From my diary

Yesterday was Valentine’s Day.  Inevitably I found myself wondering what kind of ancient or medieval literary material there was about St Valentine.

I found very little.   What little there was to be found by a Google search suggested that it was all derived at many removes from the old Catholic Encyclopedia.  The article in this is vague too.

So off I went to the Acta Sanctorum.  Feb. 14, the feast day, is in February volume 2.  There wasn’t a lot, and this is one of the oldest volumes, from 1658.

I’ve been working on a Latin Life of St George lately, so I am very much “in the zone” to work on another Latin life.  So I thought that perhaps I would OCR the Latin text, and maybe look at translating it.

Abbyy Finereader 14 is an excellent piece of software.  It supports the Latin language properly, which makes it very useful.  Indeed I remember yearning for such a thing in days gone by.

I didn’t think that a 1658 edition, complete with long-s, would OCR that well.  So I looked for the Paris reprint of the 1850’s.  This I found without difficulty, as they are all in; but the quality is not good.  Not even Finereader could make much of those grainy faint pages.

My next step was to find some more copies of the book.  As I indicated in my last post, I faintly remembered a Google spreadsheet full of links to PDFs of the Acta Sanctorum.  A kind correspondent found it, and it is here.  But … the links were all to the original edition.

So I’ve spent this morning trying to locate a better scan of one of the Paris reprint volumes.  Eventually I succeeded, in Google Books, in finding it here, in the 1864 reprint.  This, I was delighted to find, OCRs quite well.  The page layout is hardly designed for OCR, but if you manually move the text boxes around, the results are really quite decent.

Time for lunch now.  I think that I need to go out and buy the materials that I intend to cook, actually!  But I shall continue correcting the OCR after that.

Once I have a Latin text, I shall post it.  I shall then look at translating at least some of it.

I’ve yet to see any studies of the St Valentine literature, which is odd.  It must exist; if not in English, then in German or French or certainly Italian.  My search terms clearly are not good.  But I can try out some searches over lunch!

UPDATE:  Over a lunch a kind correspondent emailed me a link to an obscure German site where they have apparently uploaded the transcribed text of the whole Acta Sanctorum.  The German site itself is poorly designed, but I am assured that buried within is the entire text.  If so, of course, then there is no point in my doing it.  Once I’ve worked out how to use the site, I’ll write a post on it.

From my diary

This evening I spent some time looking at Huber’s article, Zur Georgslegende (1906).  I’d not looked at this before, so it was time to do so.  It contains five Latin versions of the Life of St George.

I also OCR’d the article, so that I could pass the German introduction through Google Translate, to see if it contained anything useful.  It was indeed very waffly and poorly structured, as is often the case at that period.  There was a lot of criticism of Papebroch, the Bollandist editor, for not printing much of the Latin versions.

But I learned from it that Arndt’s edition of the “Passicrates” Life that I am currently working on is indeed every bit as bad as I had thought.  Huber suggests that the text itself probably suffered, both from a bad translator, when it was created from Greek; and then from errors in transmission by copying.  He queries whether it has been significantly interpolated.  He also makes clear that Arndt isn’t a critical edition.  He gives as his third Passio another recension of the “Passicrates” life, which isn’t as old but is much easier to read.  My thanks to the kind correspondent who drew my attention to this.  But on the whole Huber achieves little in the pages he devotes to the question.

I came away from the exercise feeling even more strongly that a scholar needs to dedicate himself to sorting out the hagiography of St George, and write a definitive monograph.  It really can’t be that hard to list the versions, compare the texts within them, and do a proper analysis for both Latin and Greek.

My next task was to look at the possible meanings of “separo”, which usually means “separate”.  This appears at various points in Arndt’s text, in contexts where this meaning does not make sense.  Possibly “sever” will cover most of the choices.

However it is becoming clear that I ought to prepare a Word document containing the Latin, if only to use for searching through.  This will probably be my next task.  I have OCR’d and corrected chapters 12-21 already, but the rest should be done too.

Something that distracted me this evening was the tools that I am working with.  I’m using my old QuickLatin product for quick morphologies, which it does perfectly well.  But I find that I am using other PDFs and online dictionaries.  Surely these could be integrated somehow?

The problem is that it was written in Visual Basic 6, which is now some twenty years old, and only runs on Windows 10 by a special miracle.  Another tool that I use, to interleave Latin and English text, was written in VB.Net 2008, which replaced it.  This too is now more than ten years old.  Microsoft have been terrible at keeping their development tools working, and compatible, and I have complained before about their current offering, Visual Studio Community Edition, as nearly unusable by anyone but a professional.

My eye was caught by the old Delphi product, which I downloaded and played with a bit.  I always liked Pascal, the language it used.  It would be a bonus to be able to generate Android and iPhone apps.  Why can’t you do that from Visual Studio?  But of course my code is all in VB.  I have to work on this stuff in odd moments, unlike the way a professional works.  There is no way that I will ever port all this to Delphi; which is, in any case, nearly a dead tool itself.

