Mathematical and Philological Insights on Cuneiform Texts. Neugebauer’s Correspondence with Fellow Assyriologists

Abstract

When reading an ancient text, we are deeply indebted to readings made previously by scholars who edited the texts and made them available. The process of decipherment, transliteration, translation, and commentary does not provide us with the raw material, but rather with interpretations of these texts. These reading keys are not always made explicit in the publications, but they appear more clearly in the editors’ working documents, such as drafts, letters, annotations or notebooks. In recent years, working documents produced and used by Otto Neugebauer when he was preparing the earliest editions of mathematical cuneiform texts became accessible to the researchers. The aim of this chapter is to show some aspects of the impact of Neugebauer’s work on our current understanding of cuneiform mathematics. The first part provides a brief overview of Neugebauer’s papers relating to mathematical cuneiform texts. The second part presents some examples showing how the works of Neugebauer and his close colleagues (mainly Goetze, Sachs and Thureau-Dangin) shaped the editions of cuneiform mathematics.

Appendices

Appendices

Appendix A: Letters

German letters were translated in English by Sandra Hoehn.

Photo Business

YBC, Neugebauer to Stephens 1934/01/31 (in German)

Copenhagen, January 31, 1934

Dear Professor Stephens,

I would like to thank you for your letter of the 4 January and much to my honest regret, I was sorry to hear of the passing of Professor Dougherty.

The matter of the photographs of your collection was kindly arranged by Professor Flexner, New York, and led Professor Dougherty to provide me in 1932 with photographs of mathematical texts of his collection. These photographs are important for my entire enterprise on mathematical cuneiform texts. Thus far, he has forwarded me photographs of the following: YBC 4692, 4709, 4710, 4713 and promised me to send me further texts, which unfortunately did not happen due to his illness. At the time, he sent me three types of texts as photographs in order for me to ascertain which ones are important to me. They are the following: (1) metrological texts (several lists of measures such as YBC 4701), (2) multiplication and division tables such as YBC 4692, (3) purely mathematical texts such as YBC 4709/10/13.

Of these types of texts only the last two are of interest to me, while there are also texts which could be grouped in the first as well as the second type; these are needless to say also important to me.

Considering the still relatively small number of mathematical texts compared to the rest of the cuneiform literature, it is of the utmost interest to me to become familiar with even the smallest and poorly preserved fragments. Based on purely mathematical reasons, which I cannot explain in few words, I find even the seemingly straightforward tables interesting (if you are interested in peculiarities, maybe I can direct you to my research on the “Sexagesimal and Babylonian Fractions 1 to 4” in “Quellen und Studien zur Geschichte der Mathematik B 1 und 2”).

I would be very grateful if you could ensure that the photographs also contain the text margins and, if possible, include a scale. Furthermore, I would like to ask you not to mount the photographs. It goes without saying that I am prepared to pay the costs for the photographs and I would like you to inform me about this.

I hope I am not causing you too much inconvenience with my requests and would like to take the liberty to add another. Could you please get the photographs prepared soon, since I am quite advanced in my work and would shortly like to reach a relatively final overview of the material. It may be interesting for you to know that the Yale texts YBC 4709/10/13 especially represent a new and very interesting type of text (systems of quartic equations) and it is thusly of the utmost historic interest to find out how the other texts from your collections are to be classified in respect to this group.

I am looking forward to hearing from you again and would like to thank you once again for your kind efforts.

My warmest regards,

Yours respectfully

P.S. Certainly Professor Flexner will be willing to offer more information. Hence I am taking the liberty of sending him a copy of this letter.

