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在科舉大衆1954年5月號上,讀到許蒓舫所著介紹元代数學家郭守敬的文章,文中論及郭氏“弧矢割圓術”是由沈括“會圓公式”和楊輝“弧矢公式”合併變化而成,此說早見於李儼中國算學小史、中國算學史等書中,如此論証固屬正確,但其中“楊輝公式”一語,似頗有疑問之處。许李二先生所稱之“楊輝公式”,當即載於楊氏田畝比類乘除捷法一書中者,為參考之便,錄共題、術於下: [題]:圓田於內截弧矢田一段,弦長十二步、矢闊四步,問圓田元(原)徑幾步? [輝術曰]:半弦自乘為實,以矢除,而併矢,即圓田徑步也。 將此“輝術”譯成公式,就是:
In the May of the Imperial Examination of the Public in May 1954, he read Xu Shu’s article on the introduction of Yuan Shou mathematician Guo Shoujing. The article discusses Guo’s “Skew Cut Method” by Shen Kuo’s “Convex Formula” and Yang Hui’s “Sagittal Formula”. “The merger changes, this said early in the Chinese history of Li Xiao’s mathematics, Chinese history of mathematics and other books, so the argument is correct, but the ”Yang Hui formula,“ the phrase, seems quite doubtful. The ”Yang Hui formula“ referred to by Mr. Xu Li Er was immediately included in the ”Ya-Yi-Yi-Yi class“ multiplication and extermination method. For reference, he recorded the title and technique under the following: In the field of Yada, the length of the chord is twelve steps, and the width is four steps. How many steps is Yuan Tianyuan’s (original) path? [Hui Ji 曰]: The half-string is a self-multiplying fact, divided by a vector, and a dynamo that is a circular track. and also. Translate this ”hui technique" into a formula: