"Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience"

This quote by Arthur Cayley is referring to the proposals of geometry, which are mathematical statements that are utilized to explain the homes of shapes and figures. Cayley is recommending that these proposals are not just roughly true, but that they stay absolutely true in regard to Euclidean area. Euclidean area is a mathematical model of physical area, which has been used for centuries to describe the real world. Cayley is recommending that the propositions of geometry stay true in this model of physical space, which they can be used to precisely describe the physical world. This quote highlights the importance of geometry in understanding the physical world, and how it can be utilized to precisely describe the homes of shapes and figures.