It turns out that the timeline of theoricae planetarum I previously put forward was missing three important entries:
- Theorica planetarum [antiqua] (misattributed to Gerard of Cremona)
- Theorica planetarum of Campanus of Novara
- Jean de Lignieres’ abbreviation of Campanus of Novara’s theorica
- Petrus Philomena de Dacia (Peter Nightingale)’s Equatorium
- Theorica novelle
- Theoricae novae planetarum of Georg von Peurbach
In Emmanuel Poulle’s (1100+-page) work on astronomical instruments and equatoria used to calculate planetary movements (“Les Instruments de la Théorie des Planètes selon Ptolemée: Équatoires et Horlogerie Planétaire du XIIIe au XVIe siècle”, 2 Bde, Genf/Paris 1980 (Centre de Recherches d’Histoire et de Philologie V: Hautes Études Médiévales et Modernes 42)), he named the instrument modelled in the 15th century theorice novelle as the ‘Erfurt-Leipziger instrument’, after two of its manuscripts. [pp.375-416]
(And no, I haven’t got my own copy of Poulle, much as I’d like to.)
So the first question is this: what specifically differentiated this theorice novelle from, say, Campanus of Novara’s theorica planetarum?
Equatoria vs volvelles
Carrying out the computations necessary to draw up a horoscope was fiddly and boring: it required the person doing to have not only access to tables of planetary positions (typically the Alfonsine Tables), but also the spherical trigonometry skills to do a load of tricksy interpolation to determine the planetary positions at times between the entries in the Tables.
Clearly, what was needed was some kind of physical instrument – broadly along the lines of an astrolabe – to do all the heavy lifting / maths for you. The ‘theoric’ (Latin: theorica) in all these titles is in fact not just a theory about the planets, but also a physical model that physically manifests a theory about the planets, and is therefore able to perform work.
What was initially devised was an equatorium. This was (in the case of Campanus of Novara, at least) an astrolabe-like backplate with a circular hole (a mater) into which a series of plugin disc devices (one per planet) was inserted. These plugin plates physically modelled the Ptolemaic deferents, epicycles, and equants that had been used to (numerically) model planetary movements for over a millennium.
Campanus of Novara’s theorica planetarum described exactly this kind of bulky equatorium, while its updated versions (such as that of Jean de Lignieres) tried to simply its mechanisms a little, with the aim of producing something a little more lightweight. Or at least, not quite so heavyweight.
The oldest known extant equatorium is in Merton College, Oxford (Merton SC/OB/AST/2), and dates to about 1350. Here is a photo of its back:
Somewhat extraordinarily, there is also a pair of (pretty much) contemporaneous manuscripts that specifically described this equatorium, which you can read about in Seb Falk’s fascinating (2016) “A Merton College Equatorium: Text, Translation, Commentary“.
- Cambridge University Library, Ms. Gg.6.3, ff. 217v–220v (c. 1348)
- Oxford, Bodleian Library, Ms. Digby 57, ff. 130r–132v (c. 1376)
According to the text, the Merton College equatorium was based on the equatoria of Campanus of Novara, Jean de Lignieres, and also that of Profatius Judaeus. However, Falk cautions (p.2) that this last attribution is incorrect (though widespread). Its third (and indeed closest) equatorium was in fact described in a family of manuscripts known as the Semissa, described in F. S. Pedersen’s (1983) “Petri Philomenae de Dacia et Petri de S. Audomaro opera quadrivialia“, Copenhagen. (Pedersen’s 1979 dissertation solely on the Semissa is online here.)
What united these 13th/14th century theoric tracts was that they described how to build a big, fat, brass equatorium – the Big Science of the day.
By comparison, the theorice novelle manuscripts were – as I understand it – completely different: the instrument they described (and indeed manifested) was a set of paper or parchment volvelles, one volvelle per planet. This was lithe, modern, exciting, lightweight science – much more like a tech startup.
Manuscripts in the equatorium genre were widely copied and disseminated through Europe’s astronomical / astrological communities – they were ‘open source’, effectively. But what of the theorice novelle mss?
Theorice novelle manuscripts
Of the three known manuscripts in this genre, the main two are from Erfurt and Leipzig (hence Poulle’s name). Even now, these two mss languish undigitized (and close to completely unknown) in local museums:
- Angermuseum Erfurt, Cod. 3153, [1458]
- Historisches Museum Frankfurt/M., Cod. X 16027 [1458-1464]
No prizes for guessing, however, that the third one is Gotha Chart A 472 (my current favourite volvelle-heavy mysterious manuscript), dated by Zinner to 1461. Scans for this are online courtesy of Jena.
However, I suspect – admittedly without proof – that the attribution of Gotha Chart A 472 to Profatius Judaeus will prove to be just as specious as the widespread attribution to him of Peter Nightingale’s Semissa manuscript.
All the same, it will take a very much closer reading of all three manuscripts to be able to trace the origins of the theorice novelle more accurately. What we really need is to find someone who has been looking at this for some years…
Theorica novelle researchers
So here’s where it gets interesting. Post-doc Samuel Gessner of SYRTE (at the Observatoire de Paris) is/was due to give a talk in Paris on 18th June 2020:
Between astronomical diagrams and instruments: spatializing numerical data of astronomical tables
Astronomers have connected their computational methods with geometrical representations in various ways. The ways these connections were elaborated on are not universal, but historically contingent of the local astronomical practice. Parchment instruments to graphically determine (approximate) positions of the planets, i.e. the family of planetary “equatoria” instruments, saw renewed developments in the 15th century. We will start with a European case study about a particular type of instrument that emerged in manuscripts from Erfurt and Leipzig termed “Theorice novelle”. In discussing this material the talk proposes to look into possible connections between the representation of computed data in tables and corresponding diagrammatic representations on the “Theorice novelle” and similar instruments. More generally, it raises the question of how the use of tables was preparing the minds for experimenting with new types of instruments and whether this trait can be used to characterise a specific astronomical practice.
In 2019, Gessner described his research focus here:
I focus on the diverse mathematical cultures in medieval and early modern Europe and how they communicate by studying the role of mathematical instruments as conceived by both theoreticians and practitioners. Using artefacts of material culture as primary sources along side with textual documents has become my favourite approach. I currently participate in a research project on Alfonsine astronomy lead by Matthieu Husson, Paris. My longer term goal is to understand the material and mechanical realisations of Ptolemaic theory in models, equatoria and planetary clocks and their role in history of astronomy. I was a co-organiser of the Oberwolfach Workshop “Mathematical Instruments Between Material Artifacts and Ideal Machines”, December 2017.
Unsurprisingly, I’ll be emailing Samuel Gessner shortly, and will let you know what I find out…