Equatorie of the Planetis (MS Peterhouse 75.I)
The Equatorie of the Planetis in Peterhouse MS 75.I describes an instrument for calculating the positions of the planets. On the evidence of its calendar references the text was probably composed in 1393. For an astronomical work of this date, it is remarkable for being written in English. When it was brought to public attention by Derek J. Price in 1951 it naturally invited comparison with Chaucer’s A Treatise on the Astrolabe. Accompanying the Equatorie, and in the same hand, is a set of tables, one of which contains the note ‘Radix Chaucer’ (f. 5v and see image right,
taken when the manuscript was disbound). The consequent possibility that the Equatorie was Chaucer’s own composition is an issue that has occupied the attention of many scholars; however, this has now been resolved. The writer has been identified as John Westwyk, a Benedictine monk of Tynemouth Priory and St Albans Abbey, whose life was one of dramatic contrasts (Rand 2014).
The astronomical content of the manuscript is also of considerable value in its own right. The entire text (excluding the contents of the tables) has been transcribed. A key to the conventions used in the transcription is available here, and a key to the numerals used in the manuscript can be accessed here
Virtual model
Video tutorial In conjunction with the digitisation of the manuscript, a digital model of the equatorium it describes has been produced, following the instructions and diagrams in the manuscript. This fully-functional interactive equatorium can be accessed by clicking on the link above (left); we recommend opening it in a separate window if you wish to view it alongside the manuscript. Those visitors whose browser does not support the interactive model, or who require guidance on the way it works, are recommended to view the video tutorial above (right).
Writing process
The text of the Equatorie of the Planetis is clearly an author’s or translator’s autograph. It is unusual in several respects. Most obviously because it is in English – astronomical texts from this period are almost exclusively written in Latin – but also because of its distinctive appearance and the way it shows the writer at work.
The pages are very large (see Detailed description), as is the writing, which usually goes across most of the width of the page, in long lines which are not straight. There is no line ruling. The space between words and between lines is exceptionally generous. The script used is a practiced casual one, not a formal scribal one. However, the man is no amateur as a writer – he was clearly used to drafting and writing with an eye to later copying, which is what we find him doing here. He is composing a text, and apparently at the same time attempting to produce a fair copy with little scope for misunderstanding. The result is a tendency towards clarity at the expense of neatness. His most frequent way of correcting his text is through erasure (i.e. scraping dried ink off the parchment with a knife). This is obvious even to the naked eye, but under ultra-violet light (UV) it becomes clear that words have been erased and replaced by others in virtually every line. The majority of the erasures have been written over with no sign that the space available was too small or too ample, so we may assume that the changes were made when drafting. The advantage of this is obvious. Although interlinear emendations are unavoidable at a later stage of checking the text, there is less scope for ambiguity and error if they are kept to a minimum from the start. Very occasionally the writer also deleted by means of cancellation (drawing one or more straight lines through the word or passage he wished to delete) [f. 71v11; most of f. 76r] and of expunction (placing a dot under each letter to be left out) [f. 75v1]. He has also used dissolution (sponging the ink of the word or passage in question until it dissolved), but we cannot tell how often. Dissolution required well spaced words and lines, and could only be done while writing, when there was no text below or to the right. Signs of successful dissolution are virtually impossible to detect with the naked eye because the surface remains smooth. However, at f. 78r4 a smudge of pigment is left, signalling something underneath (line final ‹shal› visible under UV). Three instances around the rift in f. 77 (ff. 77r21 ‹the›, 77v20 ‹the› and 77v23 ‹thre›) show dissolved words which are only visible under UV, and only because they have not been written over.
Having composed a clear, relatively clean and above all legible draft, which could serve as an exemplar for further copying, the writer went on to the next stage, checking the contents and aiming for ease of understanding. This resulted in eighty additions and emendations to the text. These have been inserted in the wide spaces between the lines, half of them accompanied by a caret mark on the line to indicate where they should go. Occasionally they alter the substance [f. 71v11], but most frequently they add clarity to the instructions [f. 71v6], and sometimes they produce a more English syntax. The great majority of the insertions without a caret are Latin or anglicised Latin terms which amplify the text or clear up ambiguous points. The remaining twelve are glosses, i.e. English words or concepts in the body of the text are glossed by interlinear Latin synonyms (‹punctus› above ‹poynt› on 73v1, ‹id est punctus› above ‹prikke› on f. 73r31). How (if at all) the writer intended the glosses to go into the text, is not obvious. In England in the 1390s it was the Latin astronomical terms which provided the points of reference and were familiar to his readers. No English vocabulary had as yet been firmly established and it is common in English medical and scientific treatises from this period to introduce English technical terms in a text by pairing them with Latin synonyms (as does the Equatorie writer himself on f. 78v14).
