Vatican Euclid Online

Probably the most famous mathematical manuscript in the world, the Vatican Euclid, arrived online on 2016 February 15, marking a major moment in the democratization of culture as well as a key milestone in the donor-funded efforts to digitize the 83,000 manuscripts at the Vatican Library in Rome.

Ivor Bulmer-Thomas argues that Euclid (who lived about 300 BCE) is the most celebrated mathematician of all time on account of the precocity and volume of his work. The 9th-century Vatican manuscript, Vat. gr. 190, is the only codex in the world containing Euclid's work without major adulteration.

Every other surviving manuscript contains alterations by the 4th-century-CE mathematician Theon of Alexandria, who altered Euclid's language, interpolated intermediate steps and supplied alternative proofs, separate cases and corollaries. As the only non-Theonian witness, Vat. gr. 190, now bound in two parts in Rome, is one of the most precious cultural treasures of humankind.

Here is its Pythagorean Theorem, Book I Proposition 47, perhaps the most famous proof in all mathematics, on folio 39r. You could understand it without knowing a word of Greek:

The purity of the Vatican Euclid was discovered by the mathematical historian Francois Peyrard in 1808 and the codex became the basis of Heiberg’s definitive edition of Euclid's Elements.

Its arrival online overshadows everything else in the following list, even the unique Vatican Pappus, Mathematical Collections Books 2-8, Vat. gr. 218, by another Greek mathematician of vast stature, the 4th-century-CE writer Pappus. Every other Pappus in the world depends on this incomplete Rome copy, and as you can see, Book 1 is forever lost. Here's a diagram from fol. 38v:

When the Pappus figured in the Rome Reborn exhibition, Anthony Grafton described it as the "last important work in Greek mathematics". As Jeremy Norman comments, it is sometimes the only source of information about Pappus's predecessors. But the thunder of even its release is stolen by the Euclid. Both were apparently sponsored by the Polonsky project.

Here is the full list of new uploads at the Biblioteca Apostolica Vaticana, which brings the posted total on Digita Vaticana to 3,852.

1. Barb.gr.39, Cyril of Alexandria, Lexicon
2. Barb.gr.70,
3. Barb.gr.281,
4. Ott.gr.85,
5. Ott.gr.181,
6. Ott.gr.232,
7. Ott.gr.233,
8. Ott.gr.237,
9. Ott.gr.249.pt.1,
10. Ott.gr.249.pt.2,
11. Ott.gr.260,
12. Ott.gr.335,
13. Ott.gr.338,
14. Ott.gr.352,
15. Ott.gr.365,
16. Ott.gr.366,
17. Ott.gr.367,
18. Ott.gr.373,
19. Ott.gr.379,
20. Ott.gr.380,
21. Ott.gr.385,
22. Urb.gr.15,
23. Urb.gr.61, Theophrastus, Historia Plantarum and De Causis Plantarum
24. Urb.gr.136,
25. Urb.gr.137,
26. Urb.lat.143, Bonaventura
27. Urb.lat.203, Plato's Timaeus in Latin, translation
28. Urb.lat.243, Medical, Joannis filii Serapionis
29. Urb.lat.261, Archimedes, Sphere and Cylinder etc, in Latin, with Archimedes at his desk on folio 102r: Surely that's not an electric reading lamp he is snipping on in ancient Syracuse?
    
     
    But a smart historian just explained to me that he is holding up a compass, and the green "lampshade" is actually a windowsill.
30. Urb.lat.305, Valla Laurentius, on Latin style
31. Urb.lat.310, Attic Nights, Aulius Gellius
32. Urb.lat.318, Cicero, Letters
33. Urb.lat.328, Cicero, with commentary by Boethius
34. Urb.lat.360, Constantius Antonius, commentary on Ovid
35. Urb.lat.383, Cassiodorus
36. Urb.lat.387, Giannozzo Manetti, works
37. Urb.lat.400, Flavius Josephus, Antiquities of the Jews, in Latin translation
38. Urb.lat.406, Pope Pius II, bulls
39. Urb.lat.407.pt.2, Pius II, writings
40. Urb.lat.433, Eutropius, De gestis romanorum
41. Urb.lat.438, Iustini M. Iuniani
42. Urb.lat.450, Boccaccio, Genealogia Deorum (1360), a kind of study edition, with a 60-page alphabetical index of gods which Colluccio Salutati commissioned from Domenico Bandini (c.1335-1418) (discussed 1927 by Wilkins, who uses the 1879 Hortis list of Genealogia manuscripts). Compare this to Boccaccio's second autograph of the same work, online at Florence. Urb.lat.450 features Boccaccio's famous leaf-form stemmata:
    
43. Urb.lat.452, Boccaccio, etc, descriptions of Italy
44. Urb.lat.493, Genealogies of noble families of Castille and Navarre, in Spanish, dated 1620; these are textual, not diagrammatic
45. Urb.lat.495, Cafari de Caschifellone
46. Urb.lat.496, Bartholomaeus Fatius, De rebus gestis ab Alfonso I neapolitanorum rege
47. Urb.lat.501,
48. Urb.lat.510,
49. Urb.lat.514,
50. Urb.lat.525,
51. Urb.lat.556,
52. Vat.ebr.144,
53. Vat.gr.190.pt.1, Euclid, Elements, see above
54. Vat.gr.190.pt.2, Euclid and Theon, see above
55. Vat.gr.218, the Vatican Pappus, St Louis description.
56. Vat.gr.333, the Vatican Book of Kings, a richly illustrated 11th- or 12th-century manuscript which is often resorted to as a document of Byzantine warfare and customs. Here is the first washing of a newborn child (Solomon) (top), compared with a similar scene (not sure what baby) from Vat.gr.746, fol 59r (below):
    
