i was operating under the unspoken assumption that this text was actually available in 1480s Venice. But at the time I was too busy expounding my theory--before I forgot it--to examine the question. I am not one to let the absence of facts stand in the way of my theorizing!
Now, however, my theory is posted and I have researched the question: how accessible was the Theology of Arithmetic in Northeastern Italy of the late 15th century? Since others (on ATF and elsewhere) have applied the Theology to the tarot pips as well--although not as far back as 1491--this research may be of relevance to more than the Sola-Busca.
The 1988 English translation gives absolutely no information about the history of the manuscripts on which the Greek text it used was based. So I looked mightily for references by 15th or 16th century writers. I found none, but I did see a mention in Christiane Joost-Gaugier's Pythagoras and Renaissance Europe: Finding Heaven. She says,
Bessarion owned a Theology of Arithmetic, possibly that today associated with Iamblichus. (p. 246)
In a footnote she correctly notes that the author is normally cited as "Pseudo-Iamblichus." And
Though this text is preserved in the corpus of works of the famous Pythagorean Iamblichus, its author is not known.(p. 300).
Bessarion, she observes, willed his library to the Republic of Venice, which made inventories of it in 1468, 1474, and again in 1526. (The library was shipped in two installments, one before and one after his November 1472 death.) But was this the Theology of Arithmetic that I wanted? And would it have been accessible to designers of tarot cards? I needed to dig further. Joost-Gauthier gives three references: Henri Omont, "Inventaire des manuscrits grec et latins donnes a Saint Marc de Venise par le Cardinal Bessarion," Revue des Bibliotheques, IV, 1894, 129-187; Elpidia Mioni, "Bessarione bibliofilio e fililogio," Revista di Studi Bezantini e Neoellenici, n.s. 5 (XV), 1968, 61-83; and Lotte Lobowsky, Bessarion's Library and the Biblioteca Marciana: Six Early Inventories, Rome 1979. I decided to try Lobowsky, since it was in English.
THE 1474 INVENTORY
Joost-Gauthier gives no page number for her Lobowsky citation. In Lobowsky's index, I found three listings for Iamblichus, all in the 1474 inventory
25. Iamblici in epistolam Porphrii, in permagamenis.
57. Iamblici de secta Pythagorae, in peramenis.
533. Iamblici de secta pythagorearum libri quatuor, et eiusdem in epistola Porphyrii, et expositio Hieroclei in carmina Pythagorae aurea, in pergameno.
None of these would seem to be the Theology of Arithmetic.
So I tried "arithmetic." There are two references to an "expositio in arithmeticam," by an "Esculapii Tralani" (61) or "Asclepi" (570), and nine for Nichomachus Gerasenus. The first one said:
26. Porphyrii dialogus in praedicamenta Aristotelis et dialogum et arithmeticam theoligicam, in pergamenis.
No mention of either Nichomachus or Iamblichus. But at least we have "arithmeticam theologicam." The others are
94. Rhetorica Hermogenis, arithmetica Nichomachi, geometriae libri sex, et geodesia, in papiris.
99. Cleomedis, tabulae persica, Criosine, arithmetica, et imagines Philostrati, in papiris.
115. Arithmetica Nichomachi, Arati fenomina, Cleomedis, et sex libri geometiae, in papiris.
116. Arithmetica Nicomachi in Philoponum, in papiris.
117. Clemedis cum expositione et arithmetica cum expositione Philoponi, in papiris.
681. Arithmetica Nicomachi, Sophiclis tragoedia una, in grammatia plurima, heroica Philostrati, et icones iusdem, Maximi philosophi orationes, Homeri duo libri priores cum expositione technologiae, et alia diversa, in papiro.
683. Magni Logotheti, et sintaxis Ptolomei, et arithmetica, in papiro.
978. Arithmetica Nicomachi, in papiro.
None of these looks promising, because there is no "theologicum" along with the "arithmetica." Nichomachus's Arithmetic is just that, a primer on arithmetic, or more properly, what today would be called number theory. But one never knows what someone might have called something for inventory purposes. Item 26 remains the most likely.