The text of the Equatorie would appear to be partly original composition based on the writer’s own practical experience (but perhaps not with an equatorium of the size he describes) and partly translation from a Latin source (or sources). Until a source has been identified, however, the proportion of translation to composition must remain the object of speculation.
John Westwyk
Because of the autograph nature of the text, some scholars have seen the Equatorie not only as a possible addition to the Chaucer canon, but perhaps also a text in Chaucer’s own hand. No example of Chaucer’s handwriting was known in the early 1950s when Price’s edition appeared, and none has come to light since. Subsequent research (Rand Schmidt 1993) showed that the Equatorie hand differs on important points from those of all the proposed Chaucer autographs in the Public Record Office (which in turn differ from each other). Although the Equatorie is largely in the type of London dialect which Chaucer could have been expected to use, it could not be shown to be distinct to him. Quantitative studies of the prose style showed that the Equatorie is not sufficiently like the prose texts known to be Chaucer’s, and at the same time sufficiently unlike comparable non-Chaucerian texts, for the Equatorie to be identified as Chaucer’s on those grounds. The case for Chaucer’s authorship of the Equatorie of the Planetis rested on insufficient evidence.
However, new evidence has now come to light (Rand 2014, http://dx.doi.org/10.1080/00393274.2014.982355). Oxford, Bodleian Library MS Laud misc. 657 is written in the same hand as the Equatorie. The writer was a Benedictine monk who signs himself Johannes de Westwyk, and is referred to as John Westwyk in contemporary records. A detailed comparison of the script in the two manuscripts is included in Appendix 1 of Rand (2014). The Laud manuscript contains two texts by Richard of Wallingford, Abbot of St Albans (1292-1336): his Albion, and the Rectangulus. The latter is a straightforward copy, whereas the text of the former has been adapted to John Westwyk’s circumstances. John appears to have been admitted to the order at St Albans, having come from a local family, and to have had his first training in astronomy there. At some point in or near 1381, he was made to go, or chose to go, to St Albans’s daughter house at Tynemouth on the Northumberland coast. Tynemouth Priory was then in a state of disrepair and subject to constant attacks from the Scots over the border. It was frequently used as a ‘penal colony’ for recalcitrant St Albans monks, but John may have been sent there to teach. He is perhaps most likely to have written Laud misc. 657 before he went north. At St Albans he would have had easy access to exemplars for the two Wallingford texts, and to the requisite amount of parchment of uniform quality. He amended the instructions in the Albion text to accord with the latitude of Tynemouth, and with the more restricted needs of those leading a cloistered life.
By 1382/83 John Westwyk was however ready to get away from Tynemouth. In the late autumn of 1382 Henry Despenser, Bishop of Norwich, had launched a plan for a campaign against the anti-pope in Avignon in the shape of a crusade against Flanders. The Pope had given the Bishop the right to raise troops and funds in exchange for indulgences, which he successfully did. Members of the clergy had permission to take part in this holy war as soldiers. The expedition also had royal approval and Parliament’s support. When it left for Calais in May 1383, seven monks from St Albans and its daughter houses had joined, and John Westwyk was one of them.
At first the campaign was successful and significant battles and towns were won, but the Bishop’s army soon suffered losses and the troops caught dysentry. By late September there had been a complete reversal of fortune and the troops trickled back to England. The chronicler Thomas Walsingham reports that the six monks from St Albans who survived were welcomed back by the abbot, but never regained their former health (British Library, MS Cotton Claudius E.iv, vol. 2, f. 239vb; printed Riley, ii, 416).
There is nothing to indicate that John Westwyk returned to Tynemouth, but nothing is known about him for the next ten years. However, in 1393 he was writing the Equatorie of the Planetis in a location where he had easy access to large sheets of parchment. He wrote it in English, in a dialect close to a London one, but with a number of non-London dialect forms. Some of the accompanying tables in his hand contain Oxford references, a greater number contain London ones.
