Bi-Daily Venus in the Medieval Thought of William of Conches: Explaining an Uncommon Celestial Event by Circumsolarity

Introduction

Bi-Daily Venus (BDV) is a celestial phenomenon that appears when Venus can be observed twice during the same day (before sunrise, then after sunset) or twice in the same night (after sunset, then before sunrise). While not rare, it occurs only four times during an 8-year cycle (twice each in the northern and southern hemispheres). And for each of those two times per hemisphere, only one will offer optimum viewing. The second instance will be lower on the horizon and hence more subject to atmospheric effects and solar glare.

Modern astronomy explains BDV by two factors. The first is that Venus’s orbit tilts from the ecliptic plane (<4 deg). Second, the occurrence of BDV requires Venus to be near inferior conjunction with the sun. So if inferior conjunction happens to be near the point in Venus’s orbit of maximum deviation from the ecliptic plane, then it is possible to view BDV. There, the angle of Venus above the viewers horizon can be as much as 10 degrees. ¹ The farther north or south one is (for the northern or southern hemisphere), the easier it is to view BDV since the planet’s distance above the horizon increases.

Surprisingly, very little has been published in the modern literature about BDV, and among historians, the general educated populace, and even astronomers, few seem to know that BDV occurs. I do not know of any printed article or book that discusses BDV, and there exists only one web site that offers a discussion of BDV. ² This web site goes under the appellation “Naked Eye Planets,” and is the best available source for detailed information regarding BDV. ³

Given this dearth of modern knowledge regarding BDV, it is surprising to this author that William of Conches knew of the phenomenon in the twelfth century. Similar to the lack of modern documentation, extant medieval and ancient descriptions are almost non-existent. ⁴ Although William may have witnessed BDV, no records of his observations exist in any of his writings or that of others. ⁵ More likely, he copied information he read from unnamed sources he alludes to within his works.

But with regard to such a source, we have little information. Neugebauer discusses nothing regarding the subject, save for times of Venus’s invisibility during inferior conjunction. ⁶ Similarly, the early Babylonian astronomical compendium known as MUL.APIN registers Venus’s changing times of disappearance during inferior conjunction, but nothing about BDV. ⁷ Pliny stated that “Stars are also seen throughout the daytime in company with the sun, usually actually surrounding the sun’s orb like wreaths made of ears of corn and rings of changing colour.” But to assume this referred to BDV would be problematic. ⁸ Hyginus, in his De Astronomia, asserted “he [Venus] appears both at sunrise and sunset, as we have mentioned, and for that reason he is rightly given both his names, Lucifer and Hesperus.” ⁹ This passage is relevant since William of Conches mentioned Hyginus as an ancient writer of celestial fabula (myth) in at least three of his works, but did not say with which work of Hyginus he was familiar. ¹⁰ Yet since Hyginus did not clearly state that one could view Venus at sunrise and sunset on the same day, it is unclear whether he was referring to BDV. Interestingly, Evans discusses an ancient stellar analog of BDV called “doubly visible” stars, in which an observer can view certain stars before sunrise and after sunset on the same day. This knowledge came down to us from Autocylus of Pitane’s On Risings and Settings and Ptolemy’s work Phaseis. ¹¹ Yet I have not discovered any source that relates “doubly visible” stars to BDV. William himself provided a tantalizing hint of Boethius as a source in his discussion of BDV in Glosae super Boetium (see the later section), but unfortunately it remains only a hint as William left us little on which to follow through. Finally, an examination of the other major ancient works that William would have been familiar with – Plato, Pliny, Seneca, Calcidius, Capella, Macrobius, Bede, Isidore, possibly Ptolemy (Tetrabiblos), and Arabic sources such as Abu Ma’shar (Great Introduction to Astrology) and Masha’allah (Book of the Orb) – reveals no discussions or knowledge of BDV. ¹² We simply do not know William’s source(s) for BDV.

