Comparison of Thibault’s Circle and the Leiden Circle

A number of years ago, when I first started researching Gerard Thibault’s ‘Academy of the Sword’ I stumbled across an engraving of the fencing school at the University of Leiden. It showed a number of figures engaging in various martial and acrobatic pursuits and, in the center of the floor was a diagram which, with its circle and collection of lines bore a striking resemblance to Thibault’s ‘mysterious circle.’ Was it possible that this engraving showed Thibault’s fencing school at the University of Leiden? Cursory examination certainly seemed to point in that direction. A deeper look and a bit more information, however, would seem to disprove this theory.

The first strike against this being a representation of Thibault’s school comes from the variety of activities in the image. ‘Academie de l’Espée’ does include the use of the longsword, and the musket and it is clear from the frontispiece of the book that Thibault intended a section on equestrian combat. It should be noted, however, that the sections on alternate weapons are, without exception presented to show the flaws inherent in their use and to support Thibault’s rather vehemently exhorted thesis that the single rapier alone was all that a skilled swordsman needed in any situation against any weapon. Given these views, it seems rather unlikely that a representation of Thibault’s school would have included activities which the he would have considered to be of questionable martial virtue.

The more solid blow, however, arrives when with further information regarding the provenance of the Leiden engraving. According to the library at the University of Leiden, the engraving dates from 1610. In 1610, Gerard Thibault was just returning to Antwerp from his time in Spain. His public exhibition of his “new method” in Rotterdam would not occur until 1611 and, so far as we know, he would not set foot in Leiden until the autumn of 1617 (and then only briefly). In fact Thibault didn’t enroll at the University of Leiden until February of 1622, 12 years after the Leiden engraving was made.

It seems far more likely that the engraving was made to show the fencing school of Ludolph Van Ceulen. Van Ceulen arrived in Leiden around 16 years before the engraving was made and, in June of 1594 petitioned the City of Leiden for a license to open a fencing school. This was not his first such establishment. He had operated a similar fencing school in Delft from 1580-1593. After some negotiations regarding the location, he was given license to open his school in the city church provided that he repair any damage that he or his students might do to the building as a result of their exercise. We do not know precisely how long Van Ceulen taught fencing at Leiden, but in 1610 he fell ill and subsequently died on December 31 of the same year. According to various memorial markers, he continued to hold his professorship in Mathematics until his death. As we know that he was teaching fencing at least as late as 1602, it seems likely that he continued to operate the fencing school up until his illness.

None of this information, however, makes the Leiden engraving any less intriguing. If anything, it only increases the mystery. According to Herman de la Fontaine Verwey’s ‘Gerard Thibault and his Academie de l’espée,’ Thibault’s first fencing instruction came from shermmeester Lambert Van Someren, a prominent member of the Dutch free-masters. Is it possible that rather than originating with Thibault, the ‘mysterious circle’ is, in fact Dutch in origin?

Thibault’s ‘mysterious circle’ and the Leiden diagram certainly bear a striking resemblance to each other but are they, in fact, versions of the same diagram? I decided to reproduce the Leiden diagram on a flat surface, without the rest of the engraving and without the forced perspective. I got my first surprise when I began lining up the points of intersection on the lines.

I had expected the diagram to by symetrical, like Thibault’s. It isn’t. At least it isn’t across the long diameters. Laying the diagram out flat, we see that the what Thibault calls the collateral and transverse lines vary in their angles. Those at the front of the diagram (bottom) intersect with the long diameters and the inscribed square, while those at the rear of the diagram (top) intersect with the long diameters and the circumference (see diagram below).

There are any number of reasons why this may have been done. It is possible that this image is used in a different manner than that of Thibault’s. Thibault places his combatants at opposite corners of the diagram at the beginning of his demonstrations. An asymmetry could suggest that steps in one direction are shorter than steps in the other. This seems unlikely, however, since the asymmetry on the Leiden diagram occurs across the horizontal diameter rather than reflecting across one of the long diameters. Given equality of proportion, a step forward and to the left should have the same length for both combatants. The way the Leiden diagram is drawn, this would not be the case.

Likewise, it is possible that the diagram was simply misinterpreted by the engraver. There are several places in the diagram where careful examination shows that the artist altered lines partway down the walls, for example, to correct their angles. These corrections, however, do not show the kind of regularity that we find in the floor diagram. Rather, I believe that the artist altered the diagram slightly to enhance the sense of perspective. A truly symmetrical diagram would have had a tendency to ‘lift’ off of the floor slightly at the back edge. The slight alteration makes the angles at the front of the diagram look much larger than those at the back. From the original diagram, then, we are left with two possible alternate diagrams:

The first, based on the front side of the diagram, has the collateral and transverse lines intersecting with the long diameters at inscribed squares.