The next mention of John Westwyk is in May 1397, when he is recorded in the Lateran Regesta as a monk of St Albans and as having procured an indult for the confessor of his choice to grant him, being penitent, plenary remission of sins as often as he pleases (Archivum Secretum Vaticanum, Lat. Reg. 45, f. 175v; calendared in Bliss & Twemlow, v, 42). This appears to be the last extant reference to him. It seems likely that the indult was an end-of-life one, and that he died soon after.
Kari Anne Rand
November 2014
Equatorium design and astronomical tables
Although similar instruments are described in other treatises dating from the thirteenth and fourteenth centuries, this precise design of planetary equatorium is unique to the Peterhouse manuscript. Ff. 71v-74r explain first how to make the instrument; ff. 75r-78v explain how to use it to find the longitudes of the Sun, Moon and planets, and the latitude of the Moon. Celestial latitude and longitude are coordinates in the sky: longitude is measured around the ecliptic (the path of the Sun’s annual motion through the fixed stars, in a plane angled at around 23° to the celestial equator), in degrees from 0 to 360° starting from the vernal equinox (where the ecliptic and celestial equator intersect); latitude is measured in degrees from 0 to 90° north or south of the ecliptic.
The design is a simplification of the Ptolemaic model of planetary motion. In this model each planet moves at a constant velocity around an epicycle; the centre of that epicycle itself moves around a deferent circle, at a velocity which is constant with respect to another point, the equant centre. For the planets Venus, Mars, Jupiter and Saturn, the equant centre (E) and deferent centre (D) are fixed on a line running from the Earth (W) to the planet’s apogee (A, called “aux” in the treatise); D is midway between W and E. Thus five pieces of information are necessary to calculate a planet’s longitude: the direction of A, measured as an arc from the vernal equinox (♈); the size of the planet’s eccentricity (i.e. the displacement of D and E from W); the relative sizes of its deferent circle and epicycle; the location of the epicycle centre in longitude, measured as an arc at E from either ♈ or A (those arcs are known as mean longitude and mean centre, respectively); and the arc of the motion of the planet around the epicycle (mean anomaly), measured from the mean epicyclic apogee (a point on the epicycle diametrically opposite to E). The diagram below (left) shows this (each planet has a different D, E, and A).
Because the relative sizes of the deferent circle and epicycle varied between planets, early equatoria essentially consisted of separate instruments for each planet. However, the Peterhouse design accommodates models for all planets in a single instrument, as the diagram above (right) shows. The ecliptic is marked on a wooden disc (indicated by the green circle). The red deferent circle, on which is located the epicycle centre, is reduced to the radius of a large brass ring. The centre of that ring is the epicycle centre. One end of a rotating rule (the “label”) is attached to a bar running across the ring; on it are marked the radii of the planets’ epicycles. As the label turns, the planets’ epicycles are traced out.
To measure the planet’s longitude on the epicycle, the treatise instructs the user to mark out the mean longitude (the treatise calls this the “mean motus”) using a black thread from W; this is translated to E using a parallel white thread. The rim of the brass epicycle is fixed to D and the epicycle is rotated so its centre is under the white thread. The mean anomaly (“mean argument” in the treatise) is marked out by turning the label anticlockwise from the mean epicyclic apogee (where the white thread crosses the far rim of the epicycle). The black thread is then moved to the planet’s mark on the label; the planet’s longitude (“verrey [true] place”) can be read where the thread crosses the scale on the wooden disc.
The longitudes of the Sun, Moon and Mercury can be computed using similar methods. A scale on one half of the wooden disc allows the Moon’s latitude to be computed; this is sinusoidally related to its elongation from its nodes (where its orbit intersects the ecliptic). On the other half of the disc is a scale that was intended for computation of the accession and recession of the eighth sphere, which was one component of precession (by which the apogees of the Sun and planets moved against the background of fixed stars). It is clear how this scale would have worked, but it is not fully explained and would not have given as good results as the lunar latitude scale.
The tables which comprise the bulk of the codex may be divided into three parts. First (ff. 1r-13v) are a set in Hand C, giving the information necessary for the use of the equatorium as described above: annual and daily values for the mean longitudes and mean anomalies. Next are a set in Hand S (ff. 14r-62r) containing much of the same information in calendar form, as well as tables to compute planetary longitudes and latitudes independently from the equatorium. Finally, a further set of tables in Hand C (ff. 62v-71r) includes information of general astronomical and astrological interest, some of which is suited to use with the equatorium. Notes and updated values in the tables testify to their continued interest for the author of the treatise after their composition.