Eventually I decided to leave that task for another time.  I was slightly nervous today that I might get a call about a job, and need to put everything to one side.  Whatever I do, it has to survive the call to go and earn a living, and to drop everything else in the mean time.  That is quite a demand of any project.

I’d better settle down and work up a text for chapters 1-11.

Update: I have just discovered, to my utter astonishment, that Arndt prints his corrections to the text, sometimes in the text with the manuscript reading in the footnote; and sometimes in the footnote, leaving the (unintelligible) manuscript reading in the text!  Generally “corr. minimos” means that minimos is what he thinks it should be.  “se. cod.” means that he has corrected it, but the ms. read “se”.

Less clear is “seccabo prius, corr. rad.” where he has printed “secabo” in the text.  The latter is the normal spelling.  But what is “prius”? Not the manuscript?  and what is “rad.” short for?  Some of his “corrections” in the footnotes don’t even make sense.

Incredible rubbish.  Both he and his editor should have been shot.

Update: An even worse example. Footnote reads: “corr. inest” on “inextimabiles”. By this he means we should read “inestimabiles”.  Good grief.  Fortunately after the first few pages he settles down.  But clearly his editor never read any of this.

Update: A commenter has pointed out that the mistake is mine! that “corr.” indicates a feature of the manuscript, changes introduced by a “corrector”.  “rad” is for “radendo”, “scraped away”.  Thank you!

The importance of standard spelling in critical editions

A few months ago a kind gentleman offered to translate some Latin for us all.  Meaning no harm, I suggested that the earliest Latin version of the Life of St George might be a good candidate.  For narrative texts are easier to translate, and how difficult could a late antique saints’ life be?  There was a 19th century edition by Arndt, and this I sent him.

Chunks of this have proceeded to arrive over the last few months.  I commented in detail on the first couple, and then pressure of work meant that I just filed the next few.

However last week I started to collect them, and go through them, and try to create a final version.  This evening I finished with what I had.  This consists of chapters 1-8 and chapter 10 (out of 21).

I feel really rather guilty now.  It’s a nightmare to translate and revise.  The reason, simply, is that the editor, Arndt, slacked on the job.  All he seems to have done is to fix one or two obvious errors, and leave the rest as he found it, weird late spellings and all.  That makes it very hard indeed to read.

I can cope with “capud” for “caput”, “head”.  But more obscure words have frequently left me baffled and guessing.  It’s obvious that “maggana” is “magana”, “daggers”, once you know.  Other words like “amos ferreos” – “iron whatsits” – are beyond me.

These spelling choices make it very difficult to find words in dictionaries!  The tortures that St George undergoes name quite a lot of bits of the body, as the wicked emperor gloats on what he will do to the saint unless he recants.  I do have a specialist glossary for body parts.  But even so what is the noun in “nerbona incidam”?  Or what does bella in “humera et bella secabo” mean?

In these few cases, indeed, I have been quite unable to work out what the word means.  Maybe this is down to the eccentric spelling.

What on earth did Arndt think he was doing here?  If he was providing a transcription, he had no business correcting the text, as his apparatus makes clear that he did.  If he was providing a text, then using normal spellings was essential.

We will plod on, of course.  But Arndt’s laziness makes the task much harder than it should have been.

Why does paleography work, and how did we get it?

Paleography is a technique for dating hand-written copies of ancient or medieval texts by looking at the way that the actual text is written; the shapes of the letters, abbreviations used, and so on.

I’ve found by experience that laymen often don’t understand how it works, or why it works.  Only yesterday I came across a book by a German crank asserting that Augustine’s Confessions, composed before 400 AD, were in fact written by Anselm in the 11th century.  The existence of physical copies written before that – the earliest copy of the Confessions is in fact 6th century[1] – was dismissed airily; the copies were dated using paleography, and paleography was bunk.[2]  It’s not an uncommon mistake in certain circles.

I’m not a paleographer, and I only understand the fundamentals.  But I’d like to share what I have, in hopes of minimising further crass errors.

So how does it work?

Many things are best understood when we know what the problem was that gave rise to them.

After the end of the Reformation in France, and in the century before the French Revolution, the country was governed as a Catholic autocracy by the Bourbon dynasty.  The church held wide lands, much wealth, and great power.  The nobility and the various monastic orders fought among themselves to acquire yet more, under the smiling gaze of the Sun King or the other royal despots.  Junior or more recently founded orders like the Jesuits naturally found themselves at odds with older ones like the Benedictines.

The Jesuit Daniel Papebroch advanced the claim that many of the old charters, granting lands to these orders, were in fact forgeries.  Among them he listed a grant by an early Merovingian king to the Benedictine order dated 590 AD.  Of course this was no mere bit of scholarly noodling; if true, vast wealth would pass out of the hands of the order and back into royal hands.

The Dominican order took this as what it was, an attack on the privileges of the church.  They demanded that the inquisition investigate Fr Papebroch.

The Benedictine order took a different view.  The ancient Benedictine houses of France had regrouped as the Congregation of St Maur, with their headquarters in Paris at the abbey of St.Germains-des-Pres, and had emphasised scholarship.  So they saw the claim as an intellectual challenge.  The task of defending the order was given to Dom Jean Mabillon.

