If the reader has already studied the modern abacus he knows for sure why it is preferable to operate from left to right, and this is not only a question of the use of the abacus. Some old books on the abacus, for instance, Mathematical Track ( Shùxué Tōngguǐ 數學通軌) by Kē Shàngqiān (柯尚遷) (1578), demonstrate the addition using an alternating direction of operation with the obvious intention of saving hand movements. We dedicate the following chapter: Use of the 5th lower bead to this subject. Its use is demonstrated in some ancient books such as: Computational Methods with the Beads in a Tray ( Pánzhū Suànfǎ 盤珠算法) by Xú Xīnlǔ 徐心魯 (1573), but over time it ceased to appear in the manuals, perhaps as a non-fundamental technique it was no longer explained in the concise books of the past but surely it continued to be taught verbally, as a trick to abbreviate the operations. The lower fifth bead can be used in addition and subtraction operations just like its companions. Of which the first is by far the most important.ĥth lower bead First two pages of the Pánzhū Suànfǎ 盤珠算法 (1573) alternating rightward and leftward operation to save hand displacements. use of the lower fifth bead to simplify the operations.The only two additional points to consider are: There is hardly any difference between addition and subtraction with a modern abacus or a traditional one, if the reader already knows how to perform these two operations fluently with a modern abacus, he will also do well with a traditional one. Everything else has to be decomposed into a sequence of addition and subtraction. Addition and subtraction are the only two possible operations on any type of abacus. With any abacus type, addition is simulated by gathering the sets of counters representing the two addends, while subtraction is simulated by removing from the set of counters representing the minuend a set of counters representing the subtrahend.
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