The History of Mathematical Proof in Ancient Traditions

172 reviel netz

applicable (which is rare), by Heiberg. My interpretation of this evidence is

based on the facts shown above – the non-metrical character of the manu-

scripts’ diagrams – as well as those to which I now turn: their non-iconic

character.

Heiberg goes iconic

I have suggested that Heiberg goes beyond the manuscripts, in making the

two-dimensional fi gures more of a ‘picture’ of the object they are designed

to represent. So far, my argument has been based purely on the contrast of

such two-dimensional diagrams to their three-dimensional counterparts.

What we require, then, is to see whether there are cases where Heiberg’s

representation of two-dimensional fi gures inserts into them a visual ‘cor-

rectness’ absent in the manuscripts. We have to a certain extent seen this

already with the quantitative, metrical character of Heiberg’s diagrams.

Even more striking, however, is a certain systematic way by which Heiberg’s

two-dimensional diagrams are qualitatively more ‘correct’ than those of the

manuscripts.

I turn now to SC i .33 (see Figure 3.5 ). I note quickly the metrical facts.

Th e fi gure by Heiberg has A much bigger than the main circle, which is

K

Z

A

E B

H

Θ

Γ

K

Z

A

E B

H

Δ Θ Δ

Γ

Heiberg Archimedes (reconstruction)

Figure 3.4 Heiberg’s diagram for Sphere and Cylinder i.12 and the reconstruction of Archimedes’
diagram.