/
1.cmd
361 lines (307 loc) · 10.1 KB
/
1.cmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
< /resources/rules/yawnoc.cmdr
< /resources/rules/rendering.cmdr
< /resources/rules/equations.cmdr
< /resources/rules/language.cmdr
< /resources/rules/translation.cmdr
< /resources/rules/romanisation.cmdr
< /resources/rules/sun-tzu.cmdr
< /resources/rules/surrounds.cmdr
OrdinaryDictionaryReplacement: #.footer-properties-override
- queue_position: AFTER #.yawnoc.footer
* %copyright-prior-years --> get_year@%date-created--
OrdinaryDictionaryReplacement: #.boilerplate-properties-override
- queue_position: AFTER #.yawnoc.properties-override
* %cite-title --> '"Sun~Tz(uu)'s Computational Classic: Volume~I \S1"'
* %title --> "Sun~Tz(uu)'s Computational Classic: Volume~I" 《孫子算經卷上》 \S1
* %date-created --> 2019-06-09
* %date-modified --> 2023-10-21
- concluding_replacements:
#.yawnoc.typography
#.romanisation.special-characters
OrdinaryDictionaryReplacement: #.surrounds-navigation
- queue_position: AFTER #.yawnoc.properties-override
* %%surrounds-up --> [^ Volume~I](./)
* %%surrounds-previous --> [<-- Vol.~I](./)
* %%surrounds-current --> \S1
* %%surrounds-next --> [\S2 -->](2)
- concluding_replacements: #.surrounds.navigation-arrows
%%%
^^^^
- !home
- !top
- !sun-tzu
-{.breadcrumbed} !i
-{.breadcrumbed} !!1
- !cite
^^^^
# .《孫子算經卷上》 "(Sun~Tz(uu)|孫子)'s Computational Classic: Volume~I" <br>
\S1. Units of length (or distance)
%%noscript-equations
%%surrounds
--
This section introduces Chinese units of length
and gives the conversion rates between them.
--
##{#translation} Translation
--
Chinese source text: \a[4], \b[146], \c[52058], \d[11]. <br>
%%version-d-default
--
@@@@
<<
度之所起、起於忽。欲知其忽、蠶吐絲為忽。
\\
.[Of] that which measuring length beginneth from:
beginneth .[it] from floss.
Wishing to know .[the size of] floss:
the silkworm spitteth thread .[which] be floss.
>>
==
* .度: measuring of length
--
.度、入聲、 \C tok9, \M du(o\) (\gr du(o/))
--
* .起: beginneth from; \lit ariseth from
* .忽: floss
--
(Hut|忽)~(.忽), a hundred-thousandth of the Chinese inch, (ts(')un|寸)~(.寸).
[(K(')ang\-hee|康熙)'s Dictionary](https://ctext.org/kangxi-zidian/61/4#n326385),
quoting .《劉德曰》, "(Liu Tek|劉德) saith",
has .忽、蜘蛛網也, "floss, .[a] spider's web".
--
* \c[52058] has .蠶所生、吐絲為忽.
==
<<
十忽為一絲、 <br>
十絲為一毫、 <br>
十毫為一釐、 <br>
十釐為一分、 <br>
十分為一寸、 <br>
十寸為一尺、 <br>
十尺為一丈、 <br>
十丈為一引、
\\
Ten flosses make one thread; <br>
ten threads make one mil; <br>
ten mils make one cent; <br>
ten cents make one tenth; <br>
ten tenths make one inch; <br>
ten inches make one rule; <br>
ten rules make one rod; <br>
ten rods make one draw.
>>
==
* .絲: (silk) thread
--
(Ss(uu)|絲)~(.絲),
a ten-thousandth of the Chinese inch, (ts(')un|寸)~(.寸).
--
* .毫: mil; \lit fine-hair
--
(Hao|毫)~(.毫), a thousandth of the Chinese inch, (ts(')un|寸)~(.寸).
Similar to the imperial [mil or thou].
--
[mil or thou]: https://en.wikipedia.org/wiki/Thousandth_of_an_inch
* .釐: cent
--
(Lee|釐)~(.釐),
a hundredth of the Chinese inch, (ts(')un|寸)~(.寸).