While offering to modern readers the first historical account of BDV, this paper also investigates how William of Conches’s thinking on BDV evolved over some 30 years as written in three of his works. What William meant by Latin words such as superior, supra, altior, and altitudo, is considered, since they constitute William’s idea of “higher” and “above” in a planetary sense, and are key to his BDV thinking. Consequently, prior to taking up William’s statements regarding BDV, his ideas on planetary order are first addressed as they help clarify his concepts of “height” and “above” that he employed for BDV. This paper then examines William’s writings on BDV, which demonstrate how his views evolved over his career. In the mature thought of his Dragmaticon, William clearly supported an explanation for BDV – Venus’s occasional circumsolar “height” above the sun – about which he held mild scepticism during his younger writing of Philosophia. This paper argues that little evidence exists that William’s idea of Venus’s “height” meant that planet to be out of the ecliptic plane during BDV. The paper concludes by offering a diagram that explains William’s mature idea on BDV.

William of Conches and planetary order

Born in Normandy during the late eleventh century, William matured as a scholar and recognized intellectual at the Ecole de Chartres. ¹³ His youthful work Philosophia (ca. 1125) served as a basis for his mature Dragmaticon (ca. 1145). ¹⁴ Both of these works became among the best known and far-reaching accounts of natural philosophy to emerge from the twelfth century. Inheriting a Carolingian-inspired classical revivalism that emphasized Platonic interpretations of Christian thought, William sought to portray the importance of pagan ideas in a physical cosmos governed by an omniscient and benevolent creator. He also wrote commentaries (Glosae) that bear on his thinking of BDV, as they discuss astronomy, the structure of the cosmos, and planetary order. These include the Glosae super Boetium, Glosae super Macrobium, and Glosae super Platonem. William penned the works on Boethius and Macrobius at a time closer to his early-career Philosophia than the later Dragmaticon and Glosae super Platonem. ¹⁵ However, neither this latter work on Plato nor his work on Macrobius discusses BDV.

In evaluating William’s BDV discussions, it is helpful to consider his ideas on planetary order, since in those discussions William dealt with the concepts of “higher” and “above” with Latin words such as super, altior, and altitudo. The idea of height is crucial since it is important to ascertain whether William’s BDV ideas referred to height above the earth (distance from earth), or height of a planet above the horizon, the ecliptic plane, or in latitude.

William accepted the ancient Egyptian/Platonic geocentric order of earth-moon-sun-Mercury-Venus-Mars-Jupiter-Saturn, followed by the fixed stars. ¹⁶ This arrangement had some basis in the ancient distance-period relationship, whereby the longer a planet took in its period of revolution, the farther from earth it must be. ¹⁷ This concept worked well for the outer planets Saturn, Jupiter, Mars, and the moon, but failed for the sun, Mercury, and Venus as those three possessed approximately the same period of a year. William dealt with this troublesome tri-planet problem in two ways, both of which involved intersecting planetary circles, as his thinking on planetary arrangement evolved over the years: geocentric circles, and circumsolar circles.

In his earlier works, Philosophia, and Glosae super Macrobium, William stated that the three circles of sun, Mercury, and Venus were of about the same diameter, and concluded they must intersect since they cannot overlap. ¹⁸ Figure 1 depicts one such eccentric and intersecting planetary arrangement obtained from a twelfth-century copy of William’s Philosophia. Eastwood has argued that William drew upon the writings of Macrobius in formulating his ideas constituted by Figure 1. ¹⁹ In order for William to make sense of Macrobius’s concepts of “higher” and “lower” parts of the circles of Mercury and Venus, William employed an intersecting scheme for the planets’ circles. ²⁰ William’s words in his Philosophia make ample use of the Latin roots superior and inferior regarding what is high and low in this figure: ²¹

Hence they intersect in the point where the circle of Venus, in its lower (inferiori) part, intersects the higher (superiores) parts of the circle of Mercury and of the sun, encompassing more the one of Mercury than the one of the sun. The circle of Mercury, in its higher (superiori) part, intersects Venus’s one, but in the lower (inferiori) part the one of the sun. The circle of the sun, in its higher (superiori) part, intersects the inferior (inferiores) parts of Mercury and Venus’s circles: more the one of Mercury than the one of Venus. But because a description is more clearly presented to the mind through the eyes, we display that intersection for the eyes. Where the circle of the sun is touched by the lower (inferioribus) parts of the others, it is rightly defined as inferior (inferior). But, because sometimes it happens that the sun moves through the higher (superiorem) part of its circle, the other planets move through the lower (inferiores) parts of theirs, and then, they appear more liberated to shine brighter.

