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Bamberg, Staatsbibliothek, MS Class. 55
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Bamberg, Staatliche Bibliothek, Class. 55

Composite manuscript of geometrical, astronomical and computistical texts

Alte Signatur: H J.IV.22 — Parchment — i + 40 fols. + i — 258 × 205 mm — North-east France, Reims (?) — s. X2

De ordine ac positione

Excerptum de astrologia

Digital facsimile as part of the project Kaiser-Heinrich-Bibliothek

Parchment Lagen: I-V8 (ff. 1-8, 9-16, 17-24, 25-32, 33-40). Modern foliation with arabis numerals in the upper right corner. Lower margins on ff. 2, 8-24, 26, 29, 33-35, 37, and 39, probably originally blank, cut out. Written in one column with around 27 long lines. Schriftraum: 190 × 150 mm Both booklets seem to have been written by a single hand (Hand C by Hoffmann) with slightly later addition on f. 1r by two other hands (Hand A on the first 17 lines and Hand B finishing the page). Hoffmann identified Hand C also in Bamberg Class. 11, Hand A in Class. 26 and probably Hand B in Class. 45.

White leader binding from the Dombibliothek (according to Suckale-Redlefsen dated to 1611). Two metal clasps. On the upper margin of the last folio (40v) a rusty spot, which might suggest the manuscript had once a chain attached.

Herkunft: The manuscript has been labeled as a ninth-century by Leonardi, Fischer and Borst, and as a tenth-century by B. Bischoff (Katalog I, p. 49). H. Hoffmann (Bamberg Handschriften, p. 136), who could recognise all three hands working in the manuscript also in other Reims manuscripts, considered it a production of the Reims scriptorium from the end of tenth century. — Upon establishing the new Diocese of Bamberg in 1007, Henry II arranged for territorial and intellectual support for the new foundation. Almost half of todays collection can be traced based on palaeographical features to the scriptoria in Reims, Wurzburg, Reichenau, Mainz, Regensburg, Lorsch, Cluny and Corvey. Our manuscript belong to the group of books produced in Reims and, with high probability, belonging to the personal library of Gerbert. There are three scenarios how the manuscript arrived in Bamberg: a) it was acquired by the magister scholarum Meinhard, who studied at Reims and facilitated the book exchange between the two scriptoria; b) Gerbert's books were taken upon his death by Otto III and later donated to Bamberg by Henry II; c) Gerbert's manuscripts were brought from Rome to Bamberg by Leo of Vercelli. Hoffmann considered the last option as most probable. (Bamberg Handschirften, 26-30).

Selected Bibliography: Leitschuh, Friedrich and Hans Fischer.Katalog der Handschriften der Königlichen Bibliothek zu Bamberg. Vol. I,2. Bamberg, 1906. Here pp. 61-66. — Suckale-Redlefsen, Gude. Die Handschriften des 8. bis 11. Jahrhunderts der Staatsbibliothek Bamberg. Wiesbaden: Harrassowitz, 2004. Here pp.61-62 — Menso Folkerts, "Mittelalterliche Mathematik: das Quadrivium." InZählen Messen Rechnen. 1000 Jahre Mathematik in Handschriften und frühen Drucken, 12-29. Petersberg: Imhof, 2008. — Leonardi, 8. — Bischoff, Katalog I, 49. — Hoffmann, Hartmut. Bamberger Handschriften des 10. und des 11. Jahrhunderts. Hannover, Hahnsche Buchhandlung, 1995, esp.26-30 and 136. — Borst, Arno. Das Buch der Naturgeschichte: Plinius und seine Leser im Zeitalter des Pergaments. Heidelberg: Winter, 1994. Here p. 185. — Munk Olsen, Catalogue 2, p. 250. — Munk Olsen, L’ étude 3,1, p. 38. — Toneatto, Lucio. Codices Artis Mensoriae: i manoscritti degli antichi opuscoli latini d'agrimensura (V - XIX sec.). Spoleto 1995. Here pp. 888-894.

Booklet 1

1r Herigerus Lobiensis: Regulae de numerorum abaci rationibus. Si multiplicaueris singularem numerum per decenum dabis unicuique digito x et omni articulo c … — … Si multiplicaueris decenum per decenum millenum dabis digitum centum milia et articulis mille milia. Bubnov 1899, pp. 8-11. Copied in two stages by two hands.