--
* .分: tenth
--
(F(e^)n|分)~(.分),
a tenth of the Chinese inch, (ts(')un|寸)~(.寸).
--
* .寸: inch
--
(Ts(')un|寸)~(.寸), the [Chinese inch].
Of the same order of magnitude as the imperial inch,
and used figuratively as the inch is in English
to denote a small distance,
so I am happy to simply render it as "inch".
--
[Chinese inch]: https://en.wikipedia.org/wiki/Cun_(unit)
* .尺: rule; \or ruler
--
(Ch(')ek|尺)~(.尺), ten Chinese inches.
This is of the order one foot,
but I have not rendered this as "foot"
because there is no such connotation.
Some translate this as "cubit",
but a cubit is more like one and a half feet, or even two.
The term "covid" appears to have been used in colonial Hong Kong,
but I can't seem to find much about it on the internet...
thanks a lot, WHO.
--
* .丈: rod; \or measure
--
(Chang|丈)~(.丈), ten rules.
Difficult to render because Chinese dictionaries
simply define it as ten rules.
More generally its meanings are "elder male",
from the interchangeable .杖 or "walking stick",
and "to measure/survey land".
I have chosen "rod" for its few letters & monosyllabicity,
and because of the [imperial rod],
of the same order of magnitude and also related to surveying.
Also Moses had one.
--
[imperial rod]: https://en.wikipedia.org/wiki/Rod_(unit)
* .引: draw; \or pull
--
(Yin|引)~(.引), ten rods.
--
==
<<
五十尺為一端、 <br>
四十尺為一匹、 <br>
六尺為一步、
\\
Fifty rules make one end; <br>
forty rules make one length; <br>
six rules make one pace.
>>
==
* .端: end
--
(Tuan|端)~(.端), fifty rules.
--
* \b[146] erroneously has .五十引為一端.
* .匹: length
--
(P(')it|匹)~(.匹), forty rules.
This is the only unit rendering which I am unsatisfied with.
.匹 is the classifier for cloth, .一匹布 being "one length of cloth".
--
* .步: pace; \or step
--
(Pu|步)~(.步), the Chinese pace, six rules.
--
==
<<
二百四十步為一畝、
\\
Two hundred .[and] forty paces make one acre.
>>
==
* .畝: acre; \lit field
--
(Mu|畝)~(.畝), 240~square paces.
Classical Chinese mathematics did not have
a fully developed notion of dimensional analysis,
so 'square paces' were simply referred to as 'paces'.
While a (mu|畝)~(.畝) is only about a fifth of an [imperial acre],
I have chosen to render it acre
because both have the etymological meaning "field".
--
[imperial acre]: https://en.wikipedia.org/wiki/Acre
==
<<
三百步為一里。
\\
Three hundred paces make one mile.
>>
==
* .里: mile
--
(Lee|里)~(.里), the [Chinese mile],
of the order half a kilometre.
While this is much shorter than the imperial mile,
it is figuratively used as the mile is in English
to denote a large distance,
so I am happy to simply render it as "mile".
--
[Chinese mile]: https://en.wikipedia.org/wiki/Li_(unit)
==
@@@@
##{#commentary} Extended commentary
--
I can't be bothered looking up a reputable source
for the precise length of a (ch(')ek|尺)~(.尺) or rule
when (Sun~Tz(uu)|孫子)'s Computational Classic was first written,
but using 0.3~metres as an estimate,
we have:
--
$$
\begin{alignedat}{3}
1 \unit{floss~(忽)} &={} & 10^{-6} & \unit{rules} && \sim 0.3 \unit{μm} \\
1 \unit{thread~(絲)} &={} & 10^{-5} & \unit{rules} && \sim 3 \unit{μm} \\
1 \unit{mil~(毫)} &={} & 10^{-4} & \unit{rules} && \sim 30 \unit{μm} \\
1 \unit{cent~(釐)} &={} & 10^{-3} & \unit{rules} && \sim 0.3 \unit{mm} \\
1 \unit{tenth~(分)} &={} & 10^{-2} & \unit{rules} && \sim 3 \unit{mm} \\
1 \unit{inch~(寸)} &={} & 10^{-1} & \unit{rules} && \sim 30 \unit{mm} \\
1 \unit{rule~(尺)} &={} & 1 & \unit{rule} && \sim 0.3 \unit{m} \\
1 \unit{rod~(丈)} &={} & 10 & \unit{rules} && \sim 3 \unit{m} \\
1 \unit{draw~(引)} &={} & 100 & \unit{rules} && \sim 30 \unit{m} \\
1 \unit{end~(端)} &={} & 50 & \unit{rules} && \sim 15 \unit{m} \\
1 \unit{length~(匹)} &={} & 40 & \unit{rules} && \sim 12 \unit{m} \\
1 \unit{pace~(步)} &={} & 6 & \unit{rules} && \sim 1.8 \unit{m} \\
1 \unit{acre~(畝)} &={} & 240 & \unit{paces}^2 && \sim 780 \unit{m}^2 \\
1 \unit{mile~(里)} &={} & 300 & \unit{paces} && \sim 540 \unit{m}.
