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東北人民政府教育部編譯的初中代數習題第七章第一節首載“算術比例的基本性質:兩外項之和等於兩內項之和”,繼謂a-b=b-c時,a,b,c稱爲算術連比例,而對於“算術比例”一名詞未加解釋。據卡約黎數學史所述,早在紀元前約五百年,畢達哥拉斯派的學者對於比例頗多研究:設有a·b·c·d四數, 若 a-b=c-d,此四數謂之成算術級數; 若 a:b=c:d,此四數謂之成幾何級數; 若 a-b:b-c=a:c,此a·b·c三數謂之成調和級數;並熟知巴比侖人所發明的音樂級數a:a+b/2=2ab/a+b:b。依照這樣的定義,前述算術比例的基本性質,自屬顯而易見。不過“算術比例”
The junior high school algebraic algebra exercises compiled by the Ministry of Education of the People’s Government of the Northeastern People’s Republic of China contain the “basic nature of arithmetic ratios: the sum of two external terms is equal to the sum of two internal terms” in the first chapter of the first chapter of the exercises of the seventh chapter. After ab=bc, a, b, c This is called arithmetic proportionality, and there is no explanation for the term “arithmetic ratio.” According to the history of Kayoli’s mathematics, as early as about 500 years ago, Pythagorean scholars studied a large number of studies: there are four numbers of a·b·c·d, if ab=cd, this four The number is said to be an arithmetic progression; if a:b=c:d, this four number is said to be a geometric progression; if ab:bc=a:c, the three numbers of a·b·c are said to be harmonic progressions. And is familiar with the number of music invented by the Babylonians a:a+b/2=2ab/a+b:b. According to this definition, the basic nature of the aforementioned arithmetical proportions is self-evident. However, “arithmetic ratio”