翻刻
《題：帯縦開立目安割》
九九八十一ニ九掛七百廿九引九進
▲帯縦開立
千八百七拾弐坪を長横同間ニ
高サ一間高ニ方ヲ問
長横十二間
ト云
高サ十三間
法ニ位を見十間四方ニテ百坪高
サ十間ニテ千坪一進之一進千坪
引十間ト真を定開立一三ノ三
と目安ニ立高サ一間増之分ニ百
坪引残る七百七拾弐坪有ヲ目
安之三にて六進之二進ト二間ト
知六百坪引残り百七拾弐坪有
二間之二ト開立之三ト二三之六
ト目安ニ立此六ト二間之二ヲ見合
二六之百弐十坪三所之角に
引高サ壱間高キ分ニ一方ニて
現代語訳
《題：帯縦開立目安割》
九九八十一に九掛け七百二十九引いて九進
▲帯縦開立
千八百七十二坪を長さと横が同じ間数で、
高さ一間高い方を問う
長さ・横 十二間
と云う
高さ 十三間
法として、位を見るに、十間四方にて百坪、高
さ十間にて千坪。一進の、一進千坪を
引き、十間と真を定め、開立の一三の三
を目安に立てる。高さ一間増しの分に百
坪引き、残る七百七十二坪有るを、目
安の三にて六進の二進と、二間と
知る。六百坪引き、残り百七十二坪有り。
二間の二と、開立の三と、二三の六
を目安に立て、この六と二間の二を見合わせ、
二六の百二十坪を三箇所の角に
引き、高さ一間高い分に一方にて
英語訳
《Title: Taijū Kairitsu Meyasuwari (Cube Root Extraction with Accompanying Vertical Dimension — Target Divisor Method)》
Nine-nine eighty-one: multiply by nine, subtract seven hundred twenty-nine, ninth advance.
▲ Taijū Kairitsu (Cube Root Extraction with Accompanying Vertical/Height Dimension)
Problem: Find the dimensions of a solid with 1,872 tsubo [cubic units], where the length and width are equal, but the height is one ken greater than the length/width.
Length and width: 12 ken
— This is the answer.
Height: 13 ken
Method: Examining the place values — a 10-ken square gives 100 tsubo [per unit height]; at 10 ken height that gives 1,000 tsubo. After one advance, subtract the 1,000 tsubo of "one advance," fix 10 ken as the base value, and set up the "one-three of three" from the cube root [algorithm] as the target guide. For the portion corresponding to the height being one ken greater, subtract 100 tsubo; the remaining 772 tsubo — using the target guide of "three," determine this as the second of six advances, i.e., 2 ken. Subtract 600 tsubo; the remainder is 172 tsubo. Taking the "two" of the two ken and the "three" of cube root [algorithm], and setting up "two-three of six" as the target guide, comparing this six with the "two" of two ken — [calculate] "two-six" of 120 tsubo, and subtract it from the three corner positions. For the portion where the height is one ken greater, with one side—