《汉书·志·律历志下》
推算朔日：用月法乘月元余，满曰法得一，叫做积曰，余名叫做小余。
推朔日，以月法乘月元余，盈日法得一，名曰积日，余名曰小余。
Calculate the first day of the lunar month: multiply the month law by the month of the New Year remainder. If the full day law is 1, it is called the accumulated day. The remainder is called the small remainder.
<s>[INST] Given the Classical Chinese text: 推朔日，以月法乘月元余，盈日法得一，名曰积日，余名曰小余。, provide a step-by-step translation process to arrive at the English translation. [/INST]
**Step 1: Word-for-word translation**
推朔日 = calculate the first day of the lunar month
以月法乘月元余 = multiply the month law by the month of the New Year remainder
盈日法得一 = if the full day law is 1
名曰积日 = it is called the accumulated day
余名曰小余 = the remainder is called the small remainder

**Step 2: Grammatical analysis**
推朔日 is the verb phrase, meaning "calculate the first day of the lunar month".
以月法乘月元余 is the adverbial phrase, modifying 推朔日, meaning "multiply the month law by the month of the New Year remainder".
盈日法得一 is the conditional clause, meaning "if the full day law is 1".
名曰积日,余名曰小余 are the result clauses, meaning "it is called the accumulated day" and "the remainder is called the small remainder" respectively.

**Final English translation:**
Calculate the first day of the lunar month: multiply the month law by the month of the New Year remainder. If the full day law is 1, it is called the accumulated day. The remainder is called the small remainder.</s>
Given the Classical Chinese text: 推朔日，以月法乘月元余，盈日法得一，名曰积日，余名曰小余。, provide a step-by-step translation process to arrive at the English translation.
user
**Step 1: Word-for-word translation**
推朔日 = calculate the first day of the lunar month
以月法乘月元余 = multiply the month law by the month of the New Year remainder
盈日法得一 = if the full day law is 1
名曰积日 = it is called the accumulated day
余名曰小余 = the remainder is called the small remainder

**Step 2: Grammatical analysis**
推朔日 is the verb phrase, meaning "calculate the first day of the lunar month".
以月法乘月元余 is the adverbial phrase, modifying 推朔日, meaning "multiply the month law by the month of the New Year remainder".
盈日法得一 is the conditional clause, meaning "if the full day law is 1".
名曰积日,余名曰小余 are the result clauses, meaning "it is called the accumulated day" and "the remainder is called the small remainder" respectively.

**Final English translation:**
Calculate the first day of the lunar month: multiply the month law by the month of the New Year remainder. If the full day law is 1, it is called the accumulated day. The remainder is called the small remainder.
assistant