《明史·志·卷九》
里差刻漏将测到的冬至夏至时的黄道赤道内外度二十三度九十分为半弧背，用前述的方法推算出内外半弧弦为二十三度七十一分。
置测到二至黄赤道内外度二十三度九十分为半弧背，以前法推得内外半弧弦二十三度七十一分。
A half-hour of the legend will measure the inner and outer degrees of the ecliptic and the equator at the winter solstice and the summer solstice as 23 degrees and 90 minutes as the back of the half arc, and use the aforementioned method to calculate the inner and outer half-arc strings as 23 degrees and 71 minutes.