A Newly Identified Treatise on the Tables of Marseilles (Twelfth Century) and Its Non-Ptolemaic Planetary Theory

Two Latin manuscripts in Oxford and Florence preserve diverging recensions of a previously unnoticed astronomical treatise beginning Infra signiferi poli regionem (Oxford recension) or Circulorum alius est sub quo (Florence recension). It can be shown that this anonymous text was originally intended to accompany the Tables of Marseilles in Raymond of Marseilles’s twelfth-century Liber cursuum planetarum (ca. 1141). While the core tables for planetary longitudes in this set were founded on Ptolemy’s kinematic models, as known from the Almagest , this new source frequently deviates from the Ptolemaic norm, for instance by explicitly rejecting an epicyclic explanation of planetary stations and retrogradation s. In place of the latter, it argues in favour of a heliodynamic theory inspired by Roman sources such as Pliny, which underwent certain developments in the works of twelfth-century Latin writers such as William of Conche s. Rather than being wholly exceptional, these features are indicative of a degree of disconnect between planetary theory and computational practice in twelfth-century Latin astronomy, which is also detectable in other sources from this period.


Introduction
An important aspect of the transfer of new astronomical knowledge to Latin Europe during the twelfth century was the introduction of computational tables in the Ptolemaic tradition, which had the effect of radically expanding their users' abilities to track celestial motions and configurations as a function of time.1 It may seem perfectly natural to assume that the adoption of Early Science and Medicine 28 (2023) 659-686 such tables went hand in hand with the reception of Ptolemaic planetary theory.After all, the most commonly used tables for planetary equations -a class of tables used to convert mean ecliptic longitudes into true ones -were mathematical embodiments of Ptolemy's kinematic models, which in turn meant that knowledge of these models was required to understand these tables' construction as well as the rules governing their use.2Nevertheless, a closer look at the circulation of the first sets of astronomical tables in Latin Europe invites some doubts as to whether such a level of understanding was truly the norm among their early adopters.While it is true, for instance, that Abraham Ibn Ezra's Tables of Pisa (1143) were from an early stage associated with lengthy Latin treatises explaining some of their theoretical foundations,3 it seems to have been much more common initially to find tables accompanied by mere 'canons,' which provided rules of use without explaining the underlying models.4 Nothaft Early Science and Medicine 28 ( 2023) 659-686 The potential for an outright disconnect between computational practice and planetary theory becomes readily apparent from a look at the Liber cursuum planetarum (ca.1141), one of three extant works from the pen of Raymond of Marseilles.5 His astronomical tables for Marseilles, which formed a core part of the Liber, had been adapted from the Toledan Tables, a set from eleventh-century al-Andalus commonly ascribed to Ibn al-Zarqālluh (d. 1100).The textual portion is divided into two books, of which the second contains instructions for the use of the subjoined tables.A long metrical preamble opens up the first book, whose varied components include, among other things, a spirited defence of astrology.6What is missing from this work is any clear indication that Raymond was familiar with the kinematic models on which his own tables were founded.That he knew rather little about the theoretical assumptions underlying the original Toledan Tables is suggested, for instance, by his failure to acknowledge that the mean ecliptic longitudes displayed in them were sidereal and that adjusting them to a tropical coordinate system required a taking into consideration of the so-called 'access and recess' of the eighth sphere.Raymond knew of the 'access and recess' but appears to have understood it as a purely stellar phenomenon that left planetary longitudes unaffected.7 The fact that the equation tables in his Liber cursuum planetarum were based on epicyclic models for the Moon and the five planets was obvious Early Science and Medicine 28 (2023) 659-686 enough from their inclusion of columns for the epicyclic diameter-increment (diversitas diametri epicicli or diversitas diametri circuli brevis);8 yet there is little, if anything, in Raymond's discussion of these tables that would indicate that he looked at them through a Ptolemaic lens.9Outside of the computational rules for the equation tables, the epicycle makes only a single appearance, in a rather puzzling remark suggesting that the latitude of a superior planet was somehow tantamount to the latitude of its epicycle (circulus brevis).10

A Second Treatise on the Tables of Marseilles
