542 alexei volkov
[5] As for the [remaining] 5292 lượng , [one] measures this amount of
money for the awarded
[6] aforesaid corpus of 328 functionaries. Th en [if ] this money is given to
this establishment [= functionaries] and [they are] awarded in the same
way,
[7] [it is as] if [one] uses the method of ‘fl at-rate distribution’. [One] sets
above^77 the number of the persons, [one] sets below 78 this [amount of ]
money. 79 Using the divisor [one] divides [the amount of money] by the
‘evaluation division’ and by ‘returning [division]’; 80
[8] [one] immediately establishes that every person obtains 16 lượng 1 tien
3 phan 4 li. 81 Th us this money [could] not
[9] be entirely [paid and] there would be a remainder of 4 phan 8 li. 82 T o g e t
the actual [value], one can use the methods of reduction of fractions to
common denominator and of injection [of integer parts of mixed frac-
tions] into numerators. 83 [If ] these men’s categories
/p. 31b/
[1] are classifi ed as high and low, being at the same level [only within] one
rank, [then] this action is not to be called ‘analysing [correctly] the
inner structure [of it]’ 84 and there is [something]
[2] unreliable. [If ] this is so, then the ‘method of fl at-rate distribution’amount of 16000 lượng was distributed among the functionaries and why the 10708 lượng
should have been deducted from the original amount of 1000 cân.78 Or: ‘secondly’.
79 If the counting instrument supposed to be used is the counting rods, then the positions of the
operands (divisor in the upper position and the dividend in the lower position) diff ers from
the classical Chinese disposition of the operands represented with the counting rods (divisor
below and the dividend above) described in the Sun zi suan jing (see SJSSb : 262). Th e standard
methods of division performed with the abacus I am aware of all assume that the dividend is
to be set in the left (= upper) part of the abacus, and the divisor in its right part. I am thankful
to K. Chemla who drew my attention to this particularity of the Vietnamese method (private
communication, 2008).
80 For a very short discussion of the methods of division shang chu and gui (in Mandarin
transcription of the characters) mentioned here see LD1987: 181–3.77 O r : ‘ fi rstly’.81 Indeed, 5292 ÷ 328 = 16.134(14634).
82 Th at is, 5292 − 328·16.134 = 5292 − 5291.952 = 0.048.
83 Th is phrase can be understood as saying that one can obtain an exact value if a common
fraction is used instead of decimal one.
84 Th is rather rough translation of the expression ( qing qi li in Mandarin transcription)
would require a long discussion of the term qing which cannot be off ered here; the
interested reader is referred to CG2004: 970 for an interpretation of the term as employed by
Liu Hui.