So what did William mean here by inferior, superior, higher, and lower? The conclusion one can reasonably reach is that he was referring to simple distances from earth, in roughly the same plane, in some places more distant, in other places less so. Higher would mean at a greater distance, lower at a closer distance, to the earth. It would be a difficult stretch of the imagination to accept that William, without substantially more discussion, was referring to some out-of-plane height (or depth) relative to the ecliptic or to the horizon.

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Figure 1.

A celestial sphere diagram from William of Conches’s Philsophia mundi, depicting the intersecting planetary circles of the sun, Mercury, and Venus about the geocentric earth. The diagram displays the following named (in Latin) planetary order: geocentric earth, then the “circles of” moon-Mercury-Venus-Mars-Jupiter-Saturn. This arrangement permitted Venus to be “above” Mercury, Mercury “above” the sun, in a “fixed” planetary order. Yet, as the diagram shows, at times, Mercury and/or Venus could be below the sun (that is, closer to earth than the sun is), particularly when Mercury and Venus are on the opposite side from the named regions. (Biblioteca Apostolica Vaticana, Reg. Lat. 72, f. 94r, s. XII, with permission).

While in his later Dragmaticon William still accepted the same fixed planetary order as he did in Philosophia, he no longer argued that the sun, Mercury, and Venus moved upon intersecting circles about the earth. His thinking had evolved to where he considered Mercury and Venus to move in circumsolar circles about the sun. ²² And with these two attendant planets, the sun continued to circle the earth. Yet the circles of Mercury and Venus still intersected in William’s circumsolar arrangement, with much of Mercury’s circle closer to the earth than that of Venus. Figure 2 shows such an arrangement displayed in a fifteenth-century copy of the Dragmaticon. William’s words from the Dragmaticon are as follows: ²³

So, then, the [circles] of Venus and Mercury are epicycles, that is, circles existing above (supra) the earth, enclosing no part of it. The center of their orbits is in the sun, with Mercury’s in the middle of the sun, Venus’s above (supra) the middle. So that you may understand this better, I shall draw a figure, in which I shall delineate the earth, the sun, and the epicycles of Venus and Mercury, each planet in its own epicycle, in two places, namely, in the highest (summo) and the lowest (imo). So when Venus and Mercury are in the highest (superioribus) point of their [circles], they are truly above (supra) the sun, and then Mercury is nearer the sun. But when they are in the lowest (inferioribus) point of their [circles], then the sun is above (supra) them, and Venus is nearer the sun.

In addition to the words superior and inferior that William employed in the Philosophia, he here added supra to the ensemble of words used to represent planetary distance from the earth. And as in the Philosophia, there is nothing in this paragraph suggesting any direction other than away from or towards the earth, in an approximate plane encompassing all the planets. It is fairly obvious that when William referred to Venus and Mercury being in the highest or lowest parts of their circles, he was indicating, per Figure 2, either their farthest or nearest positions from the earth on their circles.

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Figure 2.

The circumsolarity of Mercury and Venus as displayed in the Dragmaticon. Each planet is depicted on its own epicycle, both of which intersect. Earth is displayed at the bottom. The sun’s eccentric circle, and the moon, are not shown. Two sets of extreme positions (not occurring simultaneously) for the planets are displayed: both planets above the sun, and both below. Note that the scribe or artist that drew this figure did not follow the exact words of William’s text. William clearly stated that Mercury’s circle was concentric about the sun, while that of Venus was eccentric. This drawing shows both epicycles to be eccentric. (Stanford Special Collections Library, MS 0412 CB, f. 29v, s. XV^med, with permission).

BDV in Philosophia

In the Philosophia, William began a discussion of BDV:

This same planet is called Lucifer and Hesperus; but Lucifer when it is seen before the sun in the morning, Hesperus when it is seen after the same in the evening. From which the question arises whether it is possible at the same time of year to be Lucifer and Hesperus. ²⁴

By the phrase “at the same time of year” William meant during the same day. William provided a threefold answer to his question, commencing with the first part: ²⁵

Certain people say this is not possible. For assuming it to be of the same speed as the sun, and carrying out nearly the same spatial course, how in the same night, in the evening it follows the sun, and in the morning it precedes it? Therefore, in one time of the year it precedes the sun, and then it is Lucifer, in another, it follows, and then it is Hesperus.

