Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call ‘additivity’ the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze and assess manuscript versions of Newton's initial argument within his initial deduction, dating from early 1685. Newton's strategy depends on distinguishing two quantities of matter, which I call ‘active’ and ‘passive’, by how they are measured. These measurement procedures frame conditions on the additivity of each quantity so measured. While Newton has direct evidence for the additivity of passive quantity of matter, he does not for that of the active quantity. Instead, he tries to infer the latter from the former via conceptual analyses of the third law of motion grounded largely on analogies to magnetic attractions. The conditions needed to establish passive additivity frustrate Newton's attempted inference to active additivity.

牛顿在《原理》上发表了他对万有引力的推论（第一版，1687 年）。为了建立引力的普遍性（粒子到粒子的性质），牛顿必须建立质量的可加性。我称“可加性”是物体的物质量具有的属性，以防万一，如果引力与该量成正比，则可以将力视为与每个粒子的物质量成正比的力的总和。牛顿关于可加性的论证是模糊的。我分析和评估了牛顿在 1685 年初的初步推论中最初论证的手稿版本。牛顿的策略取决于区分两种物质量，我称之为“主动”和“被动”，通过它们的测量方式。这些测量程序为每个如此测量的量的可加性设定了条件。虽然牛顿对物质的被动量的可加性有直接的证据，但他没有为主动量的可加性提供证据。相反，他试图通过主要基于磁吸引力类比的运动第三定律的概念分析，从前者推断后者。建立被动可加性所需的条件挫败了牛顿对主动可加性的推论。