YBC, Stephens to Neugebauer 1934/05/29

New Haven, May 29, 1934

Dear Professor Neugebauer:

After considering from every angle the question of your publishing our mathematical texts, I may now give you the following decision. You have my permission to make full use of the photographs which Professor Dougherty sent to you. They may be published in transcription, translation, autographed copied and photographic reproduction, if you desire. After examining the rest of the mathematical texts in our Collection it is very obvious that Professor Dougherty selected the best one to be photographed. Seeing that you have had some difficulty in reading even these photographs, I am sure that the majority of the texts could not be satisfactorily read from photographs without the help of someone who could have direct access to the tablets themselves. I do not feel like assuming full responsibility for doing the work that would be necessary in collating and copying many of these tablets. If you could find it possible to come in person to New Haven to study our texts at first hand I should be very glad to place them at your disposal. If this is not possible I have one other suggestion. You probably know that Professor Albrecht Goetze is to be Visiting Professor of Assyriology at Yale University next year. It has occurred to me that you may be able to secure his consent to give you the necessary assistance in handling these texts. I suggest that you get in touch with him at the following address: Esperance Alle 18, Kobenhavn-Charlottenlund. If he is willing to give you the assistance you will require I shall give my consent to the full use of all of the texts. Otherwise it seems to me that the balance of them should be reserved for publication by someone who have direct access to the tablets themselves.

I am returning to you herewith the copy of your manuscript which you kindly sent to me some time ago.

Yours very sincerely,

Ferris J. Stephens, Acting Curator

YBC, Neugebauer to Stephens 1934/06/12 (in German)

Copenhaguen, June 12, 1934

Dear Professor Stephens,

Thank you very much for your letter of the 29 May and the return of my manuscript. Moreover, I would like to thank you for putting the photographs, which are already in my possession, at my disposal and for allowing me to work on further mathematical texts. Personally, I know Professor Götze very well. By this time he is writing to you of his commitment to support me in the collation of problematic parts of the text as well as in any other way possible.

From a purely technical point of view, I would like to make the proposition that at this stage you already procure photographs of the texts in questions. It would very much facilitate and accelerate my work if I could already begin the preparatory work. In addition, it would allow me to discuss fundamental questions with Professor Götze as long as he is still here. Needless to say, I am intending to wait with any kind of publication until Professor Götze is in New Haven. I am convinced that this proposition raises no concerns, the more so because photographs of these texts are without doubt required for a general examination of the condition of the texts.

My warmest gratitude for your endeavours,

Yours respectfully

YBC, Stephens to Neugebauer 1934/07/09

New Haven, July 9, 1934

Dear Professor Neugebauer,

Since I have received your letter of the 12th of June and that of Prof. Götze of the 16th of June, in which he promises to help you with the necessary collations of our mathematical texts, I have had photographs of six additional tablets made. There are still several others which have not been photographed. I shall have them done and sent to you later. I have not sent them all at once for two reasons. First, I wish to learn if you have any suggestions concerning the technique of photographing. Second, some of the remaining tablets are in need of cleaning and perhaps baking. This will require some time. You perhaps realize that in the process of baking and cleaning tablets some damage may result to the tablet in spite of all the care we can exercise. In cases where I think it is necessary to bake a tablet do you wish to go to the additional expenses of having photograph made both before and after the baking process?

There will be no expense to you for the baking and cleaning of tablets, of course. We shall charge you only for the photographs. You need not pay for these until you have received all of them. The photographs which I am sending you today have been made at a cost of $10.00. I have a record that Prof. Dougherty once sent you photographs costing $5.00. This makes $15.00 in all.

Trusting that you will find these new photographs satisfactory, I remain,

Yours very sincerely

Ferris J. Stephens

Acting Curator

Dialect Business

YUL, Goetze to Neugebauer 1942/02/04

February 4, 1942

Dear Neugebauer:

The mathematical tablets newly found among the unbelievable richness of our collection number eight (tables excluded). It may well be that I have still overlooked one or the other piece. It is not easy task to go through unclassified material and picks out what you are looking for. So this will be for the present the best I can do for you. The tablets are in relatively good condition. Photographs have been already been taken. Stephens will take care of cleaning and baking as soon as possible. After that new photographs may be taken, or you may come down personally to make a collation.

