The way in which the sequence of fascicules and occasionally the juan 卷 of a Chinese book is expressed is sometimes more elaborate than simple numbering. Here are the various methods I have encountered over the years. I have tried to trace the less obvious numbering sequences to their earliest textual expression, which determines the order in which the sequences should be arranged.
Sets of two and three respectively, so termed because traditionally books were laid flat on the shelf with the first fascicle uppermost (and still are in the best of circles). In very common use.
The three cardinal virtues taught by Confucius in the Analects (論語, 9): wisdom, benevolence, courage. Example: Bodleian Library, Chin.d.4728.
The “four principles of Heaven and Earth” (乾卦四德), being the opening words of the Zhouyi 周易. They beggar translation, and whole books have been written on their meaning. In common use.
The first four of the “Eight virtues” (八德) explained below. They do not appear to be enumerated anywhere independently of the last four. Example: Bodleian Library, Sinica 3003 (section numbering).
The “Four teachings” (四教) of Confucius, set out in the Analects (論語, 7): scholarship, good conduct, loyalty, and truthfulness. Example: Bodleian Library, Backhouse 163 (box numbering).
The four seasons. Example: Bodleian Library, Backhouse 143.
The “Five Moral principles” (五常): benevolence，duty, courtesy，wisdom，trustworthiness. They are set forth in one of Dong Zhongshu’s 董仲舒 memorials to the throne, recorded in his biography in the Hanshu (漢書, 卷56, where 誼 is used for 義). Example: Bodleian Library, Sinica 2241.
The “Five elements” (五行), first enumerated in the Shangshu (尚書, 洪范): metal, wood, water, fire, and earth.
The “Six arts” (六藝): ritual, music, archery, charioteering, calligraphy, and arithmetic. These were the basis of education in ancient China, and are set forth by by Xu Gan 徐幹 (170-217 BC) in the first section (治學) of his Zhonglun 中論. Examples: Bodleian Library, Chin.d.7750, Chin.d.13405/9(4).
The “Eight tones” (八音) of Chinese music referred to in the Shangshu (尚書, 舜典), but first enumerated in the Zhouli (周禮, 3: 春官宗伯). They are preceded by the “Five sounds” (五聲): 宮、商、角、徴、羽, but I have not seen an example of the use of these in numbering fascicules or juan. Examples: Bodleian Library, Sinica 2875, Sinica 426, Sinica 427 (juan numbering).
The “Eight virtues” (八德) of filial piety, fraternal piety, loyalty，trustworthiness，correct behaviour，propriety，sense of honour，and sense of shame. It was difficult for me to find the earliest textual source for this sequence, but Zhu Guangli 朱光立 has told me that it is generally thought to have been Zhu Xi 朱熹 (1130-1200), but is actually the much earlier Yang Yi 楊億 (974-1020); Zhu Xi quotes the text Yang Wengong jiaxun 楊文公家訓 (which seems to be lost) in his Xiaoxue (小學, 5). Example: Muban Foundation, no.345.