Seb Falk
November 2014
Information about this document
- Physical Location: Cambridge University Library
- Classmark: MS Peterhouse 75.I
- Subject(s): Astronomy, Medieval; Manuscripts, English (Middle)
- Author(s): Chaucer, Geoffrey, -1400
- Origin Place: England
- Date of Creation: c. 1393
- Language(s): Middle English, Latin
- Extent: i + 78 + ii fols; part of early thick parchment wrapper preserved as folded endleaf; one modern blank leaf at each end.
First nine quires: Leaf height: 365 mm, width: 275 mm. Last quire: Leaf height: 335 mm, width: 245 mm. Size of written area of both table and text pages very variable; largest written area on page of text (f. 71v): Written height: 305 mm, width: 240 mm. - Collation:
The MS consists of ten quires as follows:
- 1 modern paper flyleaf (unnumbered)
- Quire 14 (fols 1-4)
- Quire 214, wants leaves 8-11, 13 (fols 5-13)
- Quire 312 (fols 14-25)
- Quire 412, wants leaf 7 (fols 26-36)
- Quires 5-612 (fols 37-60)
- Quire 74 (fols 61-64)
- Quire 88, wants leaves 1-2 (fols 65-70)
- Quires 9-104 (fols 71-78)
- Folded endleaf (early wrapper, unnumbered)
- 1 modern paper flyleaf (unnumbered)
- Material: Parchment
- Format: Codex
- Binding:
New binding by John P. Gray, Cambridge c. 1952-1955 after separation from what is now MS 75.II. Full pale brown goatskin. Cloth slipcase. Previous binding's coverskin and pasteboards used to rebind MS 75.II
- Script:John Westwyk (fols 1r-13v and 62v-78v): current Anglicana bookhand. Also annotations (some in cipher) on tables by Hand S on fols 14r-17r, 20r, 21r-22r, 23r-23v, 25r-25v, 26r, 27r-27v, 29r, 30r-32v, 36r-36v, 38v, 45r, 48r, 51r, 54v-55r and 58v)Hand S (tables, fols 14r-62r): Anglicana bookhandPunctuation: Most frequent are the wedge paragraphus and the single virgule. Double virgules, and a point followed by a single virgule also occur. Carets for insertions. Numerals in the text usually enclosed by raised points
- Layout:
Hand S's leaves (fols 14r-62r) are pricked and ruled (in both brown ink and drypoint) to accommodate tables with variable contents. John Westwyk's leaves (fols 1r-13v and 62v-78v) are not pricked; his tables ruled variously in drypoint and ink (brown and red), to accommodate contents. His text written in long lines across unruled pages with no right-hand margin. Most, but not all, pages of text have three-quarter frames. 2º fol.Medius motus
- Provenance: Seen at Peterhouse, Cambridge by John Leland between 1533 and 1538 (see CBMLC 10, UC49.44); entered in a college booklist compiled between 1589 and 1593 (Ward Library MS 400, p. 12). Possibly identical with an item added in 1472 to the 1418 college catalogue (CBMLC 10, UC48.389)
- Acquisition: Date of acquisition not known.
