Newton's Principia begins with eight formal definitions and a scholium, the so-called scholium on space and time. Despite a history of misinterpretation, scholars now largely agree that the purpose of the scholium is to establish and defend the definitions of key concepts. There is no consensus, however, on how those definitions differ in kind from the Principia's formal definitions and why they are set-off in a scholium. The purpose of the present essay is to shed light on the scholium by focusing on Newton's notion and use of definition. The resulting view is developmental. I argue that when Newton first wrote the Principia, he viewed the scholium's definitions as items of “natural philosophy.” By the time of the third edition, however, he came to view their methodological status differently; he viewed them as belonging to the more qualified “manner of geometers.” I explicate the two methods of natural inquiry and draw out their implications for Newton's account of space.

牛顿的《原理》以八个正式定义和一个霍乱开始，即所谓的时空霍乱。尽管有误解的历史，但学者们现在基本上同意，霍乱病的目的是建立和捍卫关键概念的定义。但是，关于这些定义在形式上与Principia的正式定义有何不同，以及为什么它们在书香中引人注目，尚无共识。本文的目的是通过着重于牛顿的概念和定义的使用来阐明学者。由此产生的观点是发展性的。我认为牛顿第一次写《原理》时，他认为学者的定义是“自然哲学”的项目。然而，到第三版时，他开始以不同的方式看待它们的方法论地位。他认为它们属于更合格的“几何体”。我阐述了两种自然探究方法，并阐述了它们对牛顿空间理论的影响。