Where Raymond of Marseilles's remarks on planetary motions merely look vague or ambiguous, another source dedicated to his Tables of Marseilles reveals a genuine effort to interpret the material at hand in a non-Ptolemaic manner.The work in question, which has come down to us in two significantly different versions, has never been discussed before in the literature.In contrast to Raymond's Liber cursuum planetarum, this anonymous supplement to a set of astronomical tables gives an account of the kinematic models that supposedly underlie the equation tables for the Sun, Moon, and five planets.Yet, the details of this account are repeatedly inconsistent with, or are in opposition to, the Ptolemaic models known from the Almagest and numerous later works such as al-Farghānī's ninth-century Compendium of Astronomy.11The textual evidence to be considered in the following pages comes from two manuscripts: F Florence, Biblioteca Nazionale Centrale, Conv.soppr.J.II.10 (San Marco 200), fols.227ra-231va (old numbering: 235ra-239va) (s.XIIIex-XIVin)12 O Oxford, Bodleian Library, Ashmole 361, fols.28va-34va (s.XIV1 / 4 -med).138Raymond of Marseilles, Liber cursuum planetarum Tab.[7][8][9][10][11][12]ed. d' Alverny,Burnett and Poulle, Idem, Liber cursuum planetarum 2. 6-10, ed. and  The Oxford manuscript (O) confronts us with a badly corrupted copy of an anonymous treatise comprising approximately 4500 words, the first four of which are Infra signiferi poli regionem.Its opening remarks, which address the distances between the planetary spheres, are closely dependent on a passage in Pliny's Natural History (2.83-84).From there, the author proceeds to describe the variations in apparent velocity caused by the eccentricity of the planetary deferents.This in turn sets up a series of instructions on how to construct tables of planetary mean motion (for minutes, hours, days, months, expanded years, and collected years), by starting with the mean-motion value for two minutes of the hour and multiplying it by the required factors.The author of these rules had a specific set of tables in mind, which, to judge by one side-remark, must have been included in the treatise in its original form.14From a comparison between the specific details mentioned in our text and the known astronomical tables of twelfth-and thirteenth-century Latin Europe, it seems practically certain that Infra signiferi poli regionem was written either for the exact same set as that contained in Raymond of Marseilles's Liber cursuum planetarum or for a closely related one that is now lost (perhaps an adaptation for a different meridian).The points of convergence that support this conclusion are as follows:15 -The tables for the mean motion per month are based on the Julian calendar, with the year starting in January (O, fol.28vb) -The 'expanded years' in the tables for mean motion are referred to as anni superstites.The third expanded year is always reckoned as bissextile (fol.29ra).-The mean-motion tables for each planet include a table for minutes ( fractiones) of the hour, whose entries progress by steps of 2 minutes.The initial entry (for 0;2h) is 0;0,4,56° for the Sun (fol.28vb); 0;0,0,10° for Saturn; 0;0,0,[24]° for Jupiter;16 0;0,2,37° for Mars; 0;0,3,5° for Venus; 0;0,15,3 [2]° for Early Science and Medicine 28 (2023) 659-686 Mercury;17 0;1,5,52° for the Moon; 0;1,5,20° for the lunar motion in anomaly; 0;0,16° for the motion of the lunar nodes (fol.29ra [main text] and fol.29rb [gloss in bottom margin]).-The anomaly of a planet is referred to as the planet's residuum (fol. 29rb, l. 3 and passim).-The columns that are used to enter the planetary equation tables carry the label tabula/tabule numeri (fol.29rb).18-The equation table for the Sun is entered via a column labelled linea numeri and the result is called the certificatio (fol.29rb).-Where interpolation is used to find the equation for a value of the anomaly that lies between whole degrees (i.e., involves minutes of arc), the result is called certificatio certificata (fol.29va).19In addition, it seems worth noting that the scribe in O occasionally uses xxo to write the number 28 (e.g., on fols.21va, 26va, 28vb, 32vb, with the last two instances belonging to our text).This usage reflects a twelfth-century Iberian practice of abbreviating the system of Roman numerals with the help of alphabetic letters,20 which is also attested, more fully, in all three of the known twelfth-century copies of the Tables of Marseilles.21 Having set down the rules for constructing mean-motion tables, the next three sections in O deal with the equation tables for the Sun (fol.29rb-vb), Moon (fols.29vb-31ra), and five planets (fols.31ra-32ra).Each of these gives Nothaft Early Science and Medicine 28 (2023) 659-686 a brief explanation of the underlying model before setting out the pertinent computational rules, which are often verbalized in a way reminiscent of the corresponding passages in Raymond of Marseilles's Liber cursuum planetarum.The following comparison of the passages dealing with the calculation of the lunar equation is meant to convey the overall degree of similarity: Appended to O's treatment of planetary equations is an intriguing discussion of the physical causes behind the planets' stations and retrogradations (fols.32ra-33ra), which will be discussed in more detail below.The author then moves on to give a general account of the concept of planetary latitude (fol.33ra-rb), the first half of which is a