- Date of Acquisition: not known
- Author(s) of the Record: Kari Anne Rand
- Bibliography:Leland, John, Joannis Lelandi antiquarii de rebus Britannicis collectanea, 6 vols (London: William & John Richardson, 1770) vol. 4, p. 22.Riley, H.T. (ed.), Gesta abbatum Monasterii S. Albani, a Thoma Walsingham, regnante Ricardo Secundo, eiusdem ecclesiae praecentore, compilata, Rerum Britannicorum medii ævi scriptores (Rolls Series) 28, Chronica Monasterii S. Albani 4, 3 vols (London: Longman, 1867-69) vol. 2, p. 416.James, Montague Rhodes, A Descriptive Catalogue of the Manuscripts in the Library of Peterhouse (Cambridge: Cambridge University Press, 1899) pp. 93-94.Bliss, W.H. and J.A. Twemlow (eds), Calendar of Papal Registers Relating to Great Britain and Ireland, vol 5: 1398-1404 (London: Institute of Historical Research, 1904) p. 42.Price, Derek J. (ed.), The Equatorie of the Planetis (Cambridge: Cambridge University Press, 1955).North, J. D., "Kalenderes Enlumyned Ben They: Some Astronomical Themes in Chaucer", The Review of English Studies New Series 20 (1969) 129-154, 257-83, 418-44 http://www.jstor.org/stable/512545.Poulle, Emmanuel, Les instruments de la théorie des planètes selon Ptolémée: équatoires et horlogerie planétaire du XIIIe au XVIe siècle, Collection des travaux de l'Académie internationale d'histoire des sciences 27, 2 vols (Geneva: Droz, 1980).North, J. D., Chaucer's Universe (Oxford: Clarendon Press, 1988) pp. 157-191.Rand Schmidt, Kari Anne, The Authorship of the Equatorie of the Planetis, Chaucer studies 19 (Cambridge: D.S. Brewer, 1993).Clarke, Peter D. (ed.), The University and College Libraries of Cambridge, Corpus of British Medieval Library Catalogues 10 (London: British Library in Association with the British Academy, 2002) UC48.389, p. 530; UC49.44, p. 553.Roberts, Jane, Guide to Scripts Used in English Writings up to 1500 (London: The British Library, 2005) pp. 162, 174-176.Mandelbrote, Scott, "The Library of Peterhouse, Cambridge and the Problem of the Spatial Arrangement of Knowledge during the Sixteenth and Seventeenth Centuries", in Robert Felfe and Kirsten Wagner (eds), Museum, Bibliothek, Stadtraum: Räumliche Wissenordnungen 1600-1900 (Berlin: LIT Verlag, 2011) pp. 6 note 21, 9 note 30.Falk, Seb, "The Scholar as Craftsman: Derek de Solla Price and the Reconstruction of a Medieval Instrument", Notes and Records of the Royal Society (2014) http://dx.doi.org/10.1098/rsnr.2013.0062.Rand, Kari Anne, "The Authorship of the Equatorie of the Planetis Revisited", Studia Neophilologica (2014) http://dx.doi.org/10.1080/00393274.2014.982355.
The on-line presentation of the Equatorie is the result of collaboration between the Master and Fellows of Peterhouse and the University Library, and the work is their copyright. Scott Mandelbrote oversaw the undertaking. Individual sections of text are the copyright of the contributing authors (Seb Falk and Professor Kari Anne Rand), without whose collaboration the project could not have been completed. We wish particularly to thank members of the family of Derek de Solla Price, who gave permission to adapt his translation of parts of the manuscript and to use his photograph of f. 5v. We are also grateful to Professors Rod Thomson and Liba Taub for their advice, and to Benjamin Blundell at Section9, who designed the virtual model. The generosity of Professor Joe Pesce has underpinned the project.
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- Physical Location: Cambridge University Library
- Classmark: MS Peterhouse 75.I
- Subject(s): Astronomy, Medieval; Manuscripts, English (Middle)
- Author(s): Chaucer, Geoffrey, -1400
- Origin Place: England
- Date of Creation: c. 1393
- Language(s): Middle English, Latin
- Extent: i + 78 + ii fols; part of early thick parchment wrapper preserved as folded endleaf; one modern blank leaf at each end.
First nine quires: Leaf height: 365 mm, width: 275 mm. Last quire: Leaf height: 335 mm, width: 245 mm. Size of written area of both table and text pages very variable; largest written area on page of text (f. 71v): Written height: 305 mm, width: 240 mm. - Collation:
The MS consists of ten quires as follows:
- 1 modern paper flyleaf (unnumbered)
- Quire 14 (fols 1-4)
- Quire 214, wants leaves 8-11, 13 (fols 5-13)
- Quire 312 (fols 14-25)
- Quire 412, wants leaf 7 (fols 26-36)
- Quires 5-612 (fols 37-60)
- Quire 74 (fols 61-64)
- Quire 88, wants leaves 1-2 (fols 65-70)
- Quires 9-104 (fols 71-78)
- Folded endleaf (early wrapper, unnumbered)
- 1 modern paper flyleaf (unnumbered)
- Material: Parchment
- Format: Codex
- Binding:
New binding by John P. Gray, Cambridge c. 1952-1955 after separation from what is now MS 75.II. Full pale brown goatskin. Cloth slipcase. Previous binding's coverskin and pasteboards used to rebind MS 75.II
- Script:John Westwyk (fols 1r-13v and 62v-78v): current Anglicana bookhand. Also annotations (some in cipher) on tables by Hand S on fols 14r-17r, 20r, 21r-22r, 23r-23v, 25r-25v, 26r, 27r-27v, 29r, 30r-32v, 36r-36v, 38v, 45r, 48r, 51r, 54v-55r and 58v)Hand S (tables, fols 14r-62r): Anglicana bookhandPunctuation: Most frequent are the wedge paragraphus and the single virgule. Double virgules, and a point followed by a single virgule also occur. Carets for insertions. Numerals in the text usually enclosed by raised points
- Layout:
Hand S's leaves (fols 14r-62r) are pricked and ruled (in both brown ink and drypoint) to accommodate tables with variable contents. John Westwyk's leaves (fols 1r-13v and 62v-78v) are not pricked; his tables ruled variously in drypoint and ink (brown and red), to accommodate contents. His text written in long lines across unruled pages with no right-hand margin. Most, but not all, pages of text have three-quarter frames. 2º fol.Medius motus
- Provenance: Seen at Peterhouse, Cambridge by John Leland between 1533 and 1538 (see CBMLC 10, UC49.44); entered in a college booklist compiled between 1589 and 1593 (Ward Library MS 400, p. 12). Possibly identical with an item added in 1472 to the 1418 college catalogue (CBMLC 10, UC48.389)
- Acquisition: Date of acquisition not known.
