Geometry, as the etymology of the term denotes, derives from the Greek words ge, earth, and metria, measuring. That is, a central aspect of proto-geometry has been the act of measuring—though subsequently, once the Greeks were doing geometry scientifically, measurement does not appear to have played a major role. Historically, however, geometry as mathematical science arose from the pre-scientific, intuitively given world, from the “first very primitively and then artistically exercised method of determination by surveying and measuring in general” (Husserl, 1997a, p. 26, original emphasis). The children featured in this book, however, have not been born into the same pre-scientific world. Theirs is a world in which idealities, embodied in and mediated by concrete cultural artifacts, is part of the everyday experience of growing up. They are not living in a pre-geometric world where kúbos (cube) was a die for playing with, kúlindros (cylinder) a roller, sphaîra (sphere) a ball, pyramis (pyramid) a royal tomb of Egypt, and kírkos (circle) a round or ring. At that time, all of these words pertained to real objects in the real world of the Greek. But, even though the children today do not rediscover geometry in the way that the ancient Greek did, they still do discovery work. It is measurement that allows the objects of the intuitively, non-objectively given world, to become intersubjectively available in the same way to every member of the collective. It is the art of measurement that—to paraphrase Husserl—practically discovers the possibility to choose certain empirical basis forms as measures and to use them to practically determine in an unequivocal manner their relation to other bodily forms. In this chapter, I describe how measurement emerges in this mathematics classroom at different places and times exhibiting the different functions of hand/arm movements just articulated. The emergence of measurement is tied to the practical, experienced need to be accountable for any claim, statement, or argument made. In this way, the children in the second-grade classroom reproduce geometry as an objective science precisely because measurement and accountability make objects intersubjectively available, that is, make them inter-objective.