The History of Mathematical Proof in Ancient Traditions

178 reviel netz

beyond a single argument or so). In Table 3.1 , I list for each treatise its

length in Teubner Greek pages, as well as its square- bracketed passages. I

believe that a good way of quantifying the impact of such square brackets is

not by mere word-count – excising fi ve times a single-word passage is more

signifi cant than excising a single fi ve-word passage – and instead I develop

an ad-hoc ‘logarithmic’ count, with each ‘single word’ counting for one

unit, each ‘phrase’ counting for three units, each ‘passage’ for nine and each

‘long passage’ for twenty-seven. I then sum up this logarithmic value as

the ‘Bracketing Equivalent’. I then calculate the ‘Bracketing Equivalent per

Page’ or BEPP, which is the Bracketing Equivalent divided by the number

of Teubner pages. Th is entire exercise is of course somewhat absurd, but it

does arrange the data in a useful way.

Table 3.1 Heiberg’s use of square brackets

T r e a t i s e

Length (Teubner

pages of Greek)

Bracketed by

Heiberg (~BEPP)

Notes

(discussed below)

Floating Bodies i 13 1 word (~0.05) Doric, Palimpsest

Arenarius 22 3 words (~0.15) Doric, discursive

Method 41 4 words, 2 phrases

(~0.25)

Koine, Palimpsest

Spiral Lines 60 5 words, 2 phrases, 1

passage (~0.35)

Doric

Floating Bodies ii ~26 8 words (~0.35) Doric, Palimpsest

Quadrature of

Parabola

27 6 words, 3 phrases

(~0.55)

Doric

Conoids and

Spheroids

100 10 words, 10 phrases, 2

long passages (~0.95)

Doric

Planes in

Equilibrium ii

25 3 words, 5 phrases,

2 passages (~1.4)

Doric, Eutocius

extant

Planes in

Equilibrium i

20 7 words, 12 phrases, 2

passages (~2.6)

Doric, Eutocius

extant

Measurement

of the Circle

6 7 words, 1 phrase,

1 passage (~3.1)

Koine, Eutocius

extant

Sphere and

Cylinder ii

31 12 words, 20 phrases, 12

passages, 3 long passages

(~8.7)

Koine, Eutocius

extant

Sphere and

Cylinder i

83 11 words, 48 phrases, 29

passages, 12 long

passages (~9)

Koine, Eutocius

extant

N o t e : Th e table is arranged by ascending BEPP (Stom. and Bov. are not included in this

survey).