Mabillon quickly realised that all the medieval charters, and indeed medieval books, were written in a variety of forms of writing, even though the language was always Latin.  The letter forms differed.  Here are some examples:[3]

Roman square capitals
Carolingian minuscule

Mabillon theorised that the types of “book hand” changed over time; and also that they changed from country to country, (although in fact the location proved less important).  So he compiled a big reference volume, consisting of examples of the writing from charters or books that he could date.

It’s possible to date most charters.  They come with a signature at the bottom, of somebody important, and often with a phrase like “Given at our court in Aachen on the 23rd of May, 840” or something like that.  Likewise books may have a note at the end such as “Completed by the monk Ernald in the eight hundred and twentieth year of our Lord.”  Of course the dates may be forged – that’s the question  before us – but they can’t ALL be forged!

So Mabillon started with these.  He drew up examples, with their stated dates.  And … bingo!  He was suddenly able to see, what no man had ever seen: the change of scripts over time from antiquity to his own period.

Because of the volume of data, he could see what the real book-hand was at various periods.  And, armed with this, the forgeries stuck out like sore thumbs.  Because the forgers did NOT have Mabillon’s knowledge of old scripts and the dates in which they were in use.  Indeed they didn’t actually know that scripts varied, or why.  So whatever they did, they were screwed.  It was possible to see, at a glance, that many of the early charters were indeed not what they appeared to be.  In fact the Merovingian charter that had provoked all this was shown to be written in a later hand.[4]   It was now possible, using this database, to date many other books that had no scribal note at the bottom.

Mabillon published his data and results in 1681 in his book, De re diplomatica.  It met with universal approval.  Even Papebroch hailed it as an achievement.

This was the birth of paleography.  The word itself had to wait until Mabillon’s colleage, Dom Bernard de Montfaucon, did the same task for Greek manuscripts, which he published under the title of Paleographia Graeca.

To this day, paleography adopts the same method.  The first step, in creating a paleography for any culture, is still to create an album of “dated and dateable manuscripts” – this phrase appears in the title -, with pictures of the scripts.

The next step was to refine these broad-brush classifications.  This indeed is what paleographers still do.  Parchment is expensive, so most documents and books were abbreviated with signs like “&” for “and”; or space was saved by the use of “ligatures”.  Today we have only one or two of these: “æ” for “a” and “e” saves a precious bit of space.  But there were hundreds of abbreviations and ligatures; and these too varied over time and space.  This also gives us information with which to localise the production of a book.

There are limits to the method, which are obvious.  A scribe may be active for 25 years, and write the same script in which he was trained over the whole of that period, even if a new style has come in.  Paleography becomes more unreliable, the smaller the database, the shorter the time-span.  Inevitably subjective judgements creep in.  How closely a document may be dated by paleography may be questioned.  But I would imagine that we can reduce the date to within a century without too much difficulty in most cases.  A specialist might do better.

It is often asked why carbon dating is not used instead.  But of course it was not available to scholars in 1681, or indeed until very recently.  Even then, the accuracy of carbon dating is often no better than paleography.  A further problem is that carbon dating will give the date at which the parchment was harvested, not the date at which the text was written.  Parchment was reused for centuries.  Also carbon dating requires the destruction of a portion of the book or charter, which rarely is acceptable to the owners.  Finally paleography may also give us the monastery at which an item was written, which carbon dating cannot.  But this is an area in which technology is progressing.  The size of the sample needed is reducing all the time, and probably there will be more carbon dating of manuscripts in future.

Paleography is a valuable part of the scholar’s toolbox.  It will continue to be so, for the foreseeable future.