concealed quote from Pliny's Natural History (2.66-67).Returning to the subject of equation tables, the author next discusses their structure and gives some indications of how their entries were computed (fols.33rb-34ra).This section cites Ibn al-Zarqālluh (Arzachel) on three occasions, though it is unclear from which source the relevant remarks may have been derived.24What follows is a series of loosely connected passages that inter alia address how to enter mean-motion tables for collected and expanded years, and how to check or correct tables (fol.34ra-34va).There remains some doubt as to whether the last-mentioned section is still an integral part of the text that began on fol.28va.Clearly unrelated to the foregoing text is the immediately following set of simple algorithms for finding the sign of a given planet (fols.34va-35ra).It instead stems from a tenth-century astrological text in the Alchandreana corpus, the Proportiones competentes in astrorum industria.25Of the nine thematic sections that are identifiable in O according to Tab. 1, the Florence manuscript (F) only preserves those numbered 5 to 8. It swaps out the preceding four sections for a different, though thematically related text, starting Circulorum alius est sub quo.In lieu of the introduction on planetary distances in O, this text begins by distinguishing the three circles involved in planetary models (firmament, eccentre, and epicycle) and explains the meanings of the terms aux (apogee) and residuum (anomaly).26It follows this up with a hodgepodge of information on calculating equations, which covers much of the same ground as sections 3 and 4 in O, but in a less cohesive and less clearly organized way (F, fols.235ra-237rb).Rather than discussing the Sun, Moon, and planets in succession, the text moves back and forth between them, leading to some degree of repetition.Even though this part already contains some remarks on the models for the five planets, it is followed by the entirety of section 5 as found in O, which only adds to the sense of redundancy.
It seems clear overall that the text in O, though often heavily corrupted, brings us closer to the treatise in its original form.This is supported by the way the introduction, with its tacit reliance on Pliny, coheres with later passages that make use of the same source (sections 6 and 7).At the same time, the different first half in F cannot be considered wholly independent of the original treatise, seeing as it still recognizably deals with the same astronomical tables.It also shares with the text in O some of its unusual doctrinal content, as we shall see presently.

Non-standard Lunar Models in the Twelfth Century
Although section 4 in O at one point cites Ptolemy as an authority for the idea that the apsides of the planets (other than the Moon) are fixed with respect to the firmament,27 there are no further indications that the author was familiar  and Medicine 28 (2023) 659-686 with the Almagest or even just with the specific planetary models associated with Ptolemy's work.On the contrary, a clear sign of his detachment from these models is found in his treatment of the lunar equation in the same section of the text.It assigns three different components of motion to the Moon, stating that it is moved on its eccentric circle now faster, now slower, according to its distance from the apogee, just as was written earlier about the Sun.It also accelerates and is slowed down according to its closeness and distance from the Sun.It also remains for more or less [time] in some part of its circle, owing to the width of the epicycle.It is therefore necessary [to compute] a threefold equation of the Moon, that is to say, according to its own circle and [according to] to its distance from the Sun as well as [according to] the elevation of the epicycle.28 As is evident from this passage, the author considered each of the three components of the Moon's motion to be represented by one of the individual terms displayed in the corresponding equation table.29These terms are: (i) the equation of centre (certificatio centri), which in the pertinent computational rules is treated as a function of double the elongation between Sun and Moon; (ii) the equation of anomaly (certificatio argumenti), which is a function of the true lunar anomaly (i.e., the mean lunar anomaly, as tabulated separately in a mean-motion table + the equation of centre); (iii) the increment of the equation of anomaly implied by the changing distance between the epicycle and the observer (diversitas diametri epicycli).The value of the latter is modified via a coefficient known as 'minutes of proportion,' which is another function of the aforementioned double elongation.30The correct interpretation of all three terms is far from self-evident, meaning that someone lacking prior knowledge of Ptolemy's final lunar model was unlikely to arrive at it just from studying the matching equation table.An attempt in this direction could start with the fact that one of the columns was headed diversitas diametri epicycli, which invited the conclusion that it had something to do with the apparent diameter of the epicycle.The author recognized this to some extent, although