1v-16r Ps-Boethius: Geometria I. Six blank lines left for rubrication. Geometria est disciplina magnitudinis immobilis formarumque … — … M. Propositio dispositio distributio descriptio demonastratio et conclusio. Explicit Anicii Manilii Seuerini Boethii liber V artis geumetriae [!] de greco in latinum translatus ab euclide peritissimo geumetrico [!]. Diagrams and geometrical figures. There is no complete edition of the Geometry I; the partial editions are listed in . M. Folkerts. "Die Altercatio in der Geometrie I des Pseudo-Boethius. Ein Beitrag zur Geometrie im mittelalterlichen Quadrivium." In: Fachprosa-Studien. Beiträge zur mittelalterlichen Wissenschafts- und Geistesgeschichte, ed. G.Keil, 84-114 (esp. pp.88-89). Berlin: Erich Schmidt, 1982. Reprinted in Folkerts, Essays on early medieval mathematics, VII. Aldershot: Variorum, 2003. See also. Stevens Wesley. "Marginalia in the Latin Euclid." In Scientia in Margine, ed. D. Jacquart and Ch. Burnett, 117-138, Geneva: Librairie Droz, 2005. Borst, Schriften, Vol. 1 211-12.

16v Blank. Probatio pennae.

Booklet 2

17r-19v Excerpts from Libri computi, Lib. V, 3-6: (17r-v) Pliny the Elder: De positione et cursu septem planetarum. De positione et cursu septem planetarum. Inter caelum et terram certis discreta spatiis semptem sidera pendent … — … cum tardissime a tricesima luce ad easdem uices exit. (17v) Pliny the Elder: De intervallis eorum. De interuallis eorum. Interualla eorum a terra multi indagare temptarunt … — … Ita septem tonis effici quam diapasson armoniam uocant. (In the outer margin of f. 17v) Excerpt from the Libri computi, Lib. V, 11 added later by a younger hand. [D] imensio caelestium [s] patiorum secundum quosdam. A terra ad lunam tonum[esse] pronuntiant … — … duo I totidem miliaria. Borst, Schriften, Vol. 3, p. 1280. (17v-18v) Pliny the Elder: De absidibus earum. De asbsidibus earum. Tres autem quas supra solme dicimus sitas … — … sicut in rotis radios ut subiecta figura demonstrat. (18v-19v) Pliny the Elder: De cursu earum per zodiacum circulum. De cursu earum per zodiacum circulum. Cur autem magnitudines suas et colores mutent … — … sed inter omnia haec sidera martis maxime inobservabilis est cursus.

19v-21r Excerptum de astrologia. Excerpted as part of the Libri computi, Lib. V, 1. Excerptum de astrologia. Duo sunt extremi uertices mundi quos appelant polos … — … ad ipsum usque decurrit accipiens.

21r-24v De ordine ac positione stellarum in signis. Excerpted as part of the Libri computi, Lib. V, 2. De ordine ac positione stellarum in signis. Est quidem hic ordo et positio siderum quae fixa caelo … — … Anticanis habet stellas III. Not collated by Dell'Era. Has all chapters from Dell'Era's edition.

25r-29r Excerpts from the Libri computi, Lib. VI, 1-7: (25r) De ratione unciarum. Scripulus - sex siliquae | Dimidia sextula - duo scripuli et siliquae xii … — … Assis siue as - Duodecim unciae. Text in two columns with signs for eachuncia. Borst, Schriften, Vol. 3, pp. 1305-07. (25r-v) De probatione auri et argenti. Omne aurum purum cuiuslibet ponderis omni argento … — … sicut prima lectionis huius fronte praefixum est. Borst, Schriften, Vol. 3, pp. 1307-08. (25v-26r) De mensura caerae et metalli in operibus fusilibus. In fundendis operibus cuius ponderis metallum quodlibet ad certum … — … auri librae XVIIII et duo decies octo denarii quod sunt unciae III et denarii XVI. Borst, Schriften, Vol. 3, pp. 1309-10. (26r-27r) Ambrosii macrobii Theodosii de mensura et magnitudine terrae et circuli per quem solis iter est. In omni orbe uel sphera medietas centrum uocatur … — … ambitum stadiorum habere trecenties centena milia et insuper centum septuaginta milia. Borst, Schriften, Vol. 3, pp. 1310-13. (27r-28r) Item eiusdem de mensurae magnitudine solis. His dictis quibus mensura quam terrae uel ambitus uel diametros habet … — … Ergo ex his dicendum solem octies terra esse maiorem. Borst, Schriften, Vol. 3, pp. 1313-16. (28r-v) Felicis Capellae de mensura lunae. Luna item circuli sui sexcensimam obtinet portionem … — … Ipsum uero circulum centies maiorem esse tellure. Borst, Schriften, Vol. 3, pp. 1316-18. (28v-29r) Eiusdem argumentum quo magnitudo terrae deprehensa est. Eratostenes philosophus idemque geometra subtilissimus magnitudinem terreni orbis nosse uolens … — … nullam humanae coniecturae dimensionem admittit. Borst, Schriften, Vol. 3, pp. 1318-20.

