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6.cmd
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6.cmd
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< /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
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* %copyright-prior-years --> get_year@%date-created--
OrdinaryDictionaryReplacement: #.boilerplate-properties-override
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* %cite-title --> '"Sun~Tz(uu)'s Computational Classic: Volume~III \S6"'
* %title --> "Sun~Tz(uu)'s Computational Classic: Volume~III" 《孫子算經卷下》 \S6
* %date-created --> 2022-08-14
* %date-modified --> 2023-04-29
- concluding_replacements:
#.yawnoc.typography
#.romanisation.special-characters
OrdinaryDictionaryReplacement: #.surrounds-navigation
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* %%surrounds-up --> [^ Volume~III](./)
* %%surrounds-previous --> [<-- \S5](5)
* %%surrounds-current --> \S6
* %%surrounds-next --> [\S7 -->](7)
- concluding_replacements: #.surrounds.navigation-arrows
%%%
^^^^
- !home
- !top
- !sun-tzu
-{.breadcrumbed} !iii
-{.breadcrumbed} !!6
- !cite
^^^^
# .《孫子算經卷下》 "(Sun~Tz(uu)|孫子)'s Computational Classic: Volume~III" <br>
\S6. Division utilising a rate~(1)
%%noscript-equations
%%surrounds
--
This section gives a word problem
where division by a rate is used to determine an amount.
--
##{#translation} Translation
--
Chinese source text: \a[60], \b[160], \c[52232], \d[72]. <br>
%%version-d-default
--
@@@@
<<
今有租九萬八千七百六十二斛、欲以一車載五十斛。問用車幾何。
\\
Suppose there be land-tax
nine myriad eight thousand seven hundred .[and] sixty-two barrels,
.[and we] wish to use one chariot .[to] carry fifty barrels.
.[We] ask, how many chariots useth .[it]?
>>
<<
答曰、一千九百七十五乘奇一十二斛。
\\
Answer saith: one thousand nine hundred .[and] seventy-five chariots
remainder twelve barrels.
>>
==
* .乘: chariot
--
.乘、去聲、 \C shing6 (\pm sing6), \M sh(e\)ng
--
==
<<
術曰、置租九萬八千七百六十二斛為實、以一車所載五十斛為法。
\\
Method saith: put .[down the] land-tax
nine myriad eight thousand seven hundred .[and] sixty-two barrels
as .[the] dividend,
.[and] use that carried of one chariot, .[even] fifty barrels,
as .[the] divisor.
>>
==
* \a[60] and \d[72] are missing .二 in .六十二斛.
==
<<
實如法、即得。
\\
.[Taking the] dividend as .[per the] divisor, .[we] are done.
>>
==
* In modern notation,
$$
\frac{98762 \unit{barrels}}{50 \unit{barrels} / {\unit{chariot}}}
= 1975 \unit{chariots}
+ \frac{12 \unit{barrels}}{50 \unit{barrels} / {\unit{chariot}}}.
$$
==
@@@@
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