his remarks about the epicycle's northern or southern "latitude" (latitudo) indicate that he struggled with the precise significance of this column.31Thanks to the involvement of the double elongation in computing the equation of centre, he could also tell that this particular term depended on the "closeness and distance" (vicinitas et elongatio) of the Moon from the Sun, as mentioned in the passage cited above.Yet this still left unexplained the equation of anomaly, whose actual purpose was to measure the contribution that the changing position of the Moon on its epicycle makes to its true longitude.Unaware of this aspect of Ptolemy's model, the author of our text instead assumed that the anomaly (argumentum) in the table for the lunar equation played a role analogous to the only anomaly implicit in the solar equation, such that it referred to an angular distance from the apogee on the deferent.32 As a consequence of this misinterpretation, the account of the lunar equation in Infra signiferi poli regionem distinguishes the variation in the Moon's motion that is due to the eccentricity of its deferent from another variation caused by its changing elongation from the Sun.33In Ptolemy's final model, these two factors reduce to one and the same factor, since the equation of centre is there to quantify the effect of an assumed rotation of the Moon's line of apsides on the value of the true anomaly, which is here understood as the angular distance of the Moon from the apogee of its epicycle.According to Ptolemy, the rate of this rotation is none other than the double elongation.Our author instead believed that the rotation in question was included in the Moon's tabulated mean motion in anomaly, which in his interpretation measured an increase in angular separation on the deferent between the centre of the lunar epicycle and its apogee.This forced him to find a different explanation for why the rate of elongation from the Sun had to be doubled in order to arrive at the equation of centre as well as the minutes of proportion.34According to the text in O, doubling the elongation is a merely practical ploy that made it possible to abbreviate the equation table, in which the entries for the double elongation 0°-180°, when the equation is additive, are the same as those for 180°-360° in reverse, when the equation is subtractive.By contrast, operating with the single value of the elongation would have required distinguishing between additive equations at 0°-90° and 180°-270° and subtractive equations at 90°-180° and 270°-360°.35an explanation is some confusion between the act of adding a constant of 180° and that of doubling the actual value of the elongation.
The section on the Moon in Infra signiferi poli regionem thus confronts us with the results of a bold effort to infer some kind of lunar theory from an equation table in the Ptolemaic tradition, in a situation where this table was the only source available on the specifics of lunar motion.It goes without saying that this attempt was seriously flawed in some respects, especially in that it failed to reserve a clearly defined role for the Moon's epicycle and the motion performed on it.Nevertheless, our author's non-Ptolemaic exegesis of the lunar equation table does not stand entirely isolated in a twelfth-century Latin context.We find traces of a similar interpretation in two texts by Abraham Ibn Ezra dealing with his Tables of Pisa, which respectively date from ca. 1145 and 1154.In both of these treatises, the exposition of the lunar equation of anomaly is influenced by the Indian model implicit in the ninth-century zīj of al-Khwārizmī, which is epicycle-less and relies instead on an eccentric deferent with rotating line of apsides.36Ibn Ezra's Tables of Pisa were used mid-century to create the Tables of London, which are the implicit subject of two anonymous treatises starting Investigantibus astronomiam primo sciendum (s.XII4 / 4) and Motuum Solis alius est medius (1181).37Both contain descriptions of largely identical lunar models, in which the motions assigned to the two main components of Ptolemy's model -deferent and epicycle -appear interchanged.They accordingly treat the Moon's motion in anomaly as the difference between its mean motion and the motion of the apogee of its deferent, and the double elongation as the parameter that governs its motion on the epicycle.In both cases, this 'inverted' model is presented as an alternative to the conventional model known from Ptolemy and al-Farghānī, the latter of whom is subjected to a detailed critique by the author of Investigantibus astronomiam primo sciendum.38The author of Infra signiferi poli regionem seems to have been completely oblivious to the existence of such alternatives, while his own presentation of a kinematic model for the Moon remains comparatively vague and underdeveloped.There is nevertheless a conceptual thread that connects his little work on the Tables of Marseilles with the texts on the Tables of Pisa and London just mentioned: the mistaken idea that the argumentum or anomaly involved in the lunar mean motions and equations must refer to a motion the Moon performs on its eccentric deferent rather than its epicycle.

