Royal MS 15 B IX

BOETHIUS, De institutione musica, Hermannus Contractus and Gerbertus on geometry and mathematics, &c., viz.:

1. 'De musica id est armonica institucione liber primus [-quintus] Boetii ' (see colophon to lib. I); a text with no very obvious affinities among the MSS. used by Friedlein (Teubner Ser., 1867). The diagrams are given in the fullest form, with arches, &c., in colours. Interlinear and marginal glosses in a minute hand. No tables of capitula, but the lost chapters at the end are indicated by a contemporary note 'hic desunt xi capitula'. Text beg. 'Omnium quidem perceptio sensuum '; gloss, 'Notandum quod cum omnis ars in ratione contineatur'. f. 3.

2. De mensura astrolabii, without title: the work of Hermann on the wazalchora or astrolabe of Ptolemy, printed by Pez, Thesaurus Anecd. iii, pt. ii, col. 94, reprinted by Migne, Patr. Lat. cxliii. 381. Preface beg. 'Hermannus Christi pauperum peripsima'; text, 'In metienda igitur subtilissime inuentionis Ptolomei wazalchora'. Diagram and a few marginal notes. f . 51.

3. 'De utilitatibus astrolabii secundus liber incipit', preceded by a table of twenty-one chapters as in Pez, ib. col. 109 (Migne, ib. 389-404); cf. Add. MS. 17808, f. 73 b. Beg. 'Quicumque astronomice periciam discipline'. Marginal notes. Colophon, 'Explicit tractatus astrolabii'. f. 53.

4. 'Demonstracio componendi cum circumuentibuli (sic, for circumuertibili) sciothero orologici uiatorum instrumenti'; printed by Pez, ib. col. 131 (Migne, ib.

405-410), under the title (not warranted by his Salzburg MS.) of Liber secundus de utilitatibus astrolabii, capp. i-v. Beg. 'Componitur quiddam simplex et paruulum'; ends 'labor exquirat'. With diagrams. f. 58 b.

5. 'Ad mensurandam cum quadrato astrolabii plano stantem per suam ipsius umbram quamlibet altitudinem': a chapter which apparently belongs to the Geometria of Gerbert (Pope Silvester II, 999-1003, see Olleris, Œuvres de Gerbet, Paris, 1867, p. 433, cap. xxii), cf. the next article and Pez, op. cit., iii, pt. ii, col. 42, cap. xxi (Migne, cxxxix. 120), although it is apparently omitted in the MSS. used by Olleris and is also printed from the Salzburg MS. as cap. vi of lib. ii of Hermann as above. Beg. 'Si uis alicuius arboris aut columpne'; ends'dinoscitur habere'. f. 60 b.

6. 'Ad altitudinem cum astrolabio rneciendam': the whole of the latter part of Gerbert's Geometria, viz. capp. xvi-xciv, Olleris, pp. 429-470, Pez, op.cit., col. 38, Migne, cxxxix. 117-152. Art. 5 is repeated in its proper place. Beg. 'Si fuerit altitudo in equalitate'; ends circulum scribimus. finit'. With diagrams. f. 61.

7. Further geometrical notes, without title, viz.:-(a) On the rotations of a cart-wheel travelling a league (the ratio of diameter to circumference is assumed as 7 :22), beg. 'Ratione circuli probatur';-(b) That the sum of the interior angles of any triangle is, equivalent to two right angles, beg. 'Seimus triangulum tres interiores'; -(c) On measurement by shadow;-(d) On Origen's account of the geometric cubit. This occurs also as a marginal note on f. 60;-(e) On the proportions of the human body, 'Secundum Egesippum et Eugepium';-

(f) On the construction of a celestial globe, beg. 'Primum obscruandum est in spera ut ex omni parte'. Some or all of these occur in the Oxford MS. Digby 191, f. 77. f. 68 b.

8. Epistle on spherical content, here given as from Gerbert to Adalbold (Bishop of Utrecht 1010-1027), but really from Adalbold to Gerbert and so printed by Pez, op. cit., col. 87, Migne, cxl. 1103, Olleris, p. 471. The introductory paragraphs of the printed texts and a sentence at the end of Pez' text are wanting. Beg. 'Domino suo summo pontifici et philosopho Adalboldo G. uite felicitatem ... Macrobius super somilum'; ends 'in puteorum profunditatibus'. With diagram. f. 69 b.

9. Letter [of Gerbert] to Adalbold on the area of an equilateral triangle; printed by Pez, col. 81, Migne, cxxxix. 151, Olleris, p. 477. Beg. 'Adalbaldo nunc usque dilecto . . . In his geometricis figuris'; ends 'mei semper memento'. f. 70.

10. Directions, without title, for determining the depth of a pond, &c. Probably the same as in Digby MS. 191, f. 178 b. Beg. 'Quando uis scire profunditatem'. f. 70 b.

11. For finding the hour of the day with the quadrant, perhaps as in Digby MS. 191, f. 77 b. Beg. 'Si diei horas scire desideras'. With diagram. f. 70 b.

