MULTIPLICATION
57
1, 3, 2, 3, 1, 3, 2, 6, 4, 1,
4, 1, 7, 2, 3, 1, 2, 7, 6, 7, 7, 5, 5, 5, 2, 7, 1,
and 1, 5, 4, 5, 5, 1, 5, 5, 5, 1, 1.
The product is at once given in the text as 19 ‘ quadruple
myriads 6036 ‘ triple myriads and 8480 ‘ double myriads or
19.10000 4 + 6036.10000 3 + 8480.10000 2 .
(The detailed multiplication line by line, which is of course
perfectly easy, is bracketed by Hultsch as interpolated.)
Lastly, says Pappus, this product multiplied by the other
(the product of the tens and hundreds without the bases),
namely 10.10000 9 , as above, gives
196.10000 13 +368.10000 12 + 4800 . T.0000 11 .
(iv) Examples of ordinary multiplications.
I shall now illustrate, by examples taken from Eutocius, the
Greek method of performing long multiplications. It will be
seen that, as in the case of addition and subtraction, the
working is essentially the same as ours. The multiplicand is
written first, and below it is placed the multiplier preceded by
km (= ‘ by ’ or ‘ into ’). Then the term containing the highest
power of 10 in the multiplier is taken and multiplied into all
the terms in the multiplicand, one after the other, first into that
containing the highest power of 10, then into that containing
the next highest power of 10, and so on in descending order ;
after which the term containing the next highest power of 10
in the multiplier is multiplied into all the terms of the multi
plicand in the same order; and.so on. The same procedure
is followed where either or both of the numbers to be multi
plied contain fractions. Two examples from Eutocius will
make the whole operation clear.
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