London, British Museum, Royal 15 B IX

Century	12 ex.
Language	Latin
Subject 1	Geometry \| Mathematics
Previous owners	Belonged to John Dee the astrologer (title in his handon 2b), # 74 in the catalogue of his library printed by Halliwell for the Camden Society, 1842. A note on 37b, 'The author of this booke was Boetius, and from the concords of algorismus by nimbers 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 Royal 12 G. IV, art.1. Afterwards the MS. belonged to John Theyer. Theyer sale-cat. no. 137.
Material	Membr.
Height × width	10 x 6 3/4 in.
No. of leaves	79
Gatherings	Gatherings (beg. 3) of 8 leaves (iii-v only numbered, two blank leaves cut out of viii. Sec. fol. (tect) 'succensuisse'.
Binding leaves	The fly-leaf (79) is from a commentary on Job, containing xl. 24-xli.21, in minute hand of the latter part of s. 13. Other fly-leaves ar: (a) A collection of aphorisms. Beg. 'Habitabit lupus cum agno, id est Saulus cum Anania'. Chiefly from Seneca de beneficiis (1b); (b) Another collection of aphorisms. Beg. 'Medicis et presbiteris grauis animus in questu est'; ends 'Sapiens homo paucis utitur uerbis' (2). These are in s. 13 hands; (c) An Arithmetical guessing puzzle, in verse and prose, beg. 'Quot nummi loculo sint tot triplicare iubeto' (78b); (d) An elegiac quatrain against a friar, beg. 'Quod fueram non sum, fratris caoud aspice tonsum' (78b); (e) Verses on the Latin terms for exile, beg. 'A patria profugus discedens dicitur ultro' (78). These are in s. 14 hands. Some occult memoranda by John Theyer are on 78, and on 78b is a scrap of Hebrew in a s. 13 hand, probably relating to some accompts written in pencil above.
Type of writing	Very minutely written.
Initials etc.	Initials in colours.
Printed catalogs	Casley, D., A catalogue of the manuscripts of the King's Library (1734) 240. \| CMA 6625.
Publ. descriptions	Bubnov, N., Gerberti postea Silvestri II papae Opera Mathematica (972-1003) (1899) xvi xvii xxxvi-xxxviii xciv xcvi cii civ cviif. cix.
Printed copies	Bubnov, N., Gerberti postea Silvestri II papae Opera Mathematica (972-1003) (1899) 42-5 111-47 300-9 313-65 370-5.
Source	Folkerts (1969) \| Warner & Gilson II (1921)
Type of source	cat. \| pvt. notes
Source’s source	insp.

Work 1	Title (ms.)	Varia, inter quae:
Work 1	Additional remarks	25 parts
Work 2	Author standard	Hermannus
	Title (ms.)	De mensura astrolabii
	Contents	On the wazalchora or astrolabe of Ptolemy.
	Incipit	In metienda igitur subtilissime inuentionis Ptolomei wazalchora.
	Printed copies	Printed by Pez, Thesaurus Anecd. III,2 col.94; reprinted by Migne, Patr. Lat. cxliii 381.
	Item no.	2
	Folio no.	51-
	Prolog	Hermannus Christi pauperum peripsima
	Glosses etc.	A few marginal notes.
	Math. drawings	Diagram.
Work 3	Title (ms.)	De utilitatibus astrolabii
	Incipit	Quicumque astronomie periciam discipline
	Printed copies	Table of chapters as in Pez, Thesaurus Anecd. III,2 col. 109 (Migne, Patr. Lat. cxliii 389-404).
	Item no.	3
	Folio no.	53-
	Initial lines	Preceded by a table of twenty-one chapters
	Rubric	De utilitatibus astrolabii secundus liber incipit
	Colophon	Explicit tractatus astrolabii.
	Glosses etc.	Marginal notes.
	Additional copies	Cf. Add 17808, f.73b.
Work 4	Title (ms.)	De utilitatibus astrolabii
	Incipit	Componitur quiddam simplex et paruulum
	Printed copies	Printed by Pez, Thesaurus Anecd. III,2 col. 131 (Migne, Patr. Lat. cxliii 405-10), under the title (not warranted in his Salzburg MS.) of Liber secundus de utilitatibus astrolabii, capp. i-v.
