Demonstration in Chinese and Vietnamese mathematics 541
( ).^68 Firstly,^69 there is an amount [to be distributed]; [secondly], 70
there are grades.
[9] Here is the computational problem [proposed] by those in charge, 71
and [what is below is] how I answered it. Now it is clear that what is
asked in the problem
[10] is solely concerned with the awarded money kindly dispatched to
the given groups [of functionaries]. [One] briefl y discussed the ‘fl at-
rate distribution’, [and aft er that] used the ‘distribution according to
grades’ as the principal
[11] method. I know that [this] computational method has unlimited
miraculous applications! I, so-and-so, ask for counting rods 72 t o
‘arrange and dispose’ them. 73
/p. 31a/
[1] As for the very [phrase] ‘[Let us suppose that] now there is money to
award [functionaries], the total is 1000 cân [of silver]’, [I] make it
[= this amount] uniform [with other units] using [the factor] 16,
[which is] the ‘norm’ of cân. 74
[2] Th e total amount [thus] obtained is 16000 lượng. ‘[If ] benevolence is
manifested by the superiors, [then] necessarily the subjects are kindly
awarded.’^75 As far as this money
[3] is concerned, the said functionaries cared about their benefi t and could
not themselves accept to keep [the money] privately. Th erefore
[4] what the granting authorities kept out of the amount of awarded money
was a deposited amount of 10708 lượng. 76
68 Th is is the term for weighted distribution found in chapter 3 of the Jiu zhang suan shu ; see
SJSSb : 109ff.
69 Or: ‘in the upper [position]’.
70 Or: ‘in the lower [position]’.
71 H e r e t h e t e r m may be a formal title of an offi cial; see Hucker 1985 : 162.
72 It is worth noting that counting rods and not the abacus are mentioned here. According to the
report of Giovanni Filippo de Marini (1608–82), counting rods were still in use in Vietnam
as late as the mid seventeenth century; see Volkov 2009 : 160–4. However, one cannot rule out
the possibility that the term toán may have been used here as a metaphorical reference to a
counting instrument in general.
73 Probably, a quotation from the ending of the problem ‘... [those who] arrange and dispose [the
counting rods], in order to inspect.. .’
74 Th at is, 1 cân = 16 lượng , therefore to convert an amount of money from cân to lượng one
has to multiply it by 16.
75 Th is phrase does not have any particular mathematical meaning and appears to be a quotation
from a text that I have been unable to identify.
76 Th at is, the authorities retained some amount of money for the good of the functionaries.
Th is is but a tentative rendering of a rather obscure paragraph explaining why not the entire