M181 S94 8th Th 19 May 94

Today is the day for the completion of Euclid's voyage...

Our information now on trying to bring this together, and ... let's see, our overview -- I could 
maybe reduce this in scale to the minimum -- the story of the diffusion of Euclid's Elements, the 
Latin version, into Latin Europe, and its further diffusion into the vernacular or so-called vulgar 
languages of Europe, that goes on for another 400 years. But I'm choosing to stop here as all the 
energy of this diffusion focuses on a single point in Palermo around the year 1200 with the cre-
ation of the mathematical renaissance of Europe in the person of Leonardo of Pisa, otherwise 
known as Fibinocchi, and that story is well told in Chapter 8 of our text which you're reading now. 
So there's sort of a convergence there and that's where I've chosen to stop when we get Euclid 
translated into Latin. And that's our story today. There are the two gateways, as I described them, 
of Islamic knowledge into Europe, Palermo and Cordova. From Cordova comes the so-called 
Arabo-Latin translation, so a translation from the Arabic to Latin, frequently passing through 
another language along the way, for example Catalon or Hebrew. And from the other gateway, 
Palermo, the direct translations from the original Greek to Latin and in the long run of course 
those were more accurate, having fewer steps and so on, and they come last and give us those 
translations which had dominated European education throughout the Middle Ages as described 
in most histories of mathematics, and represented in our text particularly in that sidebar called the 
translators and their translations.

So we have our sequence of main stations here -- Athens, Alexandria, Byzantium, Bagdad, Cor-
dova, Palermo, and now I could add one more column here for Latin Europe. And color- coding 
by language, we have yellow for Greek, the Platonic Academy, and then the Alexandrian Museon, 
and the University of Byzantium, and the Bate Al Hikma of Bagdad, and the University of Cor-
dova, and the University of Palermo, and then the first university in Europe, that I will describe 
today, goes on still to the present day. I left Cairo off this list, it's not really a major station, but 
another university continuing to exist today. I'll use orange for Arabic, we have in Bagdad and 
Cordova Arabic and in Palermo Arabic and Greek. So we have this red one for Latin. We had also 
Latin in Byzantium, Latin and Greek, which of course are sort of similar, and some Latin in Pal-
ermo as well. And then we had the progress of the book being carried to Alexandria early on by 
Euclid himself, and in intercourse over a number of years with Byzantium and a couple of spec-
tacular translations into Arabic.

So today we want to describe then, passage from Cordova to Europe. These are the Arabo-Latin 
translations. And then from Palermo to Europe, Greco-Latin translations. So just to review, I 
passed rather quickly over several different periods of translation in Bagdad at the Bate Al Hikma, 
House of Wisdom, and there are three periods, A, B, C, I mentioned, and these will be important 
now for the first half of today's story, because when translation is done from Arabic to Latin it 
must be a translation of one of these Arabic versions that were created in this early period of 
Bagdad. So particularly period B, there was the translation by Al Hadaj of Euclid. Of course these 
translations of Euclid are taking place in the context of a lot of different translations of other 
works, of medical works by Galen and astronomical works by Ptolome and so on, but here I'm 
just pulling out the translations of Euclid's Elements along. So we had Euclid Elements number 
one by Hadaj, and that one we called the Haruni, as it was done under Harun Al Roshid, the 
founder of this whole line, in Bagdad. And that's around the year 800, or 800 to 820. And then his 
second one, done under what I call period C, this is after the opening of the Bate Al Hikma in 820, 
and this was his second attempt translating the same work, and that was after the excession of 
Harun's son Al Mamun. He had two sons, one of them took over Bagdad and the other was in 
Merv, that was Mamum, and eventually Mamun had to take over the whole thing because Al 
Amin did a poor job or he just wanted it all, I don't know. And part of our story then, as to the 
founding of the Bate Al Hikma by Al Mamun, was his education in Merv by the Nestorian Chris-
tians and the Buddhists and Persians there. So anyway, this second translation in 840 by the same 
person, and then at a later period here, of Ishaq and Kabit -- these are both mentioned in the text in 
an earlier chapter, you might have noticed -- and their translation around the year 900. So Ishaq 
Ibin Hunane, son of Hunane. That's the Hunane who was the founder or first director of the Bate 
Al Hikma, so this is just the next generation, although there's a good span of years here. And Tabit 
is one of the famous Hakim or universal scholars of Islam. And the translation technique of Al 
Hadaj was to use a Greek-Arabic dictionary and translate every word singly, so there were a lot of 
sentences that resulted that didn't make sense, or let's say it was very difficult to understand. On 
the other hand Ishaq and Tabit, they had a more advanced technique where they would try to read 
the whole sentence and get the gist of it and then rephrase it in the Arabic sense, and so their 
translation was much more successful. So that's background for the first of our translation stories 
here.

