Over his career, Kant engages in a long attempt – which reaches a high point in the Prolegomena – to forge what in the Physical Monadology he calls a ‘marriage’ of metaphysics and geometry. The chapter traces the development of Kant’s thought on this union from its pre-critical roots to its flowering in the Prolegomena, and focuses on the role that geometric construction in natural science plays in connecting the two disciplines. This has implications both for how we should understand Kant’s desire to discover the ‘common origin’ of mathematics and natural science that is spelled out in the Prolegomena, as well as how this bears on Kant’s broader views about the status of natural science and laws.