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The Great Calculation According to the Indians, of Maximus Planudes - The Digits of the System, II

Peter G. Brown

For greater clarity let me also say the following: The number lying in the first place indicates the number of units there are. The second is the number of tens, the third the number of hundreds, the fourth the number of thousands and so on, as far as many places as the number occupies.

Note also that as the number proceeds through the four places it changes its literal name each time.9 Then in the fifth place it takes again its original name, not just the number itself, but tied to its place value. This continues 'till the eighth place in which it takes the name of the fourth, and so it continues in turn. Thus, in the previous example given above, 2 indicates and is read as 'two', 9 as 'ninety', 5 as 'five hundred' and 4 as 'four thousand'. The sign 7 is then 'seven (units of) myriads', just as we referred to 'two' (units) in the first position. Similarly the next sign is for seven, but is in fact seven myriads10, 2 is for twenty myriads; just as we had ninety in the second position, so here the sign means twenty, for both numbers are decadic. This is the same as the case with the monadic numbers that preceeded them, and so on in turn.

The cipher is never placed at the left-hand end of the digits but can appear in the middle of the number or at the right-hand side, that is, at the extreme side before the smallest (non-zero) place digit.11 Not only one, but two, three, four or as many zeros as are required may be placed in the middle or in the other aforementioned place. Just as the (number of) places increases the size of the number, so too does the number of ciphers. For example, one cipher lying at the end makes the number decadic, 50 is fifty in fact, two ciphers make it hecatontadic, thus 400 is four hundred, and so on in turn. If one cipher lies in the middle and there is only one symbol before it, it makes that number hecatontadic, thus 302 is three hundred and two, but if there are two such signs, the number is chiliadic, thus 6005 is six thousand and five.   If there is a single cipher with two signs after it, this indicates a chiliadic number, thus 6043 is six thousand and forty three, but if there are two then the number is myriadic, thus 60043 is six myriads and forty three, and so on in turn. To put it simply12, the number is to be understood by the order in which the symbols are placed.

Peter G. Brown, "The Great Calculation According to the Indians, of Maximus Planudes - The Digits of the System, II," Convergence (March 2012)