Planetary Stations and Retrogradations
In the Tables of Marseilles and the associated Liber cursuum planetarum by Raymond of Marseilles, the term argumentum is used only in connection with the Moon, whereas the equivalent term for the Sun and the five planets is residuum.The same is true of the texts in O and F. In their shared account of the planetary equations (section 5 in Tab.1), a planet's residuum is defined as its elongation from the Sun, which glosses over the fact that the elongations of Mercury and Venus are bounded and can never exceed one or two signs, respectively.No effort is made to relate the planet's elongation from the Sun to its position on the epicycle, as would be demanded by the Ptolemaic models.39Instead, the epicycle is mentioned only in the context of explaining the diversitas diametri circuli brevis, that is, the term that accounts for the changing distance of the epicycle from the observer.Equation tables such as those in the Tables of Marseilles dedicated two columns to this term, depending on whether the epicycle was at its nearer or farther distance (longitudo longior or longitudo prior).40Our text conflates these two distances with the concepts of northern and southern latitude (latitudo), claiming that the epicycle being at farther distance means that its latitude is "southern" (meridionalis), in which case "it recedes from us and moves more slowly."41It is unclear from these statements whether the slower (or faster) motion in question is performed by the epicycle or, rather, by the planet itself.In any case, it seems likely that some of the confusion in this account of the epicyclic increment was caused by the Liber cursuum planetarum, where the only remark Raymond of Marseilles makes about planetary epicycles is that they are involved in the computation of latitude.42 This greatly diminished role of the epicycle in explaining planetary kinematics is also reflected in the ensuing discussion of planetary stations and retrogradations (section 6 in Tab.1), which, rather than appealing to the concept of epicyclic motion, affirms that these phenomena are a consequence of physical effects exerted by the Sun.Although introduced as an excursus presenting different opinions on the same topic (De planetarum retrogradatione diversorum varias sententias enarrabimus), this section also functions as a continuation of the author's commentary on the planetary equation tables in the Tables of Marseilles, all of which contained a column that showed, as a function of the true centre (centrum verificatum), the arc of true anomaly (residuum verificatum) at which the planet will be stationary prior to retrogradation.43As already mentioned, our author interpreted this arc simply as a measure of the planet's elongation from the Sun without overtly tying this elongation to the planet's position on the epicycle.In his effort to address the existence of a correlation between the relative position of the Sun and a planet's stationary or retrograde behaviour, he begins by outlining a physical theory in which the decisive factor is a planet's ability to endure the heat of the Sun: Some say that the Sun, inasmuch as it is hotter than the remaining [planets], drags them along with itself through its dryness.As a consequence, they are necessarily made to stand or go back or move forward according to the distance that is between them and the Sun.And so, since Saturn is the [sydus] that is at the greatest distance from the Sun according to the order of the [planetary] circles and also differs from its properties on account of the rigidity of its coldness [horrore frigoris], it puts up with [sustinet] the Sun's heat for longer [than the others].After it [comes] Jupiter, after it Mercury, then Mars, then Venus.If Saturn is at 112 degrees from the Sun, it accordingly comes to a first standstill after having felt the heat for a while, just as someone who sees in the distance an enemy stronger than him remains immobile, being completely shaken with fear and wondering where to turn.Afterwards, as he sees the enemy approach, he flees from him.In such manner, they say, the planets, as the Sun gazes upon them more and more from an angle with a terrible light, try as they can to gain distance from it by moving backwards.After a while, having moved away from it, but not yet safe, they stand still until their fortified courage allows them to move [onward again].44 According to the theory that is outlined here in rather picturesque terms, the heat and dryness (siccitas) of the Sun is the physical quality that enables it to attract other planets and make them move in the same direction.It is further suggested that the extent of this effect depends on both the physical distance of a planet from the Sun and on its own physical nature.In the specific example given, Saturn is a cold planet as well as the planet most distant from the Sun, which means that it is able to resist the heat of the Sun for the longest.This endurance on the part of Saturn is manifested by its relatively long retrograde arc, which already begins at a true anomaly of 112°.In the order of sensitivity given in the text, Saturn is followed by Jupiter, Mercury, Mars, and Venus, which is identical with the ascending order of the minimum anomaly at first station according to the Tables of Marseilles.The value of the minimum anomaly for Saturn is here 112;44°, which is broadly in harmony with the 112° cited in the text.45 Implicit in the claim about the Sun's