    
57. Vat.gr.351,
58. Vat.gr.460,
59. Vat.gr.666,
60. Vat.gr.746.pt.2,
61. Vat.gr.788.pt.A,
62. Vat.gr.788.pt.B,
63. Vat.gr.853.pt.1,
64. Vat.gr.853.pt.2,
65. Vat.gr.1522,
66. Vat.gr.1594, this is the most famous and best of all the manuscripts of Ptolemy's Almagest, originally entitled "Μαθηματικὴ Σύνταξις" (Mathēmatikē Syntaxis). The work was written by the great Alexandrian scientist in the 2nd century and this is a 9th-century copy. The work describes the apparent motions of the stars and planets. See a description in the Rome Reborn exhibition.
67. Vat.gr.1666,
68. Vat.gr.1851,
69. Vat.gr.2249,
70. Vat.lat.34,
71. Vat.lat.46,
72. Vat.lat.131,
73. Vat.lat.141,
74. Vat.lat.157, Nicholas of Lyra, Postillae with fine coloured maps of temple
    
75. Vat.lat.159, Nicholas of Lyra, Postillae
76. Vat.lat.169, Dionysius Areopagita
77. Vat.lat.191, Tertullian, Against Marcion and other works
78. Vat.lat.208, Origen, homilies, and Gregory Nazianz
79. Vat.lat.214, John Scotus Eriugena and Didymus
80. Vat.lat.218, Lactantius, Divinarum Institutionum, De Ira Dei and some Augustine of Hippo
    
81. Vat.lat.219, Lactantius, Divinarum Institutionum
82. Vat.lat.231, Eusebius, Praeparatio Evangelica
83. Vat.lat.247, Eusebius, Chronological Canons
84. Vat.lat.4817, Angelo Colocci autograph?

It remains to note that one item was withdrawn from the site on Feb 12:
Borg.copt.109.cass.VII.fasc.65.2

At the same time, the ranks of the Palatina library online grew, not on the BAV website, but on the portal in Heidelberg, Germany which has the first right as sponsor to issue these online:

1. Pal. lat. 712 Manuale collectum de summa confessorum (Raymundi de Pennaforti) (14. Jh.)
2. Pal. lat. 718 Sammelhandschrift (15.-16. Jh.), important as a source of the Tractatus de usuris of Antoninus of Florence (1389-1459) See note 
3. Pal. lat. 717 Sammelhandschrift (14.-15. Jh.)
4. Pal. lat. 713 Fr. Baetholomei de Chaimis de Mediolano ord. minorum, Interrorogatorium siue confessionale (1477)
5. Pal. lat. 716 Michaelis Gass: Archimusici Principis Ludovici Palatini tercii directorium omnium eorum quae per tocius anni curriculum in sacello illustrissimi Principis Palatini canuntur et aguntur (1533)
6. Pal. lat. 707 Iohannis (Friburgensis): Lectoris idem opus integrum (14. Jh.)
7. Pal. lat. 705 Sammelhandschrift (15. Jh.)
8. Pal. lat. 704 Mag. Raymundi (de Pennaforti), Summa de poenitentia et de matrimonio (14. Jh.)
9. Pal. lat. 702 Summa de vitiis (13.-14. Jh.) 
10. Pal. lat. 724 Sammelhandschrift (15. Jh.) 
11. Pal. lat. 731 Digestum vetus (14. Jh.)

As I noted in my previous post, interest is now growing in the original diagrams which the Greek mathematicians drew and in undoing the editorial vandalism which Heiberg and others did to these figures.

Professor Ken Saito of Osaka, the leading figure in this work of diagrammatic reconstruction, kindly sent me earlier this month an offprint of his very important and difficult-to-find 2006 article in which he launched this returning to the source for Euclid's Elements. His precise plots of the Euclidean diagrams continue to be published on his website, GreekMath.org, and each of his surveys naturally always begins with the Vatican Euclid as its prime source. If you get puzzled, the pagination in his two PDFs is as follows:

• The Diagrams of Book II and III [and of Book IV and of Book VI] of the Elements in Greek Manuscripts: pages 39-80; 161-196 
• The Greek Manuscript Diagrams of the Elements: Book VI, Book XI, Book XII, Book XIII: pages 71-179

Of the other five Euclids used by Heiberg (Pinakes has a much longer list), most are already online:

• B: Oxford, Bodleian, D'Orville 301; (avoid http://www.claymath.org/euclids-elements, which has a lousy interface that has been broken these past two or three years)
• F: Florence, Biblioteca Medicea Laurenziana, Plut.28.03
• V: Vienna, ÖNB, Cod. Phil. gr. 31 Han, alternatively XXXI, 13 (Nessel) = philos. Gr. 103 (Lambert)
• B: Bologna, Bib. comunale dell'Archiginnasio 18-19; not digitized, see listing
• P: Paris, BNF, gr. 1042 and gr. 2739

If you have corrections or additions, please use the comments box below. Follow me on Twitter (@JBPiggin) for news of more additions to Digita Vaticana. [This is Piggin's Unofficial List 39.]

Bulmer-Thomas, Ivor. “Euclid: Life and Works.” Dictionary of Scientific Biography, 1971. Online.

Heiberg, Johan Ludvig. Euclidis Elementa. 6 vols. Leipzig: Teubner, 1883. Online.

Murdoch, John E. “Euclid: Transmission of the Elements.” Dictionary of Scientific Biography, 1971. Online.

Saito, Ken. “A Preliminary Study in the Critical Assessment of Diagrams in Greek Mathematical Works.” SCIAMVS 7 (2006): 81-144.