Systematic Treatise on Arithmetic, Vol. 3

### ○ The three styles of the cart from the lower section of the previous diagram are here combined into one to show the finished model above. ○

The outer casing resembles an ink-box original: 墨匣 (moxia). A traditional Chinese box used to hold an inkstone and ink stick. that lacks both a lid and a bottom. The wooden pieces on both sides are sized relative to the internal cross-timber, leaving enough empty space at both ends.

The horizontal beams are joined at the corners using mortise-and-tenon joints original: 栒 (sun). Specifically refers to the interlocking joints in Chinese carpentry.; the interior space is just large enough to allow the cross-timber to rotate. A "box-eye" (socket) is carved into the lower horizontal beam.

The bamboo measuring tape original: 篾 (mie). Thin, flexible strips of bamboo used here as a measuring line. exits the casing in a configuration where the back is high and the front is low. A ring can be nailed to the top, while "drilling feet" (anchors) are nailed to the bottom.

The center of the cross-timber is designed like an ink-fountain original: 墨斗 (modou). A carpenter's tool used for marking straight lines; it contains a reel of thread passed through an ink reservoir.. The winding handle original: 攪轉之心 (jiaozhuan zhi xin). Literally "the heart of the stirring/turning." is shaped like a carpenter's square original: 曲尺 (quchi). An L-shaped square. with three folds. The portion of the handle installed inside the center of the cross is square-shaped so that it does not slip; the outer portions are all rounded to allow for free movement when retracting or extending the tape, much like the mechanism of a spinning wheel.

A hole is carved beneath the upper horizontal beam of the outer casing. Each of the four ends of the internal cross-timber has a notch cut into it; whenever one of these ends aligns with the hole in the casing, it can be secured in place using a bolt.

When preparing the bamboo measuring tape, select young bamboo with straight, flat joints. At the points where the strips are joined together, bind them securely with copper wire.

Characters must be written onto the bamboo tape inch by inch:

• Each inch represents two li term: li (厘). A decimal unit of area or length; here it likely represents 0.002 of a larger unit..
• Two inches represent four li.
• Three inches represent six li.
• Four inches represent eight li.
  One does not necessarily have to follow the rule of five inches equaling one fen term: fen (分). A unit ten times larger than a li.. From one fen up to...

**Technical