  1. [1]Michael M. Gorman, “Aurelius Augustinus: The testimony of the oldest manuscripts of Saint Augustine’s works”, Journal of Theological Studies 35 (1984), 475-480, JSTOR: “Rome Biblioteca Nationale Centrale,Sessorianus 55 (S, CLA 4, 420a), probably written in Spain in the second half of the sixth century, is the oldest manuscript of St. Augustine’s Confessiones (fos. 1-79v).14 The words ‘Confessionum sancti Augustini libri XIII’ appear in a subscription of fol. 79v.”
  2. [2]Hermann Dettering, O du lieber Augustin: Falsche Bekenntnisse?, Alibri (i.e. self-published), 2015. ISBN 978-3-86569-181-1.  I have not seen the book, but a 2014 interview with Detering may be found here: “Q: Auch wenn wir Ihrer Textanalyse und der daran anknüpfenden Indizienkette bis hierhin folgen, so bleibt für Ihre These das Problem, dass die “Confessiones” in anderen Werken des frühen Mittelalters genannt werden und Abschriften vorliegen, die ins 9. Jahrhundert datiert werden – also vor Anselm…  Die Datierung der Handschriften erfolgt durchweg auf paläographischer Grundlage d.h. sie basiert auf der Schriftanalyse. Ich blende dieses Problem keineswegs aus, sondern überlasse dem Leser die Entscheidung: Er kann sich entweder auf die internen Argumente, d.h. auf seine Vernunft verlassen – oder aber auf die Kunst der Paläographen, die geirrt haben – und immer noch irren. Ich gebe in meinem Buch ein markantes Beispiel dafür. Man sollte nicht glauben, dass mittelalterliche Autoren, die unter falschem Namen schrieben, nicht gewusst hätten, wie sie ihren Texten ein archaisierendes Aussehen geben konnten, um sich in den Augen der Leser und selbst späterer Fachleute als “authentisch” zu empfehlen.” — “Q: Even if we follow your textual analysis and the related chain of indications so far, your thesis remains the problem that the “Confessions” in other works of the early Middle Ages are called and copies are available, which are dated to the 9th century – before Anselm …  The dating of the manuscripts is done on a paleographic basis, i.e. it is based on the handwriting analysis. I by no means exclude this problem, but leave the decision to the reader: it can either rely on the internal arguments, i.e. rely on his reason – or on the art of paleographers who have erred – and still wrong. I give a striking example in my book. One should not believe that medieval writers who wrote under a false name did not know how to give their texts an archaic appearance, in order to be “authentic” in the eyes of readers and even later experts.”  I owe knowledge of this to posts on the Vridar site, run by a fraternity who hope that Jesus never existed.
  3. [3]I have borrowed all of these from this marvellous site
  4. [4]In fairness, this did not mean that it was a forgery.  The passion for paperwork originated with the Normans, rather later on.  Illiterate kings may well have given grants of land orally.  But once paperwork was important, the monks then found it necessary at a later date to record them in writing.  On the other hand forgery of legal documents was rife during the middle ages.

Menelaus of Alexandria in al-Biruni

Continuing from yesterday…. A little more information about Menelaus of Alexandria can be got from Roshdi and Papadopoulos’ introduction, although not without effort.

On page 13 they tell us about the lost work of Menelaus:

The Book on the Elements of Geometry, translated by Thābit ibn Qurra, was quoted by other scholars, like al-Bīrūnī.37

With the deeply unhelpful footnote:

37. Istikhrāj al-awtār, in Rasā’il al-Bīrūnī, Hyderabad, 1948, p. 49.

One’s heart sinks, doesn’t it?  What’s the chances of getting hold of an Arabic work printed in Hyderabad in India?  And a Google search gives you nothing.  Anyway, I couldn’t read it.

Fortunately specialist J. P. Hogendijk has a webpage on al-Biruni, with bibliograph and links here, including PDFs!  The work in question turns out to be al-Biruni’s work on “Chords”.  The Hyderabad edition is there for download!  But even better:

German translation based on the Leiden ms.: H. Suter, Das Buch der Auffindung der Sehnen im Kreise, Bibliotheca Mathematica Dritte Folge, 11 (1910-11), 11-78, reprinted in IMA 35, pp. 39-106, reprinted in Suter, Beiträge vol. 2, pp. 280-347, scan,  another scan.

Yes, the links to “scan” are PDFs of the article!  And the volume of Bibliotheca Mathematica 11 (1910) is online at Europeana here.  In fact Hogendijk also tells us that the manuscript is “Leiden Or. 513, 108-129”, and provides a scan of photographs!  This is such a valuable site!

So we can now see what al-Biruni had to say about Menelaus of Alexandria.  It’s on p.31 of Suter’s article.

1. Es sollen aus zwei gegebenen Punkten zwei Gerade gezogen werden, die einen gegeben en Winkel miteinander bilden, und deren Summe gleich einer gegebenen Geraden ist, von mir.

Menelaus wollte im zweiten Satze des dritten Buches seines Werkes über die Elemente der Geometrie beweisen, wie in einem gegebenen Halbkreis eine gebrochene Linie gezeichnet werde gleich einer gegebenen Linie; er schlug aber hierzu einen sehr langen Weg ein.(1) Nachher behandelte sie (diese Aufgabe) Thäbit b. Kurra in seinem Kommentar dieses Buches (des Menelaus) auf einem ungefähr so langen Wege wie Menelaus selbst. Nachdem nun aber die Eigenschaften der gebrochenen Linie bekannt geworden sind (2), so ist die Behandlung dieser Aufgabe des Menelaus eine leichtere geworden, und sie erstreckt sich nun sogar allgemeiner auf alle Bögen eines gegebenen Kreises (nicht nur auf den Halbkreis).

1. Let us draw two straight lines from two given points, which form a given angle with each other, and whose sum is equal to a given line, by me.

In the second section of the third book of his work on the Elements of Geometry Menelaus wanted to prove how a broken line is drawn in a given semicircle, equal to a given line; but he took a very long journey for this purpose. (1) Afterwards Thabbit ibn Kurra treated (this proposition) in his commentary on this book (Menelaus) with a pathway as long as Menelaus himself. Now that the properties of the broken line have become known, (2) the treatment of this task of Menelaus has become easier and extends now even more generally on all arcs of a given circle (not only on the semicircle).

The footnotes are just references to studies.

