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宋代算学家秦九韶鉴于当时有人测雨水深度不合实际,特就雨深(?)厚的計算各举二例,以资糾正。这四个例題及其解法,載在秦著“数书九章”(1247)第四卷,清代李銳所校这部书的四庫館本(以下簡称館本)及沈欽裴宋景昌等都曾加以研究:提出解释;辨別精蕪,指明錯誤,改立水草。这些,对于国故的整理,实有所裨益;但还有須斟酌的地方。茲逐例解答,并討論之。第一例天池测雨此例首先說:“今州郡都有天池盆以测雨水,但知以盆中之水为得雨之数,不知器形不同,則受雨多少亦异,未可以所測便为平地得雨之数”。这就是說:有人不管容器的形状怎样,把器里水深当做平地雨深,是不对的。
In the Song Dynasty, an ethnographer, Qin Jiulu, made inaccurate calculations of rain depths (?) to give corrections in view of the fact that some people measured the depth of rain. These four examples and their solutions are set out in the fourth volume of the book Qin Shu’s “Single Book Chapter 9” (1247), the four-library pamphlet of the book by Li Rui’s school in the Qing Dynasty (hereinafter referred to as “Guanben”) and Shen Qinyu. Song Jingchang and others had studied it: proposed explanations; distinguished finesse, pointed out mistakes, and reformed water plants. These are indeed beneficial for the country’s consolidation; but there are also places where we must consider. We will answer them case by case and discuss them. The first case of Tianchi measures rain. This example first states: “In this county, there are Tianchi basins to measure rainwater, but knowing that the water in the basin is the number of rain, if you don’t know the shape of the basin, then how much the rain is affected is different. It was measured as the number of rain on the ground.” This means that no matter what the shape of the container is, it is wrong to treat the water depth in the device as a flat rain.