\end{alignedat}
$$
--
Silk is around 12~μm in thickness ([Luong~et~al.~(2014)])
so (hut|忽)~(.忽), "floss", is much too thin,
and (ss(uu)|絲)~(.絲), "(silk) thread", still a little thin.
Thus .蠶吐絲為忽, "the silkworm spitteth thread .[which] be floss",
is an exaggeration of the thinness of silk.
But my job is only to translate the text as it is, not to correct it.
--
[Luong~et~al.~(2014)]: https://www.researchgate.net/publication/263089345_Investigation_of_the_Silk_Fiber_Extraction_Process_from_the_Vietnam_Natural_Bombyx_Mori_Silkworm_Cocoon
--
By the later part of the (Ts(')ing|清) Dynasty,
one (ch(')ek|尺)~(.尺) or rule is 14⅝~inches in Hong Kong.
Reading through historical versions of the [Weights and Measures Ordinance]
enacted by the British in Hong Kong,
[Ordinance No.~22 of~1844 (PDF)]
gives the following conversions between Chinese length units
(consistent with those above):
--
||{.centred}
![
Image of Ordinance Number 22 of 1844, British Hong Kong. \
Measures of Length. \
Ten Fun 分 make one 寸 Tsun. \
Ten Tsun 寸 make one 尺 Chih (or Covid). \
Ten Chih 尺 make one 丈 Chang. \
Ten Chang 丈 make one 引 Yin.
](ord-1844-no-22-length.jpg)
||
--
However, it is very interesting to note that
the British only standardised these
Chinese length units with reference to English units
in [Ordinance No.~8 of~1885 (PDF)],
more than four decades later:
--
||{.centred}
![
Image of Ordinance Number 8 of 1885, British Hong Kong. \
Length. \
One Chek (foot) equal to fourteen and five eighths English inches, \
divided into ten Tsün or inches, \
and each inch into ten Fan or tenths. \
](ord-1885-no-8-length.jpg)
||
--
Eventually the (ch(')ek|尺)~(.尺) is given
the equivalent definition of 0.371475~metres,
used unto this day in Hong Kong;
see [Cap.~68 Weights and Measures Ordinance].
(Floor plans are reckoned in imperial feet though, written ".呎".)
--
--
Taiwan uses a (ch(')ih|尺)~(.尺) from the Japanese occupation
equal to 10/33 of a metre, i.e.~0.3030...~metres,
and Mainland China uses a metric-based (chi|尺)~(.尺)
equal to 1/3 of a metre, i.e.~0.3333...~metres.
In either case, ugh to recurring decimals.
--
[Weights and Measures Ordinance]: https://oelawhk.lib.hku.hk/exhibits/show/oelawhk/searchresult?stext=weight+measure&x=16&y=15&sfield=ZZ&edition=1890&no_result=10
[Ordinance No.~22 of~1844 (PDF)]: http://oelawhk.lib.hku.hk/archive/files/9c24f167a27b616a75db9691574eb925.pdf
[Ordinance No.~8 of~1885 (PDF)]: http://oelawhk.lib.hku.hk/archive/files/52fa22f83069cf6a385779d462a0f6e7.pdf
[Cap.~68 Weights and Measures Ordinance]: https://www.elegislation.gov.hk/hk/cap68
%%surrounds
%%cite
%%footer