Netz has emphasized that the Greeks of antiquity used their diagrams in a much more *topological* manner than one might expect, and perspective seemed limited. Archimedes was silent on perspective in spheres and liked to refer to the great circle therein; instead of a sphere in a cylinder, Archimedes' tombstone might have merely been a circle in a square!

In more detail, although the scholars of the 19th and early 20th century were really good at reconstructing authoritative *texts* of the ancients, along with doing really boss things like dating the time of an author's flourishing to some throwaway line the author might make about an eclipse or comet, these same scholars had the tendency to amend the figures of Euclid/Archimedes/etc. to fit the standards of rigor of the 19th/early 20th century.

Netz is one of the first to note that figures are amenable to the critical, philological method, and thus to answer @Quuxplusone's and @Matt F's questions, even if there are no extant manuscripts (on papyri) in the hand of, say, Archimedes, by comparing and contrasting the manuscripts that *are* available, one may go back centuries, maybe a millennia, to Archimedes himself (or at least to the scribe at the library of Alexandria). One such manuscript was famously hidden behind a prayer book and lost to the world until rediscovered in a monastery outside of Jerusalem.

As an example of a critical reconstruction of a diagram, consider the figure below from *On the Sphere and the Cylinder*. $\mathrm{K}$ is a cone and each of the segments $\mathrm{AZ}$, $\mathrm{ZH}$, $\mathrm{HB}$ etc are *lines* (here showed as arcs). In one branch of the manuscript tree, the bottom $\mathrm{A}$ is missing, most likely due to scribal error. Because the text refers to line $\mathrm{AB}$, one of the copies on that branch *added* a line between the left $\mathrm{A}$ and the top $\mathrm{B}$, while also fixing the segments straight. But upon reading the proof, the line $\mathrm{AB}$ is intended to be the *diameter*.

Netz follows the philological principle of "lectio difficilior potior" - the more difficult a reading is, the more likely it is to be correct. Because the manuscript tree most likely branched off relatively early, e.g. in the early 1st millennium, Netz concludes from the study that, going back at least to antiquity and maybe to Archimedes himself, the figure had an $\mathrm{A}$ on the left and an additional $\mathrm{A}$ or maybe a $\mathrm{\Lambda}$ on the bottom, along with arcs for line segments.

Netz discusses these in *The Works of Archimedes: Volume 1, The Two Books On the Sphere and the Cylinder: Translation and Commentary 1st Edition*, which is quite scholarly; he also has a popular book, *The Archimedes Codex*, with his coauthor William Noel, which provides figures available in the extant codices for the image above.