attractive force seems to be idea that the natural direction of motion for each of the planets is from east to west, although they can realize this tendency only when at a sufficient remove from the Sun.The picture painted in the above passage seems contradictory, however, inasmuch as retrogradation is also described as a kind of flight from the "terrible light" of the Sun, whose effect on the planet becomes stronger as their angle of separation increases (cum Sol eos magis ac magis ex obliquo lumine terribili intuitur … ab ipso elongari contendunt).All of this seems to suggest a repellent rather than an attractive effect of the Sun's heat.The author was no doubt aware of this tension, as he relies on it to formulate his objection against the theory in question: If the Sun's attractive nature is the reason that the planets are made stationary for the first time [and] then retrograde, it seems that [the Sun] would have to drag [a planet] more strongly towards it the closer it is to it.Consequently, when they exist together within the same sign or even degree, let alone in the same minute or second, the [planets] would in this state of bonding have to feel the attractive properties of the Sun much more than when they are separated from the Sun by a third or fourth or fifth of the firmament.Yet what we see happening is the opposite.Hence, since they do not approach the Sun at all when they are retrograde, but much rather move away from it, the cause of this would seem to be not an attractive, but rather a repellent nature.46 Early Science and Medicine 28 (2023) 659-686 Before setting out his own view on the Sun's role in causing stations and retrogradations, the author briefly notes that some seek to explain these phenomena as a consequence of the "width of the epicycle" (propter epicicli latitudinem).He signals his awareness that adherents to this view imagine the planet as being fixed to the surface of a small circle, but rejects this idea as being incapable of explaining why the stations and retrogradations only occur at certain points in a planet's synodic period.According to him, the epicycle should enable the planet to undergo these changes in motion at any distance from the Sun (in qualibet planete a Sole distantia).47This comment is further confirmation that the author was oblivious even to basic details of Ptolemy's planetary models, where each superior planet's period of motion on the epicycle is synchronized with its synodic period.
Returning to the causative role of the Sun, which is taken for granted, the author argues that it must possess more than one type of force or property to be able to produce the observable pattern in the behaviour of the planets.He accepts that the Sun does indeed have an attractive property, which he describes as the result of its hot and dry qualities and, hence, as "choleric" (colera nuncupari potest).However, rather than dragging the planets along on its course, which is how the attractive force was characterized by holders of the first opinion, its actual effect is to accelerate the planets much in the same way as heavy wind can speed up the flow of water in a river.He further notes that this force has a much stronger effect on celestial bodies close to the Sun than those more remote (potius exercet in sibi vicinis sideribus quam in remotis), which could be an allusion to the fact that Mars and the inferior planets have a much swifter rate of motion than Jupiter and Saturn.48In addition to the Sun's attractive force, the author mentions three other forces or properties, which he characterizes as "retentive" (retentiva), "expulsive" (expulsiva, also separativa), and "perceptible" (perceptibilis).49It seems plausible that some of these adjectives, in particular the use of retentivus and expulsivus, reflect the influence of the Isagoge Iohanitii and the twelfthcentury commentary tradition founded upon this text, which was a partial eleventh-century translation of Ḥunayn ibn Isḥāq's Questions Concerning Medicine.50 As one would expect, given the author's criticism of the first theory, the Sun's "expulsive" property is the one that is supposed to account for the retrograde motion of the planets, while the "retentive" one is the cause of them becoming stationary.He does not explain why these two effects only manifest themselves at particular angles of separation between the Sun and the planet in question.What he does point out, however, is that the planetary stations do not represent complete standstills, but merely apparent ones (non quod planete aliquando immobiles persistant, sed quia stare videntur).
The most surprising of the four properties mentioned in this passage is certainly the "perceptible" one, which is not directly related to planetary motion.Rather, the author makes it responsible for certain seemingly 'causeless' effects that are perceptible in the sublunary realm and belong to the remit of "occult physics" (ut sunt illa que de occulta phisica procedunt).While much of the background to these remarks seems elusive, it is possible that it was influenced by the aforementioned commentary tradition on the Isagoge Iohanitii.In one of the more prominent twelfth-century commentaries, by Bartholomew of Salerno (fl. ca. 1150), the direction of investigation in physica is characterized as proceeding from the perceptible and manifest forms of things towards their imperceptible and occult forms.51 The study of the latter might hence be described as occulta physica.