His first answer to the question of the reality of BDV was that “certain people” said it could not happen since Venus would have to move faster than the sun. Yet William remained silent on whether or not he agreed with this claim. He then moved to the second part of his answer: ²⁶

Others say that at one and the same time of year, it appears before the rising of the sun, and after its setting, although it does not precede or follow it. For this is impossible. In fact, they say that planet to be higher (altiorem) than the sun, which is why it is seen longer in the evening, even if not following the sun, and sooner in the morning, even if it does not precede it. Therefore, it is called Lucifer and Hesperus during the same time of year, not because it precedes or follows the sun, but because it appears before sunrise and after sunset due to its altitude (altitudine).

This answer of William’s requires more analysis than his previous one. Note that with the words “For this is impossible” (impossible est), William was again stating, per the “others,” that Venus does not travel faster than the sun. He stated that “others” alleged that BDV could indeed occur, just not by preceding or following the sun. Rather, it occurred because Venus was “higher” (altiorem) than the sun. Regardless of William’s apparent neutrality on the reality of this claim, what did this mechanism of the “others” mean?

The answer relies on understanding William’s two terms altior and altitudo. Here, altior was referring to a distance greater than the sun is from the earth, as I have no knowledge of authors having used that term for height above the horizon or ecliptic. But what about the noun altitudo, a word that William had not yet employed with respect to planetary position? In the last sentence of the above quotation, William was simply restating what he had said in the sentence before the last, but now using altitudine instead of altiorem. Accordingly, there is no reason to suspect that William considered altitudo to mean anything more than height above, or distance from, the earth. Therefore, Venus’s being higher than the sun meant that Venus was at a farther distance from the earth than the sun, and, as the upcoming discussion associated with Figure 4 of this paper will explain, also in a direct line with the earth and sun.

William’s third answer to whether it is possible at the same time of year for Venus to be both Lucifer and Hesperus dealt with a group whose allegation was that the occurrence of BDV was a mistaken belief. William asserted: ²⁷

A third group says that Venus and Mercury are nearly the same color and quantity, and always accompany the sun. Therefore, when they accompany the sun, because one planet precedes it, and the other follows, the preceding one in the evening is not seen due to the brilliance of the sun, but the one following after sunset does appear. However, it is contrary in the morning, the preceding one of course appears, the following one is hidden by the brilliance of the day; but since they are of one color and quantity, they are reckoned to be one and the same planet.

William was arguing that this third group did not believe that BDV could occur, as the alleged similar properties of the two planets fooled people into thinking Mercury and Venus were the same planet. Consequently, some thought they were seeing the same planet in both morning and evening, when in fact they were seeing Mercury at one time, Venus at the other.

From the Philosophia, we learn that William has heard or read about the possibility of BDV, yet expresses a certain scepticism for the three responses about which he knows: (1) BDV cannot occur since Venus and the sun travel at the same speed; (2) it does occur by virtue of the times when Venus is “higher” than the sun; and (3) it does not occur, but people have been fooled into thinking so since Mercury and Venus appear similar. To the first answer William left room for his possible belief in BDV, since he said that “Certain people say this is not possible” (leaving the impression that he may not include himself in that group). Regarding the second response, William merely related what “others” said without taking a position: BDV results from Venus’s occasional height above the sun. William likely did not accept the third response as he knew that the two inner planets are real, separate, and appear differently. So at that stage in his career, William was undecided regarding the realism of BDV. In his Glosae Super Boetium, William again took up the same three responses, but came to support BDV through the mechanism of one of those ideas.

BDV in Glosae Super Boetium

William’s discussion of BDV in this second work commenced, “He discloses another law of the stars, that the planet, which in the beginning of the night follows the sun and is called Hesperus, nevertheless precedes the sun in the morning and is called Lucifer.” ²⁸ This statement was a harbinger of what he was about to discuss in more depth. Presumably, the “He” in the previous sentence refers to Boethius, the focus of William’s work. Furthermore, was William implying here that Boethius was a source for William’s knowledge of BDV? This is a hint that remains unclear. Certainly by using the previous quotation as a lead-in for a discussion of BDV, a reader may surmise Boethius as a source. Yet William tells us no more than this regarding Boethius, and there is little information in The Consolation of Philosophy, or other extant Boethian works, that could lead one to that conclusion. ²⁹

