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When did mathematicians transition from peg and rope --> edgeto straightedege and compass?

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peg and rope --> edge and compass

In the 19th and 20th centuries, the student of classical Greek geometry used "straight edge and compass". A. Seidenberg uses the terminology "peg and cord" in proposing that altar construction motivated the development of classical Greek and Indian geometry. So one supposes that a transition occurred in which "peg and cord" were replaced by "straight edge and compass". Is this correct, and if so do we have evidence as to when this transition occurred?