Full Idea
Historically, the ordering of elements across periods was determined by equivalent weight, then later by atomic weight, and eventually by atomic number.
Gist of Idea
Elements were ordered by equivalent weight; later by atomic weight; finally by atomic number
Source
Eric R. Scerri (The Periodic Table [2007], 01 'React')
Book Reference
Scerri,Eric R.: 'The Periodic Table' [OUP 2007], p.19
A Reaction
So they used to be ordered by quantities (measured by real numbers), but eventually were ordered by unit items (counted by natural numbers). There need to be distinct protons (unified) to be counted.