Well, it doesn’t tell us very much in truth.  It confirms that Menelaus’ lost work on The Elements of Geometry did survive into the 9-10th century, and was in the hands of the translators in Baghdad, and was in at least 3 books.  We know from elsewhere that Thabit ibn Qurrah translated it into Arabic.

Still, it’s nice to get this far.  Even the baffling reference could be elucidated, with a bit of ingenuity and the use of the world-wide web.

Marvellous really, isn’t it?

You can call me al-… : Arabic sources on Menelaus of Alexandria

I ran out of time when doing yesterday’s post so I had to cut short my investigation of Arabic sources for Menelaus of Alexandria and just post what a secondary source said.

Today we only know the Sphaerica of Menelaus; but his Elements of Geometry were translated into Arabic by Thabit ibn Qurrah in the 9th century.

Apparently a certain al-Sijzī was familiar with the work in Thabit’s version, or so I learned from the article by Rashed and Papadopoulos.  I thought it might be interesting to find out more.

I’d never heard of al-Sijzī, although he is the author of some 20 astronomical works and 40 mathematical ones, most unpublished.[1]  But I discovered today that an English translation of one of his works is online in the Wayback When Machine in, here.[2]  Sadly this is not the one that mentions Menelaus.

Following R&P’s reference leads us to an unpublished source and an article inaccessible to me.[3]  So sadly we can’t see what al-Sijzi actually says.  Still, not bad going for a language that I don’t read.

While looking for references, I found that Roshdi Rashed has been extremely busy creating reference literature in French and English on Islamic science.  This is very praiseworthy.  We really do need good reference literature on Arabic texts.

  1. [1]Glen van Brummelen, “Sijzī: Abū Saʿīd Aḥmad ibn Muḥammad ibn ʿAbd al‐Jalīl al‐Sijzī” in Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, p. 1059, Online here.
  2. [2]Hogendijk, Jan P. (1996). Al-Sijzi’s Treatise on Geometrical Problem Solving (PDF). Tehran: Fatemi Publishing Co. ISBN 964-318-114-6.
  3. [3]Roshdi Rashed, Les mathématiques infinitésimales du IXe au XIe siècle, vol. 4, 2002, p.612, n.15: “Qawî Ahmad ibn Muhammad ‘Abd al-Jalil al-Sijzi fi khawàss al-a’mida al-wâqi’a min al-nuqta ai-mu’tà ila al-muthallath al-mutasawi al-adla’ al-mu’ta bi-tariq al-tahdid,: mss Dublin, Chester Beatty 3652, fol. 66r – 67r; – Istanbul, Reshit 1191, fol. 124v-125v. Cf. J. P. Hogendijk, “Traces of the Lost Geometrical Elements of Menelaus in Two Texts of al-Sijzi”, Zeitschrift fur Geschichte der arabisch-islamischen Wissenschaften, Band 13 (1999-2000), p. 129-164, p, 142 ff; et R Crozet, «Géométrie: La tradition euclidienne revisitée», dans Enciclopedia Italiana, forthcoming”.  The Rashed volume contains an excerpt from the al-Sijzi work.

Everything you ever wanted to know about Menelaus of Alexandria but were afraid to ask

I’ve just come across an ancient author who is completely unfamiliar to me.  His name was Menelaus, and he was a mathematical writer, and one of his books even survives today, his Spherics, although only just.

Let’s see what ancient sources say about him.

In the Almagest (or Syntaxis) VII.3, Ptolemy tells us that he was in Rome and making astronomical observations in the first year of Trajan; that is, in 98 AD.  Here are the two passages from that chapter of book 7.  Page numbers are from the Toomer translation.[1]

(p.336): [Thirdly] the geometer Menelaus says that the following observation was made [by him] in Rome. In the first year of Trajan, Mechir 15-16, when the tenth hour [of night] was completed. Spica had been occulted by the moon (for it could not be seen), but towards the end of the eleventh hour it was seen in advance of the moon’s centre, equidistant from the [two] horns by an amount less than the moon’s diameter.

(p.338): Similarly, Menelaus, who observed in Rome, says that in the first year of Trajan, Mechir 18/19, towards the end of the eleventh hour, the southern horn of the moon appeared on a straight line with the middle and the southernmost of the stars in the forehead of Scorpius, and its centre was to the rear of that straight line, and was the same distance from the middle star as the middle star was from the southernmost; it appeared to have occulted the northernmost of the stars in the forehead, since [this star] was nowhere to be seen.

Mechir is the Egyptian 6th month, by the way, which I am told is Feb. 8th – March 9th in our calendar.

Menelaus appears in the Moralia of Plutarch, in De facie in orbe lunae (On the face in the moon), chapter 17.[2]  This is a dialogue, most likely a Greek-style symposium, between various well-connected people.  A man who may be Plutarch’s brother is speaking:

“Yes, by Heaven,” said Lucius, “there was talk of this too”; and, looking at Menelaus the mathematician as he spoke, he said: “In your presence, my dear Menelaus, I am ashamed to confute a mathematical proposition, the foundation, as it were, on which rests the subject of catoptrics. Yet it must be said that the proposition, ‘all reflection occurs at equal angles,’ is neither self-evident nor an admitted fact….

