Triebel-Schubert C
Sudhoffs Arch. 1989;73(2):190-9.
The conception of symmetry in medical texts of the 5th century has never been connected with the development of the mathematical theory of proportions. However, we can find in Alcmaion and the hippocratic writings de vetere medicina, de natura hominis and de victu the differentiation between an arithmetical determinable measure and a qualitative determinable measure which is defined by a common lógos for incommensurable sizes. In de vetere medicina and de victu we see a conception of proportion and symmetry/commensurability, which requires the discovery of incommensurability. This discovery can be connected with the greek mathematician Hippocrates of Chios and his theorems of doubling the cube. We can detect an answer to this revolutionary development in mathematics in the methodological ideas of medical writers, who wanted to turn away medicine from the anti-descriptive and anti-empirical attitude in mathematics and philosophy.
公元5世纪医学文本中的对称概念从未与比例数学理论的发展联系在一起。然而，我们可以在阿尔克迈翁以及希波克拉底著作《论古代医学》《论人的本性》和《论饮食》中找到算术可确定度量与定性可确定度量之间的区别，后者由一个适用于不可公度大小的共同逻各斯定义。在《论古代医学》和《论饮食》中，我们看到了一种比例与对称/可公度性的概念，这需要发现不可公度性。这一发现可以与希腊数学家希俄斯的希波克拉底及其倍立方定理联系起来。我们可以在医学作家的方法论思想中找到对数学这一革命性发展的回应，这些医学作家希望让医学摆脱数学和哲学中反描述性和反经验性的态度。