In a manner similar to his Philosophia, William continued by dividing “certain people” into two groups, those who accepted the reality of BDV and those who did not. He starts by saying that “Concerning this issue [BDV], there is disagreement among certain people,” and continues first with the non-believers: ³⁰

In fact, they say this is not possible to occur at the same time of year that this planet precedes the sun in the morning, and follows it in the evening. Venus, which, as the philosophers say, has the same speed as the sun. Therefore, it is not able at the same time to follow the sun in the evening and precede it in the morning. They say that this does occur at different times of the year. ³¹

William’s reply was the same response he gave in Philosophia, where he stated the claim without taking a position. The words “different times of the year” in the last sentence of the quotation meant that Venus could be seen in the morning on certain days that were different from those days when it could be seen in the evening.

William then went on to address the believers in BDV, where he asserted, for the first time, his belief that Venus could be seen on the same day at both sunrise and sunset: ³²

But all authorities and philosophers say this occurs at the same time of year, but they do not say how this happens. ³³ But the reason is as follows. Venus is higher (altior) than the sun, since the sun is in second place [in planetary order] and Venus is in fourth place. Therefore, since it is higher (altior), then when it is near the sun, and together they are approaching sunset – whether it precedes or follows the sun – it is seen longer [and more easily seen]. By the same reasoning it is seen sooner in the morning [and more easily seen]. And so when it first appears in the evening, it is called Hesperus, when it first appears in the morning, it is called Lucifer, since it is producing light.

I have italicized the words “But the reason is as follows” in the above quotation as that was the first time William not only implied his belief in BDV, but committed to a mechanism. And, for this same mechanism that he simply noted in Philosophia, he now finds convincing in Glosae super Boetium. Note that William has equated the adjective altior with Venus’s higher place in the planetary order relative to the sun, and that he no longer employed the noun altitudo as he did in Philosophia when discussing the same issue. This use of altior in Glosae Super Boetium clarifies the meaning of the same word in Philosophia. And since the meanings of altior and altitudo were equated in Philosophia, as I previously argued, then it also clarifies the meaning of altitudo as used in Philosophia (and as used in Dragmaticon, as I will soon argue).

William was not done discussing BDV in Glosae Super Boetium, as he again addressed the issue, as he had in Philosophia, of those who did not understand that Mercury and Venus were separate planets, and were thus fooled into accepting BDV: ³⁴

Venus and Mercury are neighboring planets, and they accompany the sun since their elongation from it is small. In certain parts of the year, the sun is in proximity since one precedes the sun, the other follows it. This is again an explanation because the planets that precede the sun in the evening are not seen, but those which follow are seen. For that reason, that which follows the sun in the evening is seen. And that which follows the sun in the morning is not seen; but those which precede it are seen. Thus, that which precedes is seen. And with one so much seen in the evening, the other in the morning – either they are of the same quantity, or color, or speed, and likewise accompany the sun – or they are reckoned to be the same planet.

William again stated that some thought unless the two planets fortuitously had quite similar properties, then they were not two planets, but one and the same. Observers were thus misled into thinking that BDV was a real phenomenon. Some observers thought Mercury and Venus – one appearing at dawn and the other at sunset, or the other way around – to be the same planet, and hence the idea of BDV mistakenly arose.

Prior to leaving this section, it is interesting to speculate on a BDV-based chronology of the two works, Philosophia and Glosae Super Boetium. While many scholars acknowledge that they are among William of Conches’s earliest works, at least three modern editors have suggested that Glosae Super Boetium was likely written prior to Philosophia. ³⁵ Yet by following the arguments and quotations in this paper regarding the development of William’s thinking on BDV, one might choose to invert the order in the previous sentence – Philosophia may have been written prior to Glosae Super Boetium. In both works, William laid out the same three general responses to the validity of BDV. But in his second response, which dealt with Venus’s height above the sun as an explanation for BDV, William changed his emphasis in going from Philosophia to Glosae Super Boetium. In the former work, William merely suggested as a possibility that a BDV mechanism that relied on Venus being higher than the sun could occur. Yet in Glosae Super Boetium he became convinced that the same mechanism was operable. Since in the later Dragmaticon he developed this particular BDV mechanism even further (see the next section), and dropped the other two possibilities, it stands to reason that the logical temporal “flow” of his works regarding BDV is from Philosophia → Glosae Super Boetium → Dragmaticon. It would be implausible for William to adopt an interpretation as he did in Glosae Super Boetium, only to de-emphasize it without reason in a later Philosophia.