	Item no.	4
	Folio no.	58b-
	Rubric	Demonstratio componendi cum circumuentibuli (sic, for circumuertibili) sciothero orologici uiatorum instrumenti
	Explicit	labor exquirat.
	Math. drawings	With diagrams.
Work 5	Author standard	Gerbert
	Title (ms.)	Geometria (cap. xxii)
	Incipit	Si uis alicuius arboris aut columpne
	Printed copies	A chapter which apparently belongs to the Geometria of Gerbert (Pope Silvester II, 999-1003, see Olleris, OEuvres de Gerbert, Paris, 1867, 433, cap. xxii), cf. the next article and Pez, Thesaurus Anecd. III,2 col. 42, cap. xxi (Migne, Patr. Lat. 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.
	Item no.	5
	Folio no.	60b-
	Rubric	Ad mensurandam cum quadrato astrolabii plano stantem per suam ipsius umbram quanlibet altitudinem
	Explicit	dinoscitur habere.
Work 6	Author standard	Gerbert
	Title (ms.)	Geometria (cap. xvi-xciv)
	Incipit	Si fuerit altitudo in equalitate
	Printed copies	The whole of the latter part of Gerbert's Geometria, viz. cap. xvi-xciv Olleris, OEuvres de Gerbert, Paris, 1867, 429-70, Pez, Thesaurus Anecd. III,2 col. 38, Migne, Patr. Lat. cxxxix, 117-52. Art 5 is repeated in its proper place.
	Item no.	6
	Folio no.	61-
	Rubric	Ad altitudinem cum astrolabio meciendam
	Explicit	circulum scribimus finit.
	Math. drawings	With diagrams.
	T & K	TK 1449
Work 7	Title (ms.)	Geometrical notes
	Contents	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. 'Scimus triangulum tres interiores'; (c) On measurement by shadow; (d) On Origen's account of the geometrical cubit. This occurs also as a marginal note on 60; (e) On the proportions of the human body, 'Secundum Egesippum et Eugepium'; (f) On the construction of a celestial globe, beg. 'Primum obseruandum est in spera ut es omni parte.
	Item no.	6
	Folio no.	68b-
	Rubric	Without title.
	Additional copies	Some or all of these occur in GOxfB Digby 191, f.77.
	T & K	TK 1315 (Ratione circuli), 1405 (Scimus triangulum)
Work 8	Author standard	Adalbold
	Additional names	Gerbert
	Title (ms.)	Epistle on spherical content
	Incipit	Domino suo summo pontifici et philosopho Adalboldo G. uite felicitatem ... Macrobius super somnum
	Printed copies	Here given as from Gerbert to Adalbold, but really from Adalbold to Gerbert and so printed by Pez, Thesaurus Anecd. III,2 col. 87, Migne, Patr. Lat. cxl 1103, Olleris, OEuvres de Gerbert, Paris, 1867, 471. The introductory paragraphs of the printed texts and a sentence at the end of Pez' text are wanting.
	Additional remarks	Adalbold (Bishop of Utrecht 1010-1027)
	Item no.	8
	Folio no.	69b-
	Explicit	in puteorum profunditatibus.
	Math. drawings	With diagrams.
Work 9	Author standard	Gerbert
	Additional names	Adalbold
	Title (ms.)	Letter on the area of an equilateral triangle
	Incipit	Adalboldo nunc usque dilecto ... In his geometricis figuris
	Printed copies	Printed by Pez, Thesaurus Anecd. III,2 col. 81, Migne, Patr. Lat. cxxxix 151, Olleris, OEuvres de Gerbert, Paris, 1867, 477.
	Item no.	9
	Folio no.	70
	Explicit	mei semper memento.
Work 10	Title (ms.)	Directions for determining the depth of a pond, &c.
	Incipit	Quando uis scire profunditatem
	Item no.	10
	Folio no.	70b
	Additional copies	Probably the same as in Oxford, Bodleian, Digby 191, f.178b.
Work 11	Title (ms.)	Directions for finding the hour of the day with the quadrant
	Incipit	Si diei horas scire desideras
	Item no.	11
	Folio no.	70b
	Math. drawings	With diagrams.
	Additional copies	Perhaps as in Oxford, Bodl., Digby 191, f.77b.
