abstract:Despite the frequency and intensity of scholarly attention to Plato's important divided line passage in Republic 6, an ancient puzzle has repeatedly baffled interpreters: the two middle segments of the line are of equal length, although Socrates declares that the degree of clarity and truth increases in proportion to the contents of each of the line's four segments. The missing piece of the puzzle, I argue, is provided by the practice of ancient Greek geometry: diagrams were drawn with a compass and straightedge. Thus, as actually constructed in the fifth and fourth centuries BCE, the diagram itself vindicates Plato's text.

中文翻译：

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格劳孔画了什么？：柏拉图分界线的图解证明

摘要：尽管柏拉图在共和国 6 中重要的分界线段落受到学术界的频繁和强烈关注，但一个古老的谜题一再让解释者感到困惑：尽管苏格拉底宣称清晰和真实的程度，但中间的两条线段长度相等与行的四个段中每个段的内容成比例地增加。我认为，拼图的缺失部分是由古希腊几何的实践提供的：图表是用指南针和直尺绘制的。因此，正如公元前 5 世纪和 4 世纪实际建造的那样，图表本身证明了柏拉图的文本是正确的。