The tables are less exciting. I think they can wait until you come down for your lecture.

I am sorry that the oriental Club cannot take advantage of your coming. But it was only a very slight chance anyway. Have provision be made for living quarters? If not, don’t forget that my house is always at your disposal. This is valid also for Sachs, if he should like to accompany you.

Cordially yours

Did I ever tell you that the mathematical tablets in Old Babylonian can be divided in a northern and a southern group on linguistic grounds? The evidence in most cases confirms the information as to provenance given by the dealers from whom the tablets were purchased.

YUL, Neugebauer and Sachs to Goetze 1942/08/01

Providence, August 1, 1942

Dear Goetze:

We hope this finds you recuperated from the Summer Session of the Linguistic Society because we are herewith taking advantage of your kind affirmative answer to our request to look at the dialect(s) of our new Akkadian mathematical texts. Enclosed are the transcriptions of YBC 4608, 4662, 4663, and 4675, the only texts written in Akkadian except for the Plimpton tablet, on which the only two Akkadian words we can read with certainty are ṣi-li-ip-tim and [in]-na-as-sà-hu-ú-[ma]. In the enclosed transcription please disregard all underlining, since we used some of the carbon copies to make a vocabulary and underlined words to make sure that we didn’t miss any.

We also hope you won’t mind settling a friendly dispute which has arisen between us. Enclosed on a separate sheet is a translation of the first five lines of YBC 5037. One of us wishes to delete all the words which are in red, the other to keep them. We have decided to abide by your decision as to which of the two translations you would like to read.

We are waiting for several months now with bated breath for the new photographs of the Yale texts while the draft creeps up relentlessly toward one of us and while the other one is being loaded with more and more University duties. Stephens wrote us some weeks ago that the photographs had long been taken but the photographer did not have the time to make the prints. If you, with your usual discretion, could hurry this up, we would be very grateful. Cordially

MCT Inc.

For your convenience, the following numbers are the pages on which the beginnings of the transcriptions of the Old-Babylonian Akkadian texts will be found:

• MKT I: 108, 124, 126, 137, 143, 194, 219, 239, 244, 248, 257, 259, 267, 269, 270, 274, 278, 287, 289, 294, 303, 311, 314, 317, 319, 335, 341, 346, 351, 353, 368, 373, 516.

• MKT II: 37, 43, 60.

• MKT III: 1, 22, 29.

YUL, Goetze to Neugebauer 1942/11/14

November 14, 1942

Dear Neugebauer,

I had your letter concerning my contribution to your and Sachs’ Mathematical texts.

I am quite willing to make good promise, but I am afraid I can hardly do before the Xmas recess. There are too many various things whirling around us to make possible the necessary concentration on that task. Furthermore, if I do it, would not it be advisable to include all the texts you are going to publish and not merely the four texts the notes on which you are returning to me? This would mean that I need your transliterations of all those texts (at any event the transliteration of YBC 4675, 4608, 4662, and 4683).

The right procedure, I feel, would be this: numerate the characteristics which allow the classification (giving a number to every item). Then, listing the signature of the texts and adding the number of the characteristic with the necessary references.

Stephens has to go to Indiana suddenly in family affairs (nothing tragic), and may thereby have been prevented from mailing the photos as he intended to. He will be back next Tuesday, and I shall talk to him as soon as I see him. I have seen the copies and they were very good indeed.

Let me know your decision on the dialect business.

Cordially yours

Fig. 3

YUL, Goetze to Neugebauer and Sachs 1942/11/14

January 21, 1943

Dear Neugebauer and Sachs,

I have just typed a 14 page statement concerning the “dialect” of the mathematical tablets. It needs going over and checking and will then be mailed together with your manuscript.

You did not answer my last question: namely whether in Stbg. 366 obv. A reading sa-am-da-ka-am “triangle” makes sense.

I have include a short note on ki-i a-a in my manuscript. I certainly shall take no offense, if you are not convinced.