THE 1922 EDITOR'S PREFACE
For my next attempt to track down the manuscript, I tried the printed edition of the work prepared by Victorius de Falco in 1922. Here I got an answer, I think; but it's in Latin, not a language I'm comfortable in. So I include a scan of the first two pages of de Falco's Preface at the end of this post, in case I have misunderstood.
Codex M, the first in de Falco's list, is "olim Bessarioneus"--formerly Bessarion's, "nunc in Biblitheca Veneta S. Marci 234, membr., saec XV in., ff. 162, cm. 18 5x12..." I.e., it is now in the Bibliotheca Veneta S. Marci, i.e. the Marciana. the library of which Bessarion's donation formed the initial nucleus; and the manuscript is of the 15th century.
So I have part of my answer. The Theology was there in Venice, from 1474 on, as part of Bessarion's donation.
It seems, from my reading of de Falco, that Bessarion's copy spawned six other extant manuscript copies. In the Laurentian Library, Florence, is the "Laurentianus gr. XXX pl. 71" (L), which contains annotations by Angelo Politiano, according to Bandinio. So apparently Politiano got a copy somehow, perhaps by way of Bessarion earlier. Another copy of M is now in the Bibliotheque Nationale, Paris, the "Parisinus gr. 1943" (P). There are also two in Naples: "Neopolitanus gr. III C 8" (B), copied from L; and "Neapolitanus Gr. III C 7" (N), copied from an unknown manuscript that was similar to L. (See diagram below.) Another manuscript is "Magliabechianus gr. 14" (F), copied from N; the collection is named for a 17th century collector and is in Florence. Last is the "Codum Escurialensum Sigma III1" (Sigma), at the Escorial near Madrid, which de Falco did not examine because it was taken from the first print version, Paris 1543, based on P. (I get the manuscript names from de Falco; I get where these collections are located from the Internet.)
There are also two defective manuscripts not derived from Bessarion's at all, and which apparently date from the 14th century. These are the "Mutinensis 90 (III C 11)" (E), which I think is now part of the d'Este Library in Modena; and the "Ambrosianus gr. 780 (Et 157 sup.)" (A), in Milan. E and A are derived from a common source. Bessarion's manuscript is not derived from that one, however, but from an intermediary; E and A are derived from another intermediary. Here is what the relationships look like in diagram form (de Falco p. xii). Below that I have put de Falco's list of abbreviations for manuscripts he consulted, from just before the beginning of the Greek text. It gives all eight of the sources he used plus the previous printed versions and his abbreviations for combined sources.
As I have said, it appears that A and E are 14th century. M, L, and N are 15th century, while P and F are 16th century; and B is "XV ex. vel XVI in.," which I think means either 15th or 16th century. The dates 1543, 1817, and 1897 refer to printed versions; the 1543 was edited by Chrestien Wechel and published in Paris. It has Iamblichus as the author. The 1817 was edited by Friedrich Ast, and the 1897 by Ermenegildo Pistelli, both published in Leipzig (indicated by its Latin name, Lipsiae). I get these details from WorldCat. The de Falco 1922 is also Lipsiae/Leipzig.
So we know from de Falco that the manuscript was in Venice in the 1480s. Not only that, but good copies were in other places during the 15th century: with Politiano in Florence, and one in Naples. Now the question is, how accessible were these manuscripts? Well, I will stick to just Venice.
ACCESSIBILITY OF THE VENICE MANUSCRIPTS
Labowsky gives usable information about how Bessarion's manuscripts were kept in those years, the 1480s, and their availability to scholars.
As a condition of the donation, Venice promised in writing to Bessarion that they would give them a special building and adequate funding to keep the manuscripts both safe and available to as many readers as possible (Labowsky p. 27).