12. For finding the latitude with the quadrant. Beg. 'Diuisum autem ab huiusmodi diuisionis sapientibus'. f. 71.

13. Diagram and explanations of the astrolabe. Beg. 'Hec est figura interpretacionis uerborum Anabicorum'. f. 71.

14. 'De mensuris': a treatise on weights and measures. Beg. 'Mensura est quicquid pondere capacitate longitudine'; ends 'uncias et digitos diuiserunt'. f. 71 b.

15. On the sum of certain series. Beg. 'Si uis scire quanta summa numerorum crescat'; ends 'pro uno accipias'. f. 72 b.

16. 'De statu mundi': directions for making a tabula or dial. Beg. 'Ad inuenienduin diuersum mundi staturn'; ends 'deprehensa fuerat'. f. 72 b.

17. 'De computatione per manum', how to count up to thousands on the fingers. Beg. 'Centesimus et sexagesimus et trigesimus fructus'. f. 73.

18. Introduction to a treatise on the use and construction of the wazalchora or astrolabe of Ptolemy, derived from the Arabic. Whether this treatise is contained in artt. 19-24, in the absence of rubrics it is not clear, but the scheme of the turgidly written preface seems to differ in some respects. Beg. 'Ad intimas summe philosophie disciplinas et sublimia eius perfectionis archisteria'; ends 'quod opusculum cuiuslibet uelit complicare libro siue canonibus Ptolomei siue Vinctorio, quia ipse affluentes descriptiones horologiorum assequitur, sapientium commendo censure, dum illud sancte ecclesie representasse sufficiat'. f. 73 b.

19. Three paragraphs on the modes of determining the orientation, the solstices, and the length of day and night. See also art. 24 below. Beg. 'Dum inueniendum in aliquo loco aliquo tempore'. f. 74 b.

20. On the eight climata. Beg. 'Climata Latini taliter disponunt'; ends 'locus confessionis'. The same occurs above as a marginal note on f. 58 b. f. 74 b.

21. On the construction of the astrolabe of Ptolemy. Beg. 'Philosophi qui sua sapientia motus siderum'; ends 'et arietem pertinet'. f. 75.

22. On the use of the astrolabe of Ptolemy for finding latitude, time, conjunctions of fixed stars, and length of day and night. Part of this occurs also in Add. MS. 17808, ff. 79, 80. Beg. 'Sumpto astrolabio quo sol primum gradum'; ends 'certa ratione reperta'. f. 76.

23. To find the size of the carth : a paragraph repeated from art. 4 above (f. 59 b). Beg. '[Q]uamuis Ambrosii, Theodosii, Macrobii auctoritate'. f. 76.

24. A repetition of art. 19. Beg. 'Cum inuenien. dum'. At the end are three diagrams of astrolabes; the last two are accompanied by verses 'Sub radiis Phebi sunt hec signacula plebi, in quibus absque mora lucis dinosciturhora'; and 'Res super obscuras ueteres posuere figuras, ut ualeat uisus rationis pandere nisus'. f. 76 b.

On ff. 77 b, 78 some tables seem to have been erased. Art. 25 is in a hand of the end of the 12th or beginning of the 13th cent.

25. Tract on algorism. A similar, but not identical article occurs in Egerton MS. 2261, f. 225 b. Beg. 'Intentio Algorismi est in hoc opere doctrinamprestare procedendi'; ends 'non possis diuidere. explicit'. f. 77 b.

The last fly-leaf (f. 79) is from a commentary on job, containing xl. 24-xli. 21, in a minute hand of the latter part of the 13th cent. Other fly-leaves are:-(a) A collection of aphorisms. Beg. 'Habitabit lupus eum agno, id est Saulus cum Anania'. Chiefly from Seneca de beneficiis. f. 1 b;-(b) Another collection of aphorisms. Beg. 'Medicis et presbiteris grauis animus in questu est' ; ends 'Sapiens homo paucis utitur uerbis'. f. 2. These are in 13th cent. hands;-

(c) An arithmetical guessing puzzle, in verse and prose, beg. 'Quot nummi loculo sint tot triplicare iubeto'. f. 78 b;-(d) An elegiac quatrain against a friar, beg. 'Quod fueram non sum, fratris capud aspice tonsum'. f. 78 b;-(e) Verses on the Latin terms for exile, beg. 'A patria profugus discedens dicitur ultro'. f. 78 b. These are in 14th cent. hands. Some occult memoranda by John Theyer are on f. 78, and On f. 78 b is a scrap of Hebrew in a 13th cent. hand, probably relating to some accompts written in pencil above.

Vellum; ff. 79. 10 in. x 6³/₄ in. End of XII cent. Very minutely written. Gatherings (beg, f. 3) of 8 leaves (iii-v only numbered, two blank leaves cut out of viii). Sec. fol (text) 'succensuisse'. Initials in colours. Belonged to John Dee the astrologer (title in his hand on f. 2 b), no. 74 in the catalogue of his library printed by Halliwell for the Camden Society, 1842,. A note on f. 37 b, 'The author of this booke was Boetius, and from the concords of algorisme by nombers musicke is made. Our famous uniuersitie of Oxon. do injoyne all musitians to follow these fundamentall grownds both for cordall fistularie and vocall musicke', apparently in the hand of Henry Fowler [rector of Minchinhampton in 1618], see above, 12 G. IV, art. 1. Afterwards the MS. belonged to John Theyer. Theyer sale-cat. no. 137; CMA. 6625.