Menelaus does not reply, nor speak.  I picture him as perhaps being busy with the food tray.

In Proclus’ Commentary on the first book of Euclid’s Elements, we find this under Proposition 25:[3]

But the proofs that others have produced for the same proposition we shall recount briefly, and first the proof discovered and set forth by Menelaus of Alexandria.

This indicates that Menelaus came from Alexandria, like so many other mathematical philosophers.  There is also something in Pappus, Mathematical Collection.[4]  In book 4 he says:[5]

Some of these curves have been found worthy of a deeper study, and one has even been labelled the “paradoxical curve” by Menelaus.

In book 6:[6]

In his Spherics, Menelaus calls such a figure a “trilateral”.


He says nothing about the setting of these arcs, because the reasoning of the demonstration falls back on the distinctions relative to their rising, and a work, on which we will later put forward some considerations, has already been written on this subject by Menelaus of Alexandria.

No such “considerations” appear in the text of Pappus as it has reached us, however.  But Pappus confirms that Menelaus is from Alexandria, and indicates knowledge of a lost work by Menelaus.

There is a little more information about Menelaus’ books from Arabic sources, much later.  By the 10th century scholars in Baghdad were translating as much of Greek technical literature as they could find.

Four works are listed in al-Nadim’s Fihrist or Catalogue, which has an entry on Menelaus.[8]  It reads:


He lived before the time of Ptolemy, who mentioned him in the book Almagest. Among his books there were:

Forms of Spherics [Menelai Alexandria sphaericorum], Knowledge of Quantity in Distinguishing Mixed Bodies [De cognitione quantatis discretae corporum permixtorum]—He wrote it for Emperor Domitian.[9] The Elements of Geometry [Elementa geometriae], which Thabit ibn Qurrah rendered in three sections; Triangles [De triangulis], a small part of which appeared in Arabic.

Rather later is al-Qifti who writes:[10]

Menelaus is among the guides of the geometers of his time, before the time of Ptolemy, the astronomical observer who mentions him in his book the Almagest. He was at the forefront for the benefit of his domain in the city of Alexandria – some said Memphis. His books were once translated into Syriac, then into Arabic. Among his writings is a book On the Knowledge of the Quantity of Specification of Mixed Bodies, dedicated to the King Ṭūmāṭiyānūs.

The Elements of Geometry translated by Thabit ibn Qurrah is known to other Arabic writers.  Al-Sijzī had a copy, and al-Biruni quotes from it.[11]  It is a lost book, however.

The only work of Menelaus to survive is his Spherics.  The original Greek text is lost.  Only a few quotations survive, which were mainly collected by A.A. Bjørnbo.[12]

However a number of translations were made into Arabic, from which the text became known in the west.  The Arabic tradition is complicated and is the subject of study at the moment.  One reason for the complexity is that Menelaus did not give complete proofs of his propositions, but rather outlines of how they might be proven.  Consequently the book was invariably expanded and “rectified” by translators or editors in Arabic, in order to make the book actually useful.  The result is that a number of versions exist, and the relationship between them is unclear.  Krause in the 1930’s edited and translated into German the edition by Abu Naṣr Manṣūr[13], and Rani Hermiz translated it into English[14].  I understand that a revision of this was printed in Hyderabad.[15].  A portion of a very early translation, differing from all the others, plus the edition of al-Māhānī/al-Harawī, has recently been edited and translated into English by Rashed and Papadopoulos.[16]

A Hebrew translation made from Arabic exists.  There are 8 manuscripts of this.  Two of them attribute the translation into Arabic to Hunain ibn Ishaq, the famous translator; the other six attribute it to Ishaq ibn Hunain, his son.  But the actual text of the Hebrew translation is based on more than one of the Arabic editions, not on whatever Hunain ibn Ishaq may have produced.[17]

There is also a medieval Latin translation by Gerard of Cremona, but this also is based on a mix of Arabic editions.

The Arabic version was translated for the first time into Latin by Francois Maurolyc, and printed at Messina in 1558, in a work containing also Latin versions of the Spherics of Theodore and the treatise “Of the movement of the sphere” by Autolycus.[18]  This was reprinted at Paris in 1644 in a work by Fr Mersenne, and then with the 2nd edition of the Greek text of Theodosius by Hunt, at Oxford in 1707.  The English astronomer Halley, the discoverer of Halley’s Comet, produced two Latin editions of the work at Oxford.  These were based upon the Hebrew and the Arabic versions, both of which were accessible in manuscripts in the Bodleian Library in Oxford.[19]

That’s all I have on Menelaus, perhaps a famous man in his own day and now hardly known.  Only his Spherics has survived.

Let us hope that perhaps a copy of the Elements of Geometry lingers somewhere, in some unexplored eastern library.  It was a “religious library” in Meshed in Iran that proved to contain an Arabic version of Galen’s On my own books, so discoveries may yet be made.

