Arithmetic without numbers.
GCWs required a ratio because they used physical units which they could see and compare (visually). In any given ratio, the antecedent is known only because it is associated with a given consequent that acts like a unit.
Therefore, without algebraic measure (through the abstract unit), GCWs could perform measurements to 100% precision without even knowing anything about the concept of number. Construction workers today can’t even accomplish such precision with calculators and computers.
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