BDV in Dragmaticon

In his later work, William came down strongly in favour of Venus’s occasional “height” above the sun as the explanatory factor that permitted BDV to occur. Further, William for the first time asserted that both Mercury and Venus are in circumsolar motion about the sun. He used this claim to offer an account of how BDV was sometimes viewable.

William wrote the Dragmaticon as a dialogue between an informed, interested, intelligent, and inquisitive Duke (the historical Geoffrey Plantagenet, d. ~1151) and an anonymous philosopher (William). In their exchange on BDV, the Philosopher simply asserted that BDV occurred. The Duke countered by referring to the planetary speed issue that William had raised in both Philosophia and Glosae Super Boetium: ³⁶

This last statement by the Philosopher is quite involved and requires careful consideration, particularly the difference in meaning between the Latin terms superior and altitudo. Unlike Philosophia and Glosae Super Boetium, William has dropped any consideration regarding planetary speed or confusion over Venus and Mercury being the same or different planets. He has focused solely on the “height” of Venus above the sun as the reason for BDV.

In this statement, William has brought back the noun altitudo from Philosophia, where it was used in the same sense as altior – both terms meaning “height,” as in a greater distance than from the earth to the sun. In the above translation from Dragmaticon, do superior and altitudo retain the same relationship as altior and altitudo did in Philosophia? The answer is generally yes, as both again mean height above the sun. But in the Dragmaticon there remains a particular difference. Altitudo means at distance greater from the earth than is the sun, in any direction. But for the term superior, William not only meant “above the sun,” but directly above the sun – in a very specific direction. According to William, when Venus is superior sole it is higher than the sun, but also located on the line that runs through the centres of the earth and sun. A clue to surmising that superior has this meaning appears in the Philosopher’s last quotation above, where twice William has stated that sometimes Venus is superior sole. The first time is when he opens the paragraph with “As shown previously,” and the second time is when he closes the same paragraph by re-emphasizing the fact with the words “This never happens except . . .” Why would he twice point this out if he did not have a special and crucial meaning for superior?

William also stated that “although it [Venus] follows the sun in planetary order, nevertheless for a long time, because of its height, it is seen after the sun in the evening and before the sun in the morning.” What did this mean, and why did he use the contrasting word “although” (etsi)? By invoking Venus’s circumsolarity (per Figure 2), William was asserting that regardless of planetary order – in which William alleged Venus to be above the sun – sometimes that planet is closer to earth than the sun. It is only when Venus, in its circumsolar journey, is at a greater distance from earth than the sun (altitudo), and directly above the sun (superior), that one can observe BDV.

Alternatively, if what William actually meant by altitudo in the Dragmaticon was something like “above the ecliptic plane,” or “above the horizon,” or “at a greater latitude,” then the burden was on him to supply much more information than he did. This is particularly true, since in Philosophia he essentially gave the same meaning to altitudo as he did to altior.

William specified a diagram to explain his concept of BDV, and Figure 3 displays one fifteenth-century example. What are historians to make of Figure 3, which appears to be quite a simple diagram and in some ways merely mimics what is in Figure 2? Note that the circumsolar circle of Venus in Figure 3 appears concentric, not eccentric like that of Figure 2. Could the concentricity in Figure 3 have been William’s mode of somehow letting the reader know that his textual altitudo meant “out of the ecliptic plane” or “at a higher latitude than the sun”? Or, was concentric Venus simply drawn at the discretion of the scribe or artist? We do not know for sure. But if William’s intention was to offer a diagram depicting Venus, for example, out of the ecliptic plane, then he should have provided far more textual detail. ³⁷ What has come down to modern readers is a diagram displaying circumsolar Venus whose roughly 12 o’clock position is above the central sun (assuming the missing earth should be at the bottom of the diagram). This suggests that all William was attempting to indicate in Figure 3 was Venus being above the sun – William’s required condition for skywatchers to observe BDV.

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Figure 3.

