From Lapham's Quarterly, July 14:
Evidence of the ElementsFinding Euclid on scattered pot shards.
The ancient Greek mathematician Euclid’s original manuscripts for Elements of Geometry—a compendium of facts about space and its properties, lines and shapes, numbers and ratios, written around 300 bc in Alexandria—do not survive, nor anything like them. The papyrus on which he wrote is durable enough, in the right conditions. Scrolls hundreds of years old were not terribly unusual in the ancient world, and they could remain smooth, pliable, and legible for much longer. A story is told of a museum curator who used to display the strength and flexibility of papyrus by blithely rolling and unrolling an Egyptian sheet three thousand years old (this was in the 1930s, when attitudes to museum artifacts were perhaps less reverent than today).
In the right conditions, that is. Most conditions are not right. If it gets too wet, papyrus rots; too dry and it crumbles. Insect larvae like papyrus, and the worms destroyed many a literary reputation in the ancient world. So did the rats. Plus, the long rolls tore easily and were thrown away when they did. The upshot is that large or complete papyri surviving from the ancient world are extremely rare. What more often survive are fragments: discarded rolls, pieces reused to make mummy cases, pieces recovered from rubbish dumps or ruined houses. Rough, dark, and brittle with age, nearly all are from provincial locations in Middle and Upper Egypt, where the dry conditions preserved them. Finds have come from cemeteries along the Nile Valley and in the Faiyum Oasis, and from certain villages. From the big towns, by contrast, there is next to nothing: Alexandria itself, having a high water table, has no preserved papyri at all.
For all that, there are a lot of papyrus fragments. People have been systematically digging them out of the ground since the mid-nineteenth century, and hundreds of thousands are now amassed. And, yes, some of them contain fragments of Euclid’s Elements. Seven, in fact, totaling about sixty complete lines of the text and another sixty fragmentary lines. What parts of the Elements do they preserve? They include, written around 100 bc: Three propositions from book one, with one summary proof (these come as citations in a philosophical treatise preserved—carbonized—in Herculaneum by the eruption of Vesuvius in 79: an exception to the normal generalizations about papyrus survival). An enunciation from book two, with a rough figure, written in the Egyptian city of Oxyrhynchus around 100. Parts of two more propositions from book one, written at Arsinoë (modern Faiyum) in the second half of the second century. A second-century copy of three figures and enunciations from book one, carefully written with ruled diagrams. And a schoolteacher’s or pupil’s copy of the ten opening definitions, made in the third century.
It is not much: these are small pieces from the easy parts of the book, in one case from its very beginning. But they do reveal something about the way the Elements was spreading. It did not just stay in Alexandria: already, by the first few centuries after its composition, it—or parts of it—was being copied out by people hundreds of miles away around the Greek-speaking world.
It was moving out from the cultural center to the provinces. Euclid’s Elements will have been published in the ancient sense: sent to a scribal copying house which produced multiple copies for sale. But most of the papyrus fragments are not from those copies; only the Faiyum fragment looks like the work of a professional scribe. Instead, they bear witness to the activity of individuals copying out parts of the text for their own use, teaching or learning.
So, the writers of these papyrus fragments represent the “public” for Greek geometry: a tiny minority, in a world in which the literate themselves were already a minority. These were people who understood geometry, who accepted and shared its conventions, who knew enough of the basics and the methods to comprehend Euclid’s book. Their needs surely shaped what was written and how it was written. The very packaging of mathematics in a self-contained written form already presumes that they existed. But nothing more is known about them.
And this evidence can tell only about those places where it was dry enough to preserve papyrus fragments: for the rest of the Greek world—the islands and the mainland north of the Mediterranean, for instance—the lack of evidence reveals nothing, positive or negative. Surely the Elements went to Athens, for example: but it is centuries before there is evidence for that.
As well as papyrus there was a cheaper writing surface still: ostraca or pot shards. Literally, broken pieces of pot: waste, and therefore free. Ostraca were used in Egypt before the Ptolemies and up to the end of antiquity, in Athens from the seventh century bc: they were written on in ink or simply scratched, to form pictures or writing in Hieratic, Demotic, Greek, Coptic, or Arabic as the case might be. Schoolboys, soldiers, priests, and tax collectors all used them. (They were also used as voting tokens. If the word sounds familiar, it is because ostracism was a procedure for expelling a man from the country for ten years on suspicion of disloyalty: the votes were written on ostraca. It happened at Athens for most of the fifth century bc, and in other Greek cities, too.)....
....MUCH MORE
