You are asking about illustrations. A good sketch is very useful in geometry, and I usually insist upon it. It is not always necessary though. Greek geometers of Euclid's era were probably quite adept at visualizing these figures with no illustration at all.
The Archimedes Codex is a recent book documenting efforts to retrieve text and images from a copy of some works of Archimedes. The copy was probably produced in the 10th century AD or thereabouts. The years have not been kind to this book, and it was scribed more than a thousand years after Archimedes anyway. It might have been a faithful representation of the original though. I have tried to reproduce one of the images here.
The figure on the left is similar to one found on the ancient parchment. It is a diagram for Proposition 30 of On the Sphere and Cylinder, Book I. It represents a regular dodecagon inscribed in a circle, with another circle inscribed in the dodecagon. The sides of the dodecagon are drawn as arcs, which of course is quite a wild distortion. If that looks bad, consider the figure on the right, a geometrically precise representation of the same thing. There is so little space between the circles that it is difficult to see what is going on.
My point here is that it is unlikely that Archimedes or his contemporaries were much concerned with precise drawings. Conceptual representations, warts and all, would have served their needs.