标题： 论阿基米德关于浮体的著作的完成 显示英文标题

标题： Towards a Completion of Archimedes' Treatise on Floating Bodies

摘要： 在阿基米德关于浮体的论著中，他确定了浮动抛物线段的平衡位置，但仅限于该段的底面要么完全位于流体外部，要么完全浸没在流体中的情况。 在这里，我们给出了剩余情况下的数学模型，即用两种简单的条件以封闭形式描述平衡状态。 我们提供了可靠地找到所有平衡点的工具，并对这些平衡点进行分类。 本文可以看作是对罗特斯最近一篇文章的延续。 显示英文摘要

摘要： In his treatise on floating bodies Archimedes determines the equilibrium positions of a floating paraboloid segment, but only in the case when the basis of the segment is either completely outside of the fluid or completely submerged. Here we give a mathematical model for the remaining case, i.e., two simple conditions which describe the equilibria in closed form. We provide tools for finding all equilibria in a reliable way and for the classification of these equilibria. This paper can be considered as a continuation of a recent article of Rorres.