E [YBC 8633]. Rev. 9: I am reading now i-ta-di-… (perhaps –kum after all). You remember that the whole thing is corrected and partially squeezed in. The […] form agrees with the same form in VAT 8512 which belongs in the same group because of concidences in terminology etc. The same form should also be restored in rev. 7 (and obv. 13?).

L [YBC 7164]: I took another look at the alleged te-er-di-it-sà and also had Stephens look at it. We both agree that the correct reading is te-er-di-iz-za. The iz has the same dimensions as in is-sú-uh (l. 18) and is markedly different from the it in ú-sa-mi-it (ll. 22, 24). […] iz signs are quite normal in this period. When you look up Fossey you will sign that originally the sign was rather wide and became gradually narrower. Moreover te-er-di-it-sà is (as far as I can judge) an “Unform” in OB.

M: eh-re-e is necessary just as ep-te-e and el-qé-e among other. In Babylonian the Umlaut (caused be “sharp laryngeals”) affects every preceding or following a and causes shift into e. This is one of the differences between Babylonian and Assyrian.

P: At the ends of ll. 3, 4 and 6a are erasures. In l. 3 the ma seems to be erased. In l. 6a I read an-nu-um-ma as-su with an erasure following. The an is certain. Your translation “now (?)” is hardly correct. The particle should be (and is almost everywhere else) a-nu-um-ma. The spelling with nu points to a form of the demonstrative pronoun.

The chief passage for tallum in my omen texts is YBC 4629 II 48 ff. There, one finds omina which begin šumma ta-al-lu. If one does not know what it is, one can hardly learn it from there.

Since I have not yet made out slips of all texts, I can quote at present only one passage for tarahhum (perhaps there is only this one). Iit is YBC 4678 IV 51 ff.: šum-ma mar-tum (52) li-pi-a-am (53) ta-ra-ha-a-sa u-ka-al-la “supposing the gall-bladder, its two tarahhu hold “fat”.

[?]: In l. 13 of the obverse can be no doubt as to the reading ne-pu-šu. The pu is perfect, i. e. contains four Winkelnaken. Obviously the photograph did fool you.

Cordially yours

YUL, Goetze to Neugebauer and Sachs 1943/01/25

January 25, 1943

Dear Neugebauer:

Here enclosed you will find the statement on the “dialects” of the mathematical tablets which I promised you some time ago. At the same time I am returning the pages of your manuscript which you so kindly placed at my disposal.

Not that I am entirely satisfied with the result. You will see that I felt completely to attempt some grouping of the texts. On this point I expect your criticisms. It is my feeling that I rather encroached on your domain. I would feel much better, if you could be persuaded to handle this subject in a special chapter which should precede mine. As it is, I could give only some hints in footnotes. You have expressed yourself the intention of doing some grouping at the head of your glossary. And I think the subject calls for some fuller treatment.

Otherwise, I think, it turns out neatly enough.

Expecting your reaction,

cordially yours

YUL, Neugebauer and Sachs to Goetze 1943/02/17 (the letter is erroneously dated 1942)

Providence, February 2, 1942^sic

Dear Goetze,

We still owe you a detailed reaction to your contribution to MCT in addition to the short words of thanks we have already sent you. We should have done this long ago, but we were both pretty tired out, partly from work on MCT (preparing the final manuscript and copying the texts) and stupid teaching in ever increasing amount. Fortunately enough, Brown University ran out of oil, and this gave us a chance to recover and to write to you under less unreasonable conditions.