So I think I'm going to boil this down to a list of the translators and their stories. Now the first 
time I ever told this story, which was in this course six years ago, I described, I kind of made this 
up or I did my best to interpret the history books, but Adalaide, whocis this monk in Bath, which -
- some of you heard about Bath, it's still there, the Roman Bath in England and now a beautiful 
town to live in west of London a day's drive, pretty far up north compared to our source here, Cor-
dova. There's so much information we could get out of this picture if I just draw it better. In Byz-
antium, for example, a university was founded, and then the king withdrew his support, so then 
there was a gap. Then it was restarted again. I told this story about Constantine versus Justinian 
and so on in the past. When it was restarted, it probably had to do with a feeling of competition 
with Bagdad and the border on -- the eastern border between the Roman Empire and Islam had 
this (?) going back and forth capturing and recapturing areas of Syria and the competition of the 
two kings for the splendor and general culture and beauty of their courts and so on have an impor-
tant role in the story. So here where you see the (Teefer) translation there is then also the juxtapo-
sition of two different cultures and two different languages the competition and interaction of 
which somehow stimulate, well, the evolution of mathematics, as we have going on say in Cali-
fornia with the juxtaposition of Spanish and American or English culture whatever we call it, and 
the possibility or the hope for renewal of our dying American culture. 

Similarly, on the western boundary between Islam and Latin Europe, there was this oscillation of 
boundaries and also the competition between cultures and that's somehow part of our story. Any-
way, I told this one first. I mentioned last time the analogy of these twin gateways as pots of honey 
and then there are these columns of ants coming from all over Europe to get the goodies. You say, 
ªWell why didn't they just go to Byzantium where the original Greek books were kept?º but they 
didn't know Greek any better than they knew Arabic. The people in Byzantium of course knew 
Greek and they knew Latin, so how come they weren't doing the translations there? So besides the 
things that are on this map, there are the things that are not on the map, and what about this one, 
from Byzantium directly to Latin Europe? So somehow in Byzantium here not a single translation 
was done between the year 600 and the year 1200, so this, you know, the vitality here was some-
how missing. There was a revival around the year 1000, I think we spoke about that before also, a 
revival of mathematics in the university and Platonic studies under the leadership of Michael 
(Selis). Anyway, my fanciful story was that this Adalaide, this monk way out in the wstern fron-
tier of the Roman Empire, he rode a donkey down to Cordova where he put up in a convenient 
motel and did the translation, which took a matter of several months, and I got this story in a 
dream or something, it's an intuition, and it turned out to be right, except he didn't go to Cordova, 
what happened was he went to Syria, and while in Syria he rode the donkey around to these differ-
ent monasteries and he learned to speak and read and write Arabic, and then he went back to Bath, 
and in Bath he received a copy from someone else, the Jewish traveler from Cordova went to 
England carrying a manuscript in Arabic which Adelaide was able to read and translate, and that 
one was with Al Hadaj number one, and so in 1126 in Bath he translated Al Hadaj number one, 
the Haruni, into Latin. And it was a complete translation of all 15 books. But the translation of Al 
Hadaj from the Greek or maybe even Syriac into Arabic had many flaws, so it's not exactly clear 
how much of this we could understand today reading it in Latin, but people have studied it in -- 
they collect photographs, the scholars of the history of mathematics have collected photographs of 
all the manuscripts from the different libraries where they're kept and then they've put photos of 
corresponding pages -- copies of corresponding, like take one page, like the first page of book 10, 
and all known extant editions in all language, and then they put them on the wall and then they try 
to match them up to see which one is translated from which and very detailed studies have been 
done of this, so if one wanted to have a cursory glance at Adelaide's handwriting, that's possible, 
and then you could see Latin's not so hard to read for us who come from this Latin-European tra-
dition, and you could compare it to Heath, the English edition, (?) go to the sci lib and see how 
understandable it it. So he did a lot of other translations as well, but that's the first crucial and 
important Latin edition of Euclid, and that's it, and there, in Bath. And it has to diffuse downward 
throughout Germany and Italy.

Okay, the next one. Herman of Corinthia and Robert of Chester. These two guys traveled around 
together and were inseparable. They did these translations and of course I like to think of them as 
a gay couple and eventually Robert went back to England, abandoning Herman in Germany or 
somewhere, and then the translations ended, so I think that they could only work together. So any-
way, their version, in 1138, they were working in Cordova. They went there and they stayed for a 
long time and they translated many works -- the astrology of Saul, the astronomy tables of Al 
Korismi, the major astrology of Jacfar, Tolome's Planisphere -- as well as Euclid's Elements, but 
just selecting this one feat, they did over the first 10 books and they followed Al Hadaj number 
one, and according to the people who've studied the things on the wall of the corresponding trans-
lations, they claim that Herman definitely had Adelaide's translation in front of him as they 
worked. So it's sort of a derivative of this one.