29r-32r Excerpts from the Libri computi, Lib. VII, 2-4: (29r-30v) De mensuris et ponderibus. Mensura est iuxta isidorum quicquid pondere capacitate longitudine … — … apud germanos unam restam efficiunt. Borst, Schriften, Vol. 3, pp. 1322-26. (30v-31r) De ponderibus. Ponderum pars minima calculus est qui constat ex granis … — … Centenarius autem dicitur eo quod centum libris constet. Borst, Schriften, Vol. 3, pp. 1326-28. (31r-32r) De mensuris in liquidis. Mensurarum in liquidis coclear est pars minima … — … Duo gomor chorum reddunt duo chori chulleum quod sunt modia LX. Borst, Schriften, Vol. 3, pp. 1329-32.

32r-34v Series annorum mundi nova. Adbreuiatio chronicae. Adam cum esset centum triginta annorum genuit seth … — … Sunt autem totius summae ab origine mundi anni usque in praesentem annum I̅I̅I̅I̅DCCLXI.

35r-39r Excerpt from the Libri computi, Lib. III, 2-4 and 9-10: (35r) De anno et partibus eius. Annus solaris habet quattuor tempora menses XII … — … Unum momentum habet ostentum I et dimidium. Borst, Schriften, Vol. 3, p. 1186.. (35r-v) Quot atomos habeat annus uel pares eius. Ostentum habet atomos CCCLXVI. momentum habet atomos DLXIIII … — … punctos XLIIICC horas VIII DCXL partes proprias CCCLX. Borst, Schriften, Vol. 3, pp. 1187-89. (35r-36r) Quot modis soleat annus nominari. Primus modus est de luna qui quinquifariae accipitur … — … ubi primum statuta fuerunt et DXXXII annis impletur. Borst, Schriften, Vol. 3, p. 1189. (36r-39r) Qualiter per quattuor annos bissextus adcrescat. Primo igitur anno praeparationis bissexti prima hora noctis … — … prima hora noctis quae praecedit XV KL martii arietem possit ingredi. Borst, Schriften, Vol. 3, p. 1192. Jones, Charles.Bedae Opera de temporibus, Cambridge (Mass.): The Medieval Academy of America, 1943, 649-653. (39r) Anni ad incarnatione domini anno praesenti sund DCCXCIII … — … et ideo bissextus dicitur quis bis VI KL martii habet.

39v-40v Excerpt from the Libri computi, Lib. IIII, 31a, 32a, 33a, and 28a: (39v) Argumentum quot horis luna in unaquaue nocte luceat. II. I. III Si uis scire quot horas luna in unaquaue lucet nocte … — … ante ascenderat interum discendit computandi ratio. Borst, Schriften, Vol. 3, pp. 1237-39. (39v-40r) Expositio de eadem re. Traditur autem secundum quosdam argumentum qui horam quattuor punctis … — … id est hora dodrantem pro punctis III semisse pro II quadrante pro I. Borst, Schriften, Vol. 3, pp. 1239-40. (40r-v) De accensione lunae. Si quis nosse desiderat qua hora luna renouetur et quando hoc … — … In decimae horae noctis primo puncto finem accipit. Borst, Schriften, Vol. 3, pp. 1240-42. (40v) Ianuarius et december hora prima et undecima pedes XXXII … — … Iunius et iulius hora VI pedes III. Borst, Schriften, Vol. 3, pp. 1232-34.