First of all, we must emphasize that we are very glad that we asked you for this contribution, which brings a very interesting new element into our own discussion. As you know, we are unable to establish any local distinction in our material – an attempt (MKT 387 f.) to localize the “Series Texts” at Kish must now be abandoned because new evidence gained from analysis of an MCT text shows that sig₄ never means “volume”, but always “brick(s)”. It is therefore of great interest to learn that a clear “southern” group can be isolated. Unfortunately, we cannot contribute anything to this view of yours from the point of view of content. Our arrangement (A, B, C, D, etc.) is purely arbitrary according to content e.g., geometrical problems, irrigation problems, etc. The more material we get, the more we begin to realize to how great an extent we are at the mercy of the accidental character of the excavation and preservation of our texts. Grouping which seemed to be quite reasonable in MKT (e. g. “series texts”) disappear more and more. All we can say at present is that the content of the Old-Babylonian mathematical texts is so homogeneous and uniform that from this point of view one cannot make any classification with regard to origin or time (of course, the clear distinction from Seleucid material remains). We therefore intend to incorporate your contribution with no essential alterations as a separate chapter at the end of the large section dealing with problem texts. As the title of this chapter we suggest: “The Akkadian Dialects of the Old-Babylonian Mathematical Texts. By A. Goetze”. On the title page of MCT we would like to mention your name in the form “MCT by O.N. and A.S. with a chapter by A.G.” Please let us know if you are in agreement.

We might suggest a few minor alterations to conform with our own manuscript. We will send you the final copy of your chapter with our suggestions incorporated when it is typed; at that time, you will have the opportunity of approving all details or making any alteration that you may wish.

We are slowly approaching the end of our work – provided that you don’t discover new material. In the meantime, we wish to repeat our warmest thanks for your manuscript, which will contribute considerably to the rounding out of MKT and MCT.

Cordially yours

MCT, Inc.

Competition with Thureau-Dangin

YBC, Stephens to Neugebauer 1936/04/03

New Haven, April 4, 1936

Dear Prof. Neugebauer:

Thureau-Dangin has requested me to send him photographs of eight of the mathematical tablets which you published in transcription, but without the autographed copy, in MKT. These are YBC 4668, 4669, 4673, 4695, 4696, 4697, 4698, and 4711. These are eight of the nine texts concerning which you wrote me under date of 28.12.35 that you intend to publish the autographed copies, and that you then had your manuscript practically ready for the press. In my letter of December 6, 1935 I stated to you that, “our policy is to allow no one to study a tablet which has been assigned for publication, without the consent of the one to whom it had been assigned, until after it has been published.” Th-D writes, “je n’ai nullement l’intention de publier ces photos. Je désire seulement être en mesure de contrôler les copies ou transcriptions de Neugebauer”. Nevertheless, it becomes my duty to refuse his request, unless you give your consent to his having the photos of the above mentioned tablets. The decision is in your hands; please let me know your pleasure as soon as possible.

Yours sincerely,

Ferris J. Stephens

Acting Curator.

YBC, Stephens to Neugebauer 1936/06/16

New Haven, June 16, 1936

Dear Prof. Neugebauer:

Under date of April 3, 1935 I wrote you to decide whether or not Thureau-Dangin should be given photographs of 8 of the mathematical tablets which you intent to publish in autograph in your Nachtragsheft to MKT. He has stated that he has no intention to publish the photographs, but only wishes to be able to control the transcriptions as already given by you in MKT. I think he feels that he should be permitted to have the photographs. Nevertheless I am bound not to furnish them to him without your consent, because of our policy not to allow any one to study a tablet which has been assigned for publication without the consent of the one to whom has been assigned.

May I hear from you at an early date concerning this matter, and also concerning the progress of your Nachtragsheft?

Yours very sincerely,

Ferris J. Stephens

Acting Curator.

YBC, Neugebauer to Stephens 1936/06/27 (in German)

Copenhagen 27.6.36

Dear Professor Stephens,

Thank you very much for your letter of the 16 June. Within the next weeks I am going to send off my supplement on the MKT for printing. Unfortunately, I was incapable to work due to illness for an extended period of time and I have only now finished the autographs. Hence, I would be indebted to you if you could refrain from releasing photographs of these texts to Mr. Thureau-Dangin until the publication of my supplement (which is likely to happen this autumn). The texts in question are YBC 4668, 4669, 4673, 4695, 4696, 4697, 4698 and 6504.