After arriving, the chests of manuscripts were stacked up in the Sala Novissima of the Doge's palace, Labowsky says. A rudimentary system of identifying manuscripts by box number or letter was set up, although sometimes the number was just the number of manuscripts in that box. There was some sort of record of who checked out books; but the evidence today is just of books that could not subsequently be found, either because they weren't returned or because they were misfiled. Given the substantial number of such entries, Labowsky concludes that
Such as it is, the evidence shows that, almost immediately after the arrival of the consignment in 1474, books from it were taken out on loan--a sign that, at least in certain circles, there was a lively interest in the libri Nicaeni. (p. 57)
And so it went, until a "conflagration" in 1483 destroyed the old part of the Palazzo. The books were unharmed, but their quarters were now needed for the civil court. In what follows, bear in mind that we are talking about the greatest collection of Greek manuscripts ever seen in the West, along with one of the finest group of Latin ones.
...it was therefore decided in the Collegio that, under the supervision of the Procuratori, the boxes containing Bessario's donation should be placed at one end of the hall, "one on top of the other, fitted tightly and closely together, so as to take up as little room as possible", and that a strong wooden wall should partition off this space from the rest of the room in order to protect the Library from theft (footnote: Lobowsky document VI, p. 127). In these conditions the books were to remain for the next forty years.
It is obvious that the manner in which the books were being stored, especially after 1485, made it impossible for the Library to be properly 'governed'. The room where they were being kept had no facilities for reading or copying manuscripts; the only method of consulting them was borrowing. To this inconvenience we have to add the drawbacks deriving from a lack of unified authority and any professional method of library administration. According to an unconfirmed tradition one of the procuratori was, in the early years of its existence, always supposed to be specially concerned with the libri Nicaeni as Bibliothecarius Sancti Marci, but there is no evidence that either of the two patricians said to have borne this title were actively engaged in the running of the Library (footnote to Lobowsky's Document VI; also Apostolo Zeno, Marci Antonii Coccii Sabellici Vita, 1718, and Morelli, loc. cit.cap. VII). Nor is there evidence that any administrative activity was exercised by their successor Marcantonio Cosso Sibellico, the distinguished humanist then resident in Venice, who was the first to combine the office of Librarian with the function of Historiographer of the Republic (footnote to Zeno and Morelli). Such evidence as we have shows that the Library was until 1516 the collective responsibility of the Procuratori di supra. We have noted above in some of the codices Marciani traces of a rudimentary system for the registration of loans, and the list of 'libri non restituidi', covering the period of 1474-1493, presupposes records from which it was excerpted. These were kept by the officials of the Cancelleria inferiore, who dealt with them among the other business of the Procuratia. (Footnote to books about the hierarchies of Venetian administration.)
The list of unreturned books also shows a flagrant disregard of the conditions laid down by Bessarion in the Act of Donation and sanctioned in the papal Bull attached to it: (1) With the authorization of the Signoria a codex was dispatched to a papal secretary in Rome, and (2) no deposit seems to have been taken for any of the books mentioned. (p. 59f)
I have not yet located in previous footnotes the book by Morelli. In 1530, Pietro Bembo was appointed librarian, and things started to change. In 1559-1565, the codices finally moved to their new, handsome quarters across the Piazza San Marco, and the terms of Bessarion's bequest were fulfilled.
So how easy would it have been in the 1480s to check the Theology out for an extended period of time? Lobowsky says
Both the complaints about the loss of books and the records of loans from the period before 1531, i.e. when the books were still being kept in their chests, are evidence, that at the end of the fifteenth century and during the first third of the sixteenth, Venetian noblemen and citizens, as well as teachers at the university of Padua and favoured foreign residents in Venice, were able to use Bessarion's books, though the ease and speed with which loans could be obtained probably varied very much in different cases (Footnote refers us to Lobowsky p. 100, which gives the book by Morelli). Foreign visitors who wished to browse among the collection evidently had difficulties in being allowed access to it, such as Politiano and Pico experienced during their visit to Venice in 1491, in spite of their excellent connections in the city and the efforts of their friends.(Lobowsky p. 62f)
For this last, she cites G. Presenti, "Diario Odeporico-Bibliogrifico ineditito del Poliziano" and Poliziano's letter to Lorenzo de' Medici from Venice, 20 June 1491. Politiano and Pico were denied access, Labowsky reports--perhaps more out of embarrassment and apprehension regarding how the books were being kept than anything else.