	T & K	TK 1446
Work 12	Title (ms.)	Directions for finding the latitude with the quadrant
	Incipit	Diuisum autem ab huiusmodi diuisionis sapientibus
	Item no.	12
	Folio no.	71
	T & K	TK 444
Work 13	Title (ms.)	Diagram and explanations of the astrolabe
	Incipit	Hec est figura interpretacionis uerborum Arabicorum
	Item no.	13
	Folio no.	71
Work 14	Title (ms.)	A treatise on weights and measures
	Incipit	Mensura est quicquid pondere capacitale longitudine
	Item no.	14
	Folio no.	71b
	Rubric	De mensuris
	Explicit	uncias et digitos diuiserunt.
	T & K	TK 870
Work 15	Title (ms.)	On the sum of certain series
	Incipit	Si uis scire quanta summa numerorum crescat
	Item no.	15
	Folio no.	72b
	Explicit	pro uno accipias.
	T & K	TK 1474
Work 16	Title (ms.)	Directions for making a tabula or dial
	Incipit	Ad inueniendum diuersum mundi statum
	Item no.	16
	Folio no.	72b
	Rubric	De statu mundi
	Explicit	deprehensa fuerat.
Work 17	Title (ms.)	How to count up to thousands on the fingers
	Incipit	Centesimus et sexagesimus et trigesimus fructus
	Item no.	17
	Folio no.	73
Work 18	Title (ms.)	Introduction to a treatise on the use and construction of the astrolabe
	Incipit	Ad intimas summe philosophie disciplinas et sublimia eius perfectionis archisteria
	Additional remarks	Derived from the arabic.
	Item no.	18
	Folio no.	73b
	Explicit	quod opusculum cuiuslibet uelit complicare libro siue canonibus Ptolomei siue Vinctorio, quia ipse affluentes descriptiones horologiorum assequitur, sapientum commendo censure, dum illud sancte ecclesie representasse sufficiat.
	Additional copies	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.
Work 19	Title (ms.)	On the modes of determining the orientation, etc.
	Contents	Three paragraphs on the modes of determining the orientation, the solstices, and the length of day and night.
	Incipit	D<C?>um inueniendum in aliquo loco aliquo tempore.
	Item no.	19
	Folio no.	74b
	Additional copies	See also art. 24.
Work 20	Title (ms.)	On the eight climata
	Incipit	Climata Latini taliter disponunt
	Item no.	20
	Folio no.	74b
	Explicit	locus confessionis.
	Additional copies	The same occurs as a marginal note on 58b.
Work 21	Additional names	Ptolemaeus
	Title (ms.)	On the construction of the astrolabe of Ptolemy
	Incipit	Philosophi qui sua sapientia motus siderum
	Item no.	21
	Folio no.	75
	Explicit	et arietem pertinet.
Work 22	Title (ms.)	On the use of the astrolabe
	Contents	On the use of the astrolabe of Ptolemy for finding latitude, time, conjunctions of fixed stars, and length of day and night.
	Incipit	Sumpto astrolabio quo sol primum gradum
	Item no.	22
	Folio no.	76
	Explicit	certa ratione reperta.
	Additional copies	Part of this occurs also in Add. 17808, ff.79,80.
Work 23	Title (ms.)	To find the size of the earth
	Incipit	Quamuis Ambrosii, Theodosii, Macrobii auctoritate
	Item no.	23
	Folio no.	76
	Additional copies	A paragraph repeated from art 4 (59b).
Work 24	Title (ms.)	On the modes of determining the orientation, etc.
	Contents	Three paragraphs on the modes of determining the orientation, the solstices, and the length of day and night.
	Incipit	Cum inueniendum
	Additional remarks	On 77b, 78 some tables seem to have been erased.
	Item no.	24
	Folio no.	76b
	Math. drawings	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 dinoscitur hora; and 'Res super obscuras ueteres posuere figuras, \| ut ualeat uisus rationis pandere nisus.
	Additional copies	A repetition of art. 19.
Work 25	Scribe(s)	In a hand of the end of s. 12 or the beginning of s. 13.
	Title (ms.)	Tract on algorism
	Incipit	Intentio Algorismi est in hoc opere doctrinam prestare procedendi
	Item no.	25
	Folio no.	77b
	Explicit	non possis diuidere.
	Colophon	explicit.
	Additional copies	A similar, but not identical, article occurs in Egerton 2261, f.225b.