It is interesting to reflect that, when Menelaus was taking his observations in the capital of the world, and chatting with Plutarch, the apostle John was still alive.[20]  Doubtless neither Menelaus nor his important friends had ever heard of John.  But it was John who changed the world.  It’s a reminder to us, not to take the valuations of our world at face-value.

  1. [1]G. J. Toomer, Ptolemy’s Almagest, Duckworth, 1984.
  2. [2]The Loeb translation is online at Lacus Curtius here.  Beware: chapter 18 appears before chapter 17.
  3. [3]Proclus: A commentary on the first book of Euclid’s Elements, tr. Glenn R. Morrow, 1970, p.269.
  4. [4]Paul ver Eecke, “Pappus d’Alexandrie: La collection mathematique”, Paris, 1933.
  5. [5]p.208.
  6. [6]Proposition 1, p.371.
  7. [7]Proposition 56, p.459.
  8. [8]Bayard Dodge, The Fihrist of Al-Nadim: A Tenth-Century Survey of Muslim Culture, 1970, 2 vols. Chapter 7, p.638.
  9. [9]Lit. “King Ṭūmāṭiyānūs”, so R&P, ch. 1, p.11.
  10. [10]Quoted from R&P, p.12, rather than directly.
  11. [11]See R&P for details.
  12. [12]A.A. Bjørnbo, Studien über Menelaos’ Sphärik (Leipzig, 1902): pp.22-25.  Online at here.  A few more were located in the scholia to the Almagest : F. Acerbi, “Traces of Menelaus’ Sphaerica in Greek Scholia to the Almagest,” SCIAMVS 16 (2015): p.91-124; online at here.
  13. [13]M. Krause, Die Sphärik von Menelaos aus Alexandrien in der Verbesserung von Abū Naṣr Manṣūr b. ‘Alī b. ‘Irāq, Berlin: Weidmannsche Buchhandlung, 1936.
  14. [14]Rani Hermiz, “English Translation of the Sphaerica of Menelaus”, California State University San Marcos, MA diss., 2015.  Online here.
  15. [15]Naṣr al-Dīn al-Ṭūsī, Kitāb Mānālāwus, Taḥrīr, Hyderabad: Osmania Oriental Publications Bureau, 1940
  16. [16]Roshdi Rashed, Athanase Papadopoulos, Menelaus’ ‘Spherics’: Early Translation and al-Māhānī/al-Harawī’s Version. Scientia Graeco-Arabica 21.   Berlin; Boston:  De Gruyter, 2017.  Pp. xiv, 873.  ISBN 9783110568233. There is a Google Books preview here. I am indebted to the Bryn Mawr review of this by Nathan Sidoli of Waseda University for much of the above.  The review is here.
  17. [17]So R&P.
  18. [18]Theodosii Sphaericorum elementorum libri. III. ex traditione Maurolyci Messanensis. Online here.
  19. [19]Menelai Sphaericorum libri III, ed. Ed. Halleius, Oxonii 1758; and Menelai Sphaericorum lib. III, quos olim collatis mss. hebraicis et arabicis typis exprimandos curavit Ed. Halleius, praefationem addidit G. Costard.  Oxonii, 1758.  Online at Google Books here.
  20. [20]Irenaeus, Adversus Haereses, book 2.

A daguerreotype of the Roman forum from 1842

A kind correspondent has drawn my attention to an article in the New York Times, on an exhibition of daguerreotypes.  These were early photographs which possessed a 3-D quality hard to reproduce today.  The Metropolitan Museum in New York possesses a collection taken by Frenchman Girault de Prangey (1804-1892).  They were all taken in 1842, shortly after Daguerre invented photography, and must be some of the first photographs of everything they depict.  All are of great value.  For instance they include a photograph of the old palace of the Tuileries, destroyed in 1870.

The image that concerns us here is possibly the first photograph of what it depicts.  It’s the Roman forum, viewed from the Palatine hill.  Is that the Arch of Septimus Severus there in centre right?  I wish we had the same view in a modern photograph, for comparison!  (I looked but was unsuccessful).

Here it is:

Marvelous to see this!  Of course this is Papal Rome.  The Victor Emmanuel monument has yet to be built.  The demolitions of Mussolini have yet to take place.

The NYT article is well worth a read.

UPDATE:  A kind correspondent has pointed out that the NY Times has printed the image back to front!  Flipped it looks like this:

with the ramp up to the capitoline in the left.  He also sent in a Google maps view:

My mistake!

The Annals of Eutychius of Alexandria (10th c. AD) – chapter 1 (part 6)


13. At that time people spoke only one language and one dialect.  Some say that they spoke Syriac, others instead that they spoke Hebrew, and others that they spoke Greek. For me the latter are more reliable, because the Greek language is much more vigorous, richer and more varied than both Syriac and Hebrew (44). Seventy-two of them gathered together and said: “Let us build a city and gird it with walls, and erect in it a tower that reaches up to heaven, because if one day there is a flood we will be protected”.  For three years they made crude bricks and put them to bake.  Each brick was thirteen cubits long, ten wide and five high.  Then they built a city between Sūr and Bābil.  The city was three hundred and thirteen bā‘ long (45) and it was a hundred and fifty-one bā‘ wide.  The height of the wall was five thousand five hundred and thirty-three bā‘ and its thickness thirty-three bā‘.  The tower was ten thousand bā‘ tall.  They built it in forty years.  While they were still intent on building, God sent them an angel (46) from heaven who confused their tongues and altered their language, so that when one spoke to another he could not understand what he was saying.  That place was called Babil because it was there that the languages ​​became confused, and it was from there that they spread out across the land.  Forty-six years had passed since the birth of Fāliq.

