Mrs. S.: I assume your command of English will provide me a translation of the Abstract below--possibly relating to how ancients measured the earth.

Quote of the Abstract of Erik P. Verlinde's paper, On the Origin of Gravity and the Laws of Newton

"Abstract: Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic."

Although a bit troublesome in areas, if you download the entire 29 page paper (click on the Abstract above and then click on "Download"), a couple of the graphics directly relate to your question as to how the size of the earth was measured before the yardstick was invented.