The writer is considering the subject as a physicist might. Euclid’s figures are ideal objects, they don’t have errors. It’s assumed that your construction is a

The writer is considering the subject as a physicist might. Euclid’s figures are ideal objects, they don’t have errors. It’s assumed that your construction is an approximation. Euclid might have drawn his figures on sand with lots of “errors”, still the figures are idealized no matter how you draw them. For instance, Euclid represents numbers as lines. There are not units and no errors. His proofs are still valid if I don’t draw his lines exactly as he drew them (I’m talking about Book IX where there are propositins about numbers).