My tentative conclusion is that Bessarion's library did have a copy of the Theology of Arithmetic, arriving in Venice by 1474 and readily available to interested Greek-reading residents, one of whom might have created the program for the Sola-Busca pips. Also, if Politiano had a copy in Florence, there is an outside chance that he played a role.
It is also interesting that after a certain amount of high-level interest in the Theology, the bottom seems to have dropped out of the market. The first printed edition (in Greek) was in 1453 Paris. After that there was nothing, except for a manuscript copy made for the Escorial in 1469, until the next printed edition of 1817.
In any case, as a new ancient text acquired by Bessarion, the Theologoumena Arithmeticae evoked some interest, enough that a few people were willing to pay to have it copied. And since it was in Venice and readily obtainable on loan, I feel more confident now that it was the inspiration for the Sola-Busca pips. There remain the questions of (a) what we can infer from the 14th century manuscripts about the availability of the text before Bessarion, and (b) the text's influence on the interpretation of pip cards and on cartomancy after the Sola-Busca but before 1817. I will defer these issues.
APPENDIX: DE FALCO'S LATIN PREFACE
If it is any help, here is my transcription of the first two pages of de Falco's Preface, minus the Greek and the footnotes. I will spare you Google's "translation." (If you want it, just ask.) The scans follow.
De Arithmeticae Theologoumenorum codicibus perbreviter H. Pistelli unus disseruit, qui praeter libros manu scriptos quinque, quos novit, alios quosdam exstare coniecit. Hi vero, quod sciam, novem sunt, de quibus disserendum nunc censeo.
Cod. olim Bessarioneus (f. 1v, 4...), nunc in Bibliotheca Veneta s. Marci 234, memb. saec. XV in., ff. 162, cm. 18, 5x12, y. continet: ... f.1, f.83, ff. 79v, 80-82, 132v, 157v-162 vacc. Codicem hunc, Laurentianum et Parisinum descripsit Ricardus Foerster.
Laurientanus gr. XXX pl 71 (cf. Bandini III 14 sq.), membr., ff. 174, in ff. 1r et 152 adnotatiunculas quae, Bandinio teste, Angeli Politiani sunt, exhibens, actatis paullo scripturae, eadem eodem ordine quae Marcianus ipse continet; ... f.2, ... f. 92, ... f. 145, ff. 1v 90-91, 174 vacc.
Praeter haec indicia consanguinitatis inter L et M, ambo in omnibus fere lectionibus its congruunt, ut dubitari non possit quin alter ab altero pendeat. Interdum tamen librarius codicis L vitiose verba transscripsit vel quod litterae in M nimis artae et obscurae sunt vel sua ipsius neglegentia; cf. e. gr. p. 9, 9 ... M (litterae ios tam stipatae ut facile iai lectori parum attento videantur) ...
Parisinus gr. 1943 olem CCCCCLII 484, 21127, chart, saec. XVI, ff. 256 continet:.... Codicem hunc Venetiis exaratum esse demonstravit R. Foerster. Plurimis locis Parisinus a Marciano dissentit, set semper, ut primo obtutu patet, merea neglegentia atque scribae ignorantia.
Alteram manum correcticem passus est hic codex, quem inspicere non potui, quod qui Bibliothecae Parisinae praesunt eum exportari vetnerunt; in usum meum contulit Henricus Lebegue, cui maximas gratias ago.
Neapolitanus gr. III C 8 (cf. Cyrill. II 352), chart., saec. XV ex. vel XVI in., cm 16, 4x11, 2, ff. 173 immo 174 nam fol. 40 bis num., in quaterniones divisus, continet:...