And then Gerard of Cromona in 1175, and he used this translation of Ishaq and Tabit, and he 
worked I believe in Toledo, which is just a little bit to the north of Cordova. And in this oscillation 
of the boundary, the fractal boundary in between Islam and Latin Europe, there was initially the 
penetration of Islam into France and up as far as Tour and then they were gradually pushed back 
in what is called the Reconquest of Spain, so the boundary of Latin Europe then reexpanded into 
the north of Spain past Pirani, past Norbonne and those little border towns where the train goes 
through, and finally down to Toledo, and later down to Cordova, and so with each successive 
advance whatever universities, libraries, scholars, especially Christian and Jewish scholars, who 
didn't retreat, then they became encapsulated into Europe and therefore these batteries as it were 
of Medieval learning then started radiating into Europe. To Gerard went to Toledo after the recon-
quest of Toledo, and he set up shop there and created a kind of school of translation where he had 
a 100 of people, staff, working translating everything. Gerard of Cromona went to Toledo, north 
of Cordova, also a great library and university of Islam, in search of the Armagast. He founded a 
school for translators there and supervised over 80 Arabo-Latin translations working with local 
Arabo-Spanish translators. 

For a long time, that's it. And as you see on the map here, this period of translation will be fol-
lowed very closely by the Greco-Latin period, and those translations being better and this whole 
industry of Arabo-Latin translations eventually came to an end. But the largest collections by a 
mile were in Cordova, and considering not only Euclid's Elements, but the entire corpus of Greek 
and Arabic works, this translation industry in the long run was much more prolific than this one 
that followed, but these are better translations. 

So going on to Palermo then, we have -- I'm trying to avoid giving the detailed chronologies here 
of all the events concerning people we've never heard about. The Norman conquest was in 1105, 
I'll just make a line with the beginning and the end. So this is a chronology of Palermo and Sicily. 
The Normans arrived earlier in Italy and gradually came down Italy and reached the boot and in 
1105 made it over to Sicily pushing the Arabs back. And then in 1266 the so- called (homstafen) 
conquest, so Catholic Europe and especially the kingdom of the Vatican conquered the Normans. 
In other words, the Italians replaced the French in control of this island. And at that time all of the 
books collected by Count Roger I, King Roger II, William I, William II and so on -- all these 
books moved to the Vatican in Rome. So we could consider that this transition then moved over to 
Rome and then continues actually on to the present day when many of these manuscripts are still 
found in the Vatican Library. So the story in a nutshell: King Roger II collected manuscripts from 
Byzantium. So we have this Byzantium to Palermo for sources, and they maintained a lot of direct 
contact and not too far apart. Under William I the chief administrator Aristipus translated Plato, 
Aristotle and Ptolome from Greek to Latin and then the first translation of Euclid's Elements hap-
pened 1160, by an anonymous translator. This was just recently discovered and therefore you 
don't find it in the usual history books of Euclid's Elements. So this was later than Adelaide, see, 
in 1126, just a little bit later, but it's a direct and much better translation. 

There's three main periods of hot mathematical activity in Palermo. The time of William I, 1154-
1166, so that includes this translation, William I. Then during the time of Frederick II, 1194-1240, 
and we don't have a translation of Euclid to report during this instant time or renaissance of Fred-
erick II, but he was a big supporter of mathematics and was interested in mathematics and science 
himself, and very interesting works by him do come down to us today, including a geography and 
sort of a scientific text on falconry, indicating his close connection with Arabic culture where it 
was a popular sport. And then in this Vatican period, 1266- 1300. 

So under Frederick II we have the history of the very interesting Michael Scott who, although he 
didn't do a translation of Euclid, did translations of many other works, was a serious mathemati-
cian himself, and posed the actual introduction of Leonardo of Pisa. Fibonocchi, the greatest 
mathematician in Renaissance Europe, introduced him actually to Frederick II and stimulated 
Leonardo to write his first book on mathematics, which -- Leonardo kind of the European analog 
of Al Corismi, one of the greatest. So there's a story here I'm not going into with Fibonocchi, just 
going to put it on the map here as it were.

And then in the third period we have the -- date this, 1200, his first book, Liberobocchi, 1202. And 
then in this period, Companis, where he enrolled at the Vatican, did another translation direct 
from Greek to Latin of Euclid's Elements, and after that there were many more, but this is the 
whole story, then, of the Greco-Latin translation in its early and fundamental period, and we could 
put these in an ordered list. Abelard is 1126 and then 1138 is Herman and Bob, and then anony-
mous in 1160, and then Gerard in 1175, and Companis in 1260. So what we have today, these 
Latin editions are still around, and which are the ones that had an effect? It turns out that Adelard, 
he made three translations or anyway three versions. The first one was the complete translation 
that I've mentioned and afterwards he had a shorter version with like the theorems without the 
proofs and then a third version that was a little bit longer than the second but not as complete as 
the first. So the second one, the radically shortened version, Abelard II, because popular and 
spread all over Europe and somehow was the main stimulus of the mathematical renaissance and 
eventually was supplanted by the Companis version which of course is much better. And in 
between we have Fibonocchi, which is here. So somehow we can get an idea of the timespan 
between the access of the materials in Arabic and Greek and the beginning of new mathematical 
activity in Europe. And that's a good stopping place for this story, because the next thing to hap-
pen here is the Renaissance, our timeframe here is 1500. 

Now in retrospect we can reconsider the question on the relationship between the traces of the 
book and the main bifrications of cultural history.