You may be wondering why I am asking you to refrain from releasing the texts at the moment, but I have unfortunately had some very strange experiences with Mr. Thureau Dangin and would prefer to complete my work without his interference. He himself has made some texts from the British Museum, which are a direct extension of my texts, unobtainable to me. Moreover, he is so inclined to beat me at every corner that in return I see no reason to facilitate his run in this race, which he started despite me repeatedly communicating my urge for friendly but factual cooperation.

I hope that I do not cause you any discomfort. Needless to say, I would not like you to understand my message in any other way than as an expression of my personal wish, which is in no way binding to you. Please act solely at your own discretion.

With kind regards and warm gratitude for your courtesy,

Yours respectfully

YBC, Stephens to Neugebauer 1936/07/17

New Haven, July 7, 1936

Dear Prof. Neugebauer:

I have your two letters of the 18th and 27th of June. I am sorry to learn that you have been hindered by illness, and hope that you have now fully recovered.

Be assured that your wishes will be respected concerning the giving of photographs to Thureau-Dangin. I have allowed him to have photographs of the tablets whose texts you have already published in autographed copy. The rest has been with-held.

In regard to your earlier question concerning YBC 4697 I beg to report that, while it has not been baked in the furnace, it is as clean as it can be made. The surface is badly preserved on both sides, and this accounts for the numerous spots on the photographs. Ne cleaning would do any good at these places for the writing is obliterated. I do not think anything at all can be done to improve the legibility of this tablet.

With kindest greetings,

Yours sincerely,

Ferris J. Stephens, Curator.

YUL, Goetze to Neugebauer 1937/02/14 (in German)

February 14, 1937

Dear Mr. Neugebauer,

My deepest gratitude to you for sending me the third volume of your mathematical cuneiform texts. It is a worthy extension of your earlier work. Many thanks for this valuable gift.

With surprise and honest regret I have come to know that a certain animosity has developed between Thureau-Dangin and yourself. Personally, I feel it is most unfortunate since I have always treasured Thureau-Dangin and never had the slightest reason to doubt his excellent character. Isn’t this a rare case among Assyriologists. It almost seems as if Assyriology ruins one’s character!

It is astonishing how deeply you have acquainted yourself with the Assyriology (of your texts). All reasonable persons will surely forgive minor philological oversights and simply be pleased there are not more of them. Philologists have always been incapable of tackling these texts and thus they must be delighted with what you have done with them.

P. Schaumberger dropped by. He is trying to find astronomical texts in America. I don’t know, if he will be successful. The American collections are to a large extent assembled by purchase. However, mathematical and astronomical tablets are extremely rare. I think Chicago has some; maybe one can also expect some in Philadelphia. But unfortunately, a vast quantity of tablets are still stowed in boxes and the chances are that, no one truly knows, what they contain. The museum in Philadelphia would need an Assyriologist solely for the inspection and publication of the tablets.

With kind regards,

Yours

YUL, Neugebauer to Goetze 1938/03/21 (in German)

Copenhagen, March 21, 1938

Dear Mr. Götze,

I have just been made aware of the fact that Thureau-Dangin is looking for someone to edit the Mari texts. Could you be so kind as to write to Thureau-Dangin and recommend Oppenheim? After all, he is the ideal man for this job. I would rather avoid doing so and needless to say, I do not wish to be mentioned at all. I suppose Thureau-Dangin is not too fond of me and therefore I dare say that my involvement in the matter would have the opposite effect.

In haste, my best regards,

Your

Appendix B: Photos and Transliterations

Damaged Tablet or Damaged Photo? YBC4710

The following pictures show problem 4 on YBC 4710 (obv. col. i, li. 14–24) in the photo used by Neugebauer, the copy in MKT, and the current photo (see Fig. 4).

