[Math] How did ancient greek geometers represent solids

ho.history-overviewmg.metric-geometry

I've seen plenty of ancient diagrams representing plane figures.* But I'd like to know how ancient geometers, especially around the time of Euclid, might have represented solids. Did they use diagrams with perspective? Three dimensional models?

*cf. David Fowler, "The Mathematics of Plato's Academy", see the plates between pages 6 and 7

Best Answer

Greek mathematical diagrams are composed of lines, arcs, and letter labels, and may be used to represent two- or three-dimensional objects. Drawing aids such as ruler and compass were sometimes, but not always, used in their construction, while curves in mathematical papyri were typically drawn freehand. Three-dimensional objects in diagrams were drawn using foreshortening of certain elements, as opposed to "painterly" techniques such as shading or consistent perspective. The technique of foreshortening does not work for spheres, and so for problems involving spheres special techniques were required, such as depicting the objects hidden by a sphere as though they were outside it.

Courtney Roby, in The Encyclopedia of Ancient History (2012).

The encyclopedia entry is based on the analysis of Reviel Netz in The Shaping of Deduction in Greek Mathematics.