This material has been published in Historia Mathematica, 1979,
6:164-188, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.
The Jiuzhang suanshu ("Arithmetic in nine chapters") is a
mathematical book of the late first century A.D. It gives practical problems
and states algorithms for their solution, with no explanation. A commentary
attributed to Liu Hui , of the third century A.D., gives an explanation of each
algorithm; these explanations satisfy many of the criteria for what we would
call a proof. In this article Liu Hui's explanation of the formula for the
volume of a particular kind of pyramid is translated and discussed.
Das Jiuzhang suanshu ("Neun Bücher arithmetischer
Technik" ist ein mathematisches Buch aus dem späten ersten Jahrhundert
unserer Zeitrechnung. Es stellt praktische Probleme der und gibt Algorithmen,
jedoch ohne jede Erklärung, für ihre Lösung. Ein Kommentar, der
Liu Hui aus dem dritten Jahrhundert zugeschrieben wird, erläutert jeden
einzelnen Algorithmus; diese Erläuterungen weisen viele der Merkmale auf,
die bei uns einen mathematischen Beweis charakterisieren. In diesem Artikel
wird Liu Hui's Erläuterung von der Formel vom Rauminhalt einer besonderen
Art Pyramide übersetzt und näher besprochen.
For this Web version I have converted the transcription to Pinyin and inserted the Chinese characters. Otherwise virtually no changes have been made to the original article.
("Arithmetic in nine chapters") is a mathematical book of the late first century A.D. It gives practical problems and states algorithms for their solution, with no explanation. A commentary attributed to Liu Hui
, of the third century A.D., gives an explanation of each algorithm; these explanations satisfy many of the criteria for what we would call a proof. In this article Liu Hui's explanation of the formula for the volume of a particular kind of pyramid is translated and discussed.