Fig. 4

Three pictures of problem 4 on YBC 4710 (obv. col. i, li. 14–24)

The following transliteration of YBC 4710 #4 shows that Neugebauer and Thureau-Dangin used the same blurred photo. The text is, in fact, perfectly preserved, and doesn’t require the use of brackets.

MKT I, p. 402	TMB, p. 149	After collation (Proust 2009)
14. a-ša3 1(eše3) GAN2 uš ša	14. eqlum ebel ikîm šiddim	14. a-ša3 1(eše3) GAN2 uš-ta
15. a-na ba-zi nu-zu	15. mala assuhu ul(a) îde	15. a-na ba-zi nu-zu
16. šá u[š-ta b]a-zi	16. šá ina šiddim uštakil	16. nig2 uš-ta ba-zi
17. KI íb-t[ag4 u]š ì-kú	17. itti šapitti šiddim assuhu	17. ki ib2-taka4 uš i3-gu7
18. sag [íb-si8 ù 1 (eše)] gán (?)	18. a[na pû]tim [aš]ši	18. sag-še3 bi2-il2
19. a-š[à (?) K]I (?) šá uš ba-zi	19. eq[lam] ù šá < ina > šiddim assuhu	19. a-ša3 u3 nig2 uš ba-zi
20. ì-kú-ma (?)	20. uštakil-ma	20. i3-gu7-ma
21. ì-kú u-gù ì-k[ú]	21. ì-kú eli ì-kú	21. i3-gu7 ugu i3-gu7
22. 1,48 d[irig]	22. 1.48 î[ter]	22. 1.48 diri
23. [š]á uš-ta ba-[zi]	23. šá i[na] šiddim as[suhu]	23. nig2 uš-ta ba-⌈zi⌉
24. [u]-gù íb-t[ag4 u]š 6 dir[ig]	24. [e]li ša[pilti šid]dim 6 îter	24. ⌈ugu⌉ ib2-taka4 ⌈uš 6 diri⌉

In the Goetze’s collations (notes in Aaboe-Britton Archives, folder YBC 4710 dated February 3, 1935), it is clear that the text was better preserved than thought by Neugebauer (Fig. 5):

Fig. 5

Goetze’s collations of YBC 4710, Aaboe-Britton Archives

Dirty Tablet and Blurred Photo: YBC 4668

The following pictures show problem 33 on YBC 4668 (obv. col. ii, li. 59–61) in the photo used by Neugebauer, the copy in MKT, and the current photo (Fig. 6):

Fig. 6

Three pictures of problem 33 on YBC 4668 (obv. col. ii, li. 59–61)

Neugebauer’s transliteration (MKT I, p. 425)

• 59. a-[ša₃ 1(eše₃) GAN₂ igi-3-g]al₂ uš

• 60. [igi-4-gal₂ sag a-na uš ugu sag diri]

• 61. [a-ra₂] 2 e-tab-ma uš sag

Thureau-Dangin’s transliteration (TMB, p. 169)

• 59. eq[lum ebet ikîm šaluš]ti šiddim

• 60. [rabiat pûtim mala šiddum eli pûtim îteru]

• 61. [a-ra₂] 2 ^e êṣip-ma šiddum pûtum

Translation after recent collation (made by C. Proust in 2009)

• 59. a-ša₃ 1(eše₃) GAN₂ igi-3-gal₂ uš

• 60. igi-4-gal₂ sag a-na uš < ugu sag diri>

• 61. a-ra₂ 2-e tab-ma uš sag

References

Archives

Aaboe-Britton Archives: currently at the Institute for the Study of the Ancient World, New York University, New York, USA.

IAS Archives: The Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, USA.

YBC Archives: Yale Babylonian Collection, Yale University, New Haven, USA. Two folders are used here: Neugebauer 1931–1957, and Sachs 1942–1955.

YUL Archives: Yale University Library, Manuscripts & Archives Yale University, New Haven, USA. The folder used here is Albrecht Goetze papers, MS # 648, box # 15.