailed information regarding the Egyptian or the Greek abacus. " This indicates a primitive and instrumental mode of counting with aid of pebbles.