Early Science and Medicine 28 (2023) 659-686 According to what the author himself tells us, the written authorities that underpinned his explication of the Sun's active properties were three: "Iulius Firmicus, Albumasar, and Adile."52The precise identification of these sources poses something of a problem.Indeed, Adile is not a known author and may be the result of some textual corruption.Since Iulius Firmicus is mentioned again a few lines later as the originator of words that are actually lifted from Pliny's Natural History,53 it seems likely that the author simply confused the two Roman writers and that "Iulius Firmicus" refers to Pliny even in the first instance.At the same time, it seems worth noting that the Mathesis, Iulius Firmicus Maternus's fourth-century treatise on astrology, alludes to the Sun's role in bringing about stations and retrogradations, if only briefly.54Such 'heliodynamic' alternatives to an epicyclic explanation of retrograde motion are also encountered in several other classical sources accessible to medieval readers.Besides Firmicus and Pliny, these include Vitruvius' On Architecture, Lucanus' Civil War, and the popular works by Martianus Capella and Macrobius.55Albumasar (Abū Maʿšar), the ninth-century Persian astrologer, is not known to have been a proponent of this view.The appeal to his name in the passage under discussion could nevertheless have been motivated by the chapters on the origins of the planetary houses and exaltations in Part V of his Great Introduction to Astrology.There Albumasar rejects an ancient tradition that sought to explain stations and retrogradations as the consequence of physical Early Science and Medicine 28 (2023) 659-686 first station according to the Tables of Marseilles.60 Also part of this passage is Pliny's theory according to which the perceived standstill of a planet at first station is merely an illusion, as the planet is actually elevated to a greater distance from the observer.This appears to be the idea behind the author's statement earlier in the text that the planetary stations do not involve a literal stop.That said, his decision to label the relevant solar property "retentive" does not fit particularly well with the idea that the Sun physically elevates a planet.
Aside from the concrete background provided by Pliny's demonstrable influence, it is possible to compare the statements made in our text with other heliodynamic explanations offered in Latin sources of the twelfth century.A prominent writer in this regard is William of Conches, who discusses planetary motions in several of his works, including the Philosophia mundi (ca.1125) and Dragmaticon (ca.1144/49).61They reflect his familiarity with at least two different variants of the heliodynamic theory, both of which have approximate counterparts in our text.One relies on the idea of an attractive force exerted by the Sun, which William in the Dragmaticon likens to the effect of a magnet on iron.While this quasi-magnetic force causes literal stations, an opposing view insists that the planets' fiery nature would prevent them from ever standing perfectly still.The stations and retrogradation are, hence, merely apparent, being the result of a change of distance from the observer.William explains this effect with the heat of the Sun, which desiccates the celestial bodies and makes them lighter, allowing them to ascend.They will descend again once they have re-accumulated enough humidity to become heavy.62 Another twelfth-century text that considers in some detail the physical effects of the Sun's heat on planetary motion, using the specific example of Mercury, is the Cambridge commentary on Martianus Capella's De nuptiis Philologiae et Mercurii, possibly a work by Bernardus Silvestris.The commentator argues that the Sun desiccates and rarefies the planet whenever it is nearby, such that Mercury's altered gravity will cause it to go ahead or lag behind Sun, or to rise 'up' in a straight line.Once it has reached a certain distance from the Sun, it will return to its natural coolness and stop moving, that is, become stationary.It will eventually regain its former humidity, which helps explain why the planet always resumes its direct motion after becoming retrograde: the heat of the Sun attracts humidity and hence draws the planet back towards its own direction.63This line of reasoning, according to which the Sun manages to attract planets via the effect of heat on humidity, is developed somewhat differently in an anonymous twelfth-century commentary on Martianus Capella preserved in a Berlin manuscript.According to this commentator, the way in which the Early Science and Medicine 28 (2023) 659-686 Sun affects a planet such as Mercury depends crucially on where the planet is located in the zodiac.If Mercury is found in the domicile of a humid planet such as Venus, its humidity is fortified, allowing it to prevail and continue on its direct course away from the Sun.By contrast, if Mercury is found in the domicile of a dry planet such as Mars, it will be easier for the Sun to slow it down and draw it in the opposite direction.In the latter event, the observable consequence is a station followed by a period of retrograde motion.The commentator approves of this explanation, which he considers superior to the hypothesis according to which Mercury moves on an epicycle.In his opinion, the doctrine that Mercury is directed by the heat of the Sun, but in ways that are modified by its position in the zodiac, has the advantage of making intelligible why there are variations in the length of Mercury's period of revolution.64

