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Notes (a) The so-called "projective transformation of space into itself" provides the fundamental and most general basis of measure-as-such, and with it metrication, which is a systematisation of measurement. (b) The concept of an absolute, replicable and additive "unit" (one-off) of size, associating number with geometric elements, needs clarification, and proper definition for the projective context. (c) Correction and redefinition of tacit, spatial intuitions concerning geometric elements and intervals— for example, Euclid's "First Common Notion", concerning distributed, absolute equality and its "self-evidence". Self-evidence is just intuition, i.e., that which is "known" tacitly, without proof, as in (b), above. |