William of Conches’s diagram from the Dragmaticon that represented Venus in circumsolar orbit, and that he employed to explain BDV. The darkened arc on the Venus-side of the sun (Sol), running from approximately 11 o’clock to 5 o’clock – not specified by William, but created by the scribe or artist for this particular copy – represented the “dark” side of the sun not viewable from earth, suggesting that Venus was above the sun in this diagram. William used this diagram to explain the twilight and dawn appearances of Venus on the same day. (Stanford Special Collections Library, MS 0412 CB, f. 30r, s. XV^med, with permission).

What is particularly interesting about Figure 3 is the dark shadow area on the approximate side of the sun facing Venus. ³⁸ This is likely representing the “dark” side of the sun, facing away from earth. The scribe, or artist, who drew Figure 3 apparently was trying to inform the reader that Venus is indeed above the sun in this diagram, and on the opposite side of the solar body from the earth (i.e. approaching superior conjunction).

A diagrammatic explanation of BDV

A possible explanation of William’s planetary height theory of BDV is presented in Figure 4. ³⁹ That diagram assumes nothing more than Venus remaining at its highest point (farthest distance from earth) above the sun in its circumsolar motion about the sun, during the sun’s daily journey about the earth. Venus is not required to be out of the ecliptic plane in order for the mechanism displayed to be operable (which is contrary to our modern understanding that Venus must be near its maximum out-of-ecliptic-plane position for BDV to occur). The diagram shows the sun on its ecliptic pathway during its daily sojourn about the central earth in three positions: morning before sunrise, at noon, and in the evening after sunset. Also shown is circumsolar Venus at its highest position above the sun (greatest distance from earth) for all three times.

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Figure 4.

A diagram explaining William of Conches’s conception of BDV. Depicted is the sun in motion about the geocentric earth. In turn, circumsolar Venus is displayed at the peak height of its position above the sun, and at the greatest distance from earth. In the pre-sunrise dawn on the left, Venus appears to precede the sun and an earthly observer can see Venus projected onto the sun’s ecliptic pathway due to that planet’s extreme height above the sun. As the sun continues to rise, Venus is lost in the glare. Around noon, at the top of the diagram, Venus is unable to be viewed due both to the sun’s glare and the planet being fully eclipsed. But in the post-sunset twilight on the right, Venus once again comes into view as it now appears to follow the sun. As Venus moves away from its top-most position in its circumsolar journey, it eventually loses its BDV capability.

Starting on the left before sunrise, the earth-bound viewer cannot yet see the sun, but can see Venus just above the eastern horizon. Venus appears to be preceding the sun, but this is merely an illusion caused by the viewer’s projection of Venus onto the sun’s pathway. As the sun rises above the horizon in the east, its glare obliterates any remaining view of Venus. Continuing westward near noon, Venus still remains invisible due not only to the sun’s glare but also now as a result of the sun’s total eclipsing of that planet (for the viewer shown). Yet as the sun drops below the horizon in the west (on the right side of the diagram), Venus reappears as its position above the sun permits a time window during which the sun’s glare has sufficiently diminished for earthly viewing prior to Venus dropping below the horizon. At sunset, Venus appears to follow the sun, but like the morning, this is an illusion caused by the viewer projecting Venus onto the ecliptic pathway. Note that in Venus’s high position at sunrise or sunset, only a limited angular position above the sun will allow for BDV. If Venus is too far eastward or westward in its circumsolar position, then it will be viewable at sunrise or sunset, but not both. There is a small angular width above the sun – a sweet spot – wherein BDV is viewable. This is why William’s phrase for Venus of superior sole must mean directly above the sun.

Insofar as this diagram correctly reflects William’s thinking on BDV, it is symbolic of an innovative use of circumsolar Venus. I know of no other ancient or medieval author up to the time of William who attempted to explain an astronomical event by use of the circumsolarity of Mercury and Venus, other than trying to solve the ancient planetary order problem associated with the sun, Mercury, and Venus, or for explaining the bounded elongation of those planets. Medieval commentators took up the association of circumsolarity and bounded elongation with the problem of planetary order prior to William. ⁴⁰ Yet employing circumsolarity to explain BDV demonstrated William’s skill in applying what he learned from his wide reading to a problem of which apparently few knew. It is unknown whether William’s BDV source(s) also wrote of circumsolarity as a causal mechanism. But since William did not combine BDV and circumsolarity until one of his latest works (Dragmaticon), it suggests that his earlier source(s) did not consider circumsolarity.