Of those seventy-two men, twenty-five belonged to the Banū Sām.  They lived from the Euphrates and Mosul as far as the Far East, and from them came the Syrians, the inhabitants of Diyār Rabī‘a and Mesopotamia, the Garāmiqa, the Chaldeans, i.e. the inhabitants of Bābil, those of Fāris, of Khurāsān, of Farghāna, of  Sind, of India, of the peninsula as-Sin, the Hebrews, the inhabitants of Yemen, of at-Tā’if, of al-Yamāma, of Bahrayn and the different Arab lineages.  They have eight forms of writing: Hebrew, Syriac, Persian, Indian, Chaldean, which is the Babylonian writing, Chinese, Himyarite and Arabic. The Sāmites touched, out of the great watercourses, the Euphrates and the Balikh river.

Of those [seventy-two men], thirty-two belonged to the Banū Hām.  They inhabited Syria – also called the land of Kan‘ān because Hām had a son named Kan‘ān – up to the extreme West and there are derived from them the Canaanites, the Philistines, the Egyptians, the Copts, the Mans (47), the lineages of Sūdān, Abyssinia, Nubia, the Bugāhs (48), the Zang, the Zutt, the inhabitants of Qarrān, the Samaritans, the Zābig, the Maghrebins and the Berbers.  They have twenty-six islands, including Sardinia (49), Malta and Crete, and a part of the island of Cyprus and others. They have six forms of writing: Egyptian, Nubian, Ethiopian, farangis (50), Punic and qunquli (51).  The Hāmites touched,  out of the great watercourses, the Nile.

Of those [seventy-two men], fifteen belonged to the Banū Yāfit.[1]  They lived from the Tigris to the far north and there are derived from them the Turks, the Bağnāk, the Tugharghar, the Tubt, the inhabitants of Yāğūg, of Māğūğ, of Khazar, of Lān, the Anğāz, the Sanābirah (52), the inhabitants of Ğarzān, the inhabitants of Great and Little Armenia, of Hawrān, of Antioch, of al-Khālidiyyah, of Paphlagonia, of Cappadocia, of Kharshana, the Greeks, the Romans, the Byzantines, the Russians, the Daylamites, the Bulgarians, the Slavs, the Lombards, the Franks, the Galsatīn and the Spaniards. They have twelve islands, including Rhodes, Sicily, Cyprus, Samos and others. They have six forms of writing: Greek, Roman, Armenian, Spanish, Frankish and ğurzāni. Of the great watercourses, the Yāfitites touched the Tigris.  From the deluge to the construction of the tower and the confusion of languages five hundred and seventy-eight years had passed, and from Adam to the construction of the tower two thousand eight hundred and thirty-four.

14. At one hundred and thirty Fāliq had Rāghū (53) and he was thirty when Qīnān died in the month of Ab, i.e. Misrà, at the age of four hundred and thirty years.  Fāliq lived in all three hundred and thirty-nine years.  At the age of one hundred and thirty two years Rāghū had Shārū‘ (54). In his day men worshiped idols and everyone worshiped and venerated what he liked (55). Some worshiped the sky, others worshiped the sun, others the moon, others the stars, others the birds, others the earth, others the beasts, others the rivers, others the trees and others the mountains (56).  There were those who made themselves an idol in the likeness of their father, mother and those whom they loved more than others and filled with favours, and when one of them died, they adored him and made him a god (57).  Others made idols of gold, silver, stone, or wood.  The inhabitants of Egypt, Bāhil, and Ifrangis and the inhabitants of the coasts began to do this.  In another text they are said to be only imitators.  It is also said that the origin of the worship of idols goes back to the custom that they had, of placing on the tomb of a dead person an idol similar to him so that they did not forget his memory. So it was that the earth was filled with idols made in the image of men, women and children (58).  At that time a rich man died, having a son who made an idol in the image of his father and placed it on his grave, placing his servant as guardian.  But the thieves came and stole everything the young man had at home.  The young man rushed to his father’s grave and began to cry and moan at that golden idol just as if he was complaining to his father. The devil spoke to him from the belly of the idol and said to him: “Do not cry. Instead, bring your youngest child here and offer him as a sacrifice. Then bathe in his blood and I will give you back everything you had”.  The young man left and returned with his son, slaughtered him in front of the idol and bathed in his blood. The demon then came out of the idol and entered the young man and taught him magic and incantations.  It was from that time that men began to sacrifice their children to demons and to practice magic (59).



  1. [1]i.e. Japeth, obviously.