Conclusion
When Stephen of Pisa, a translator based in the Crusader state of Antioch during the late 1120s, wrote the preface to the fourth book of his Liber Mamonis, he treated the Ptolemaic planetary models described in this book as the desperately needed answer to a problem that previous Latin writers had failed to solve, namely how the bodies of the five planets, whose course as ordered by nature is eastwards, can become retrograde and fall back from east to west.To admit the truth, this is a worthy problem to tackle and solve, but it has not been solved by any of them.This should not surprise us, since it is an abstract matter that is to be investigated and confirmed by geometrical proofs, which the Latin world has no knowledge of and therefore has long been enshrouded by many popular misapprehensions.Thus, as even the most intelligent among them could in no way find the true reason of the proposed matter, they allowed the sun's rays to have something imaginary and forceful, saying that the planets became retrograde by those rays' stronger impact, as if the sun's rays could be more powerful than the eternal courses of the spheres in which the planets move.65

Nothaft
Early Science and Medicine 28 (2023) 659-686 Stephen's incisive criticism of the heliodynamic theory focused on its failure to reduce the retrograde behaviours of the five planets to a single cause.Attributing retrogradation to the power of the Sun neither accounted for the observable differences between the superior and inferior planets nor could it explain why Saturn, despite being the planet farthest away from the Sun, had the largest retrograde loop: Furthermore, if the power of the sun's rays made the planets retrograde by repelling them from the position opposite the sun, Venus and Mercury would not have retrogradation.For they can never reach until opposition.
And if one said that they were dragged back also from conjunction, by the same reasoning also the other planets would become retrograde a second time; and, these two could never precede the sun, for as soon as they caught up with the sun by their faster motion, they would be thrown back by the force of the rays and follow behind.Thus, being thrown back over and over again, they could never be in conjunction with the sun.This long lasting doctrine shall therefore fall together with the error that taught it, and in our little treatise we shall find how these phenomena are to be assessed in the most certain way.66Despite Stephen's clearly articulated hope, the twelfth century did not witness the complete collapse of heliodynamism.While it is broadly true that Arabic-to-Latin translations paved the way for the epicyclic models of Ptolemy's Almagest to attain quasi-orthodox status in Latin schools by 1200, non-Ptolemaic ideas of the Sun as the physical cause of planetary anomalies continued to receive prominent exposure in a significant number of texts, amongst which were the aforementioned commentaries on Martianus Capella.67 Writing his encyclopaedic work De proprietatibus rerum in the Early Science and Medicine 28 (2023) 659-686 second quarter of the thirteenth century, Bartholomew the Englishman still considered it appropriate to present, without criticism, the view according to which "the force of the solar rays sometimes pushes back [the planets] and makes them retrograde, at other times attracts them and thus forces them to stand still."Curiously, Bartholomew attributed this position to al-Farghānī, while briefly acknowledging that Ptolemy gave a different explanation of stations and retrogradations.68 The previously unstudied treatise discussed in this article helps us expand this overall picture, inasmuch as it offers the first documented case of heliodynamism having found explicit endorsement in a specialized work of mathematical astronomy, written to explain the use of astronomical tables.The tables in question, which are those of Raymond of Marseilles's Liber cursuum planetarum, were originally compiled in or shortly before 1141, at a relatively early stage in the twelfth-century Latin assimilation of Graeco-Arabic astronomy.Our text's striking combination of computational rules rooted in Ptolemaic astronomy, on the one hand, and pre-Ptolemaic ideas about the causes of planetary anomalies, on the other, appears to reflect a historical situation in which this assimilation had not yet been completed.The same can be said about this text's non-standard description of the three motions of the Moon, which arose in part because computational tables in the Ptolemaic tradition had begun to spread well ahead of written accounts of the underlying theories.Even though the text is only poorly transmitted in two relatively late manuscripts (s.XIII/XIV and s.XIVmed), its content thus gives us reason to consider a date of composition closer to Raymond of Marseilles, perhaps as early as the middle decades of the twelfth century.Whatever the precise truth about its origins, this anonymous source deserves attention for the way it exemplifies the sometimes tortuous path by which Ptolemaic astronomy arrived in Latin Europe.