- Date of Acquisition: not known
- Author(s) of the Record: Kari Anne Rand
- Bibliography:Leland, John, Joannis Lelandi antiquarii de rebus Britannicis collectanea, 6 vols (London: William & John Richardson, 1770) vol. 4, p. 22.Riley, H.T. (ed.), Gesta abbatum Monasterii S. Albani, a Thoma Walsingham, regnante Ricardo Secundo, eiusdem ecclesiae praecentore, compilata, Rerum Britannicorum medii ævi scriptores (Rolls Series) 28, Chronica Monasterii S. Albani 4, 3 vols (London: Longman, 1867-69) vol. 2, p. 416.James, Montague Rhodes, A Descriptive Catalogue of the Manuscripts in the Library of Peterhouse (Cambridge: Cambridge University Press, 1899) pp. 93-94.Bliss, W.H. and J.A. Twemlow (eds), Calendar of Papal Registers Relating to Great Britain and Ireland, vol 5: 1398-1404 (London: Institute of Historical Research, 1904) p. 42.Price, Derek J. (ed.), The Equatorie of the Planetis (Cambridge: Cambridge University Press, 1955).North, J. D., "Kalenderes Enlumyned Ben They: Some Astronomical Themes in Chaucer", The Review of English Studies New Series 20 (1969) 129-154, 257-83, 418-44 http://www.jstor.org/stable/512545.Poulle, Emmanuel, Les instruments de la théorie des planètes selon Ptolémée: équatoires et horlogerie planétaire du XIIIe au XVIe siècle, Collection des travaux de l'Académie internationale d'histoire des sciences 27, 2 vols (Geneva: Droz, 1980).North, J. D., Chaucer's Universe (Oxford: Clarendon Press, 1988) pp. 157-191.Rand Schmidt, Kari Anne, The Authorship of the Equatorie of the Planetis, Chaucer studies 19 (Cambridge: D.S. Brewer, 1993).Clarke, Peter D. (ed.), The University and College Libraries of Cambridge, Corpus of British Medieval Library Catalogues 10 (London: British Library in Association with the British Academy, 2002) UC48.389, p. 530; UC49.44, p. 553.Roberts, Jane, Guide to Scripts Used in English Writings up to 1500 (London: The British Library, 2005) pp. 162, 174-176.Mandelbrote, Scott, "The Library of Peterhouse, Cambridge and the Problem of the Spatial Arrangement of Knowledge during the Sixteenth and Seventeenth Centuries", in Robert Felfe and Kirsten Wagner (eds), Museum, Bibliothek, Stadtraum: Räumliche Wissenordnungen 1600-1900 (Berlin: LIT Verlag, 2011) pp. 6 note 21, 9 note 30.Falk, Seb, "The Scholar as Craftsman: Derek de Solla Price and the Reconstruction of a Medieval Instrument", Notes and Records of the Royal Society (2014) http://dx.doi.org/10.1098/rsnr.2013.0062.Rand, Kari Anne, "The Authorship of the Equatorie of the Planetis Revisited", Studia Neophilologica (2014) http://dx.doi.org/10.1080/00393274.2014.982355.
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