日食度 - 翻刻

翻刻

　此＿レ列＿二多数＿一内減＿二少数＿一為＿レ実以＿レ方乗＿レ実得
　商五連収＿レ之以＿レ億命＿レ度為＿レ差也
一加減差
　二月加差空度三十五分九十秒
　八月減差空度五十三分九十五秒
　　陳曰盈差￣カ与縮差￣カ置＿レ右遅差￣カ与疾差￣カ与
　　置＿レ左左右相比盈遅相並縮疾相並為＿二
　　之同名＿一相加也又縮遅相並盈疾相並

　　為＿二異名＿一相減也其盈与遅相並者盈￣ト与＿レ疾
　　相並者謂＿二之加差＿一也其縮￣ト与＿レ疾相並者縮￣ト与
　　遅相並者謂＿二之減差＿一也
　　　此術中亦其位準＿下求＿二盈縮差＿一者＿上也
○求＿二二月加差＿一術曰
　盈差遅差左右列＿レ之即同名也左右相加以＿二入
　転日転定度一十四箇四七八＿一除＿レ之得商為＿二加
　差＿一也

現代語訳

この列の多数の中から少数を減じたものを実とし、方をもって実に乗じ、商を得て五連収し、億をもって度に命じ、差とする。

一、加減差
　二月（盈暦）の加差：空度三十五分九十秒
　八月（縮暦）の減差：空度五十三分九十五秒

　　陳が言うには：盈差と縮差を右に置き、遅差と疾差を左に置く。左右を比較して、盈・遅が並ぶ場合と縮・疾が並ぶ場合は「同名」として互いに加え合わせる。また縮・遅が並ぶ場合と盈・疾が並ぶ場合は「異名」として互いに減じ合わせる。盈と遅が並ぶ場合、および盈と疾が並ぶ場合を「加差」という。縮と疾が並ぶ場合、および縮と遅が並ぶ場合を「減差」という。
　　この術の中においても、その位は盈縮差を求める方法に準じる。

○二月の加差を求める術に曰く：
　盈差と遅差を左右に列べる。すなわち同名である。左右を相加えて、転日・転定度十四箇四七八をもって除し、得た商を加差とする。

英語訳

From the listed larger number, subtract the smaller number to obtain the *shi* (dividend/operand); multiply the *shi* by the *fang* (square/multiplier); obtain the quotient by five successive reductions; designate it as degrees using *yi* (hundred million), and this becomes the difference (*cha*).

**I. Additive-Subtractive Difference (加減差, Jiājiǎn Chā)**
　Additive difference for the 2nd month (Ying calendar): 0 degrees, 35 minutes, 90 seconds
　Subtractive difference for the 8th month (Suo calendar): 0 degrees, 53 minutes, 95 seconds

　　Chen states: Place the Ying difference (盈差) and Suo difference (縮差) on the right; place the slow difference (遅差) and fast difference (疾差) on the left. Compare left and right: when Ying and slow (遅) are paired together, or when Suo and fast (疾) are paired together, they are "same-name" (同名) and are added together. When Suo and slow (遅) are paired together, or Ying and fast (疾) are paired together, they are "different-name" (異名) and are subtracted from each other. When Ying is paired with slow, or Ying is paired with fast, this is called the "additive difference" (加差). When Suo is paired with fast, or Suo is paired with slow, this is called the "subtractive difference" (減差).
　　In this method as well, the positional values follow the same standard as those used in seeking the Ying-Suo difference.

○Method for finding the additive difference of the 2nd month:
　List the Ying difference and the slow difference side by side on left and right — these are same-name. Add left and right together, divide by the transit-day transit-fixed-degree value of 14 units [×] 478; the resulting quotient is the additive difference.