算例：增乘開平方術

[jingkecn]

緒

增乘開平方法乃北宋數學家賈憲所創，原作已佚，幸由南宋數學家楊輝引於《永樂大典》得傳。

文

增乘開平方法，以商數乘下法遞增求之。
商第一位。上商得數以乘下法為乘方。命上商除實。上商得數以乘下法入乘方。一退為廉，下法再退。
商第二位。商得數以乘下法為隅。命上商除實訖。以上商乘下法入隅，皆名曰廉。一退，下法再退，以求第三位商。
商第三位。用法如第二位求之。

圖

參見楊輝算草。
另有現代代數直式開方圖解：

引

[1] 增乘開平方法——維基百科
[2] 力扣（LeetCode）第六十九題：中 | 英（附題解）

[LingDong-]

Thanks for fixing, let me know when it is ready :)

[jingkecn]

Thanks for fixing, let me know when it is ready :)

It should be ready now :)

[LingDong-]

@jingkecn It seems to be causing an infinite loop... Did it work for you? It hangs for me in both browser and the command-line.

[jingkecn]

@jingkecn It seems to be causing an infinite loop... Did it work on you? It hangs for me in both browser and the command-line.

Strange. I'll check it and tell you when it's ready.

[jingkecn]

@jingkecn It seems to be causing an infinite loop... Did it work for you? It hangs for me in both browser and the command-line.

It should really be OK, now. I forgot to retrieve 商 from the result of 取底除 to update my 實, which causes an infinite loop...😂

[LingDong-]

Looks good! Thanks for the new example!