The second, based on the back side of the diagram, has the collateral and transverse lines intersecting with the long diameters at the circumference.

Shown together in perspective, notice how the original version of the Leiden diagram appears to be lying down while the to variants seem to be almost pulling up at the back edge.

It seems likely, that the asymmetry in the Leiden diagram is a function of perspective rather than of usage, but we are still left with the question of how it compares to Thibault’s circle. If the two are variants on the same diagram, it is obvious that the Leiden diagram is a much simpler variant.

By itself, however, this does not mean they aren’t related. If the artist was willing to make adjustments for perspective, might he not also have simplified the image for clarity? To find out, I overlaid the Leiden diagram with Thibault’s circle. The blue lines in the image represent lines which both diagrams share. The red lines belong to the Leiden diagram and the black lines belong to Thibault’s ‘mysterious circle.’

Seen in this way, the points of difference become immediately apparent. The primary difference between the two lies in the orientation of the inscribed square. Thibault’s inscribed square is oriented so that its edges are parallel to the long diameters while the inscribed square in the Leiden diagram has its edges parallel to the short diameters. While this may seem like a minor shift, it effects all of the dependent intersections in the diagram.

Unless we assume that the artist simply did not know what he was looking at, we must conclude that Thibaults ‘mysterious circle’ was not directly appropriated from an identical Dutch image. One cannot, however fail to contemplate a similarity of origin. It seems likely that Thibault learned to fence with the aid of similar diagrams and, finding them pedagogically useful, designed the ‘mysterious circle’ in their image.


Greer, John Michael (Translator). Academy of the Sword. Highland Village: Chivalry Bookshelf, 2006

Thibault, Gerard. Academie de l’Espée. Amsterdam: Elzevier Press, 1630

Verwey, Herman de la Fontaine. “Gerard Thibault and his Academie de l’espée,” Quarendo. Vol VIII 4/Autumn 1978

[Oomes 2000] Pi in de bibliotheek: catalogus bij een tentoonstelling over Ludolph van Ceulen en de berekening van het getal pi, in de Leidse Universiteitsbibliotheek, 4-18 juli 2000. Leiden: Universiteitsbibliotheek, 2000.

[Oomes 2000a] “Het grafschrift van Ludolph van Ceulen”. Nieuw Archief voor Wiskunde 2, 156-161. 2000.

Published on April 20, 2008 at 2:25 pm  Comments (12)  

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  1. Fantastically interesting, very good analysis. I have a hypothesis on the subject. According to the Wikipedia article (from which I obtained the link to this site) Van Ceulen was a teacher of mathematics. Given that he had a professional interest in mathematics as well as in swordplay, might he have adopted the diagram in the engraving as a means of teaching a more classical variant of the Spanish system. I am not quite sure whose circle might have predated whose. But, on simply a stylistic basis, it seems like the all-important orientation of the inscribed square (and the outermost square as well) indicates a use of the earlier system.

    Firstly, the geometrical diagrams of Carranza, Narvaez, Tamariz and most of the other Spanish writers have far simpler diagrams than these two, and thus the simpler version would seem, inductively, to be more closely related to them.

    Secondly, and far more strongly, squares are a specific type of parallelogram, and that is important, because in the classical Destreza, the parallel linea infinita would correspond to the sides of the outer most square, while the vertex of the inscribed square is evidently the point at which the cross of the combatant’s sword would be at the beginning of the fight (and also his toe). Incidentally, if you look up Tamariz you will find that in his diagrams the verticies of the inscribed square lie on the linea infinita, and thus if the linea infinita were extrapolated, so to speak, into a square it would be the same in orientation, and probably in proportion, to the Leiden circle. Note that Thibault has no linea infinita proper.

    Ultimately it seems to me that the Leiden circle is likely a functional splicing together of several of the more general diagrams of the Spanish School’s writers, which retained the basic pedagogy of that system, and likely its more orthodox techniques, while Thibault was evidently a creative renagade.

    • Mr Wright,

      I think that your hypothesis may run into a some issues in terms of support.

      La verdadera destreza was not, by any stretch the only fencing system to make use of floor diagrams as teaching aids. While it is true that most of the diagrams take the form of simple grids, we do begin to see circle based floor diagrams being used in some Italian treatises as well. Given that we cannot claim Spanish primacy on floor diagrams, I would want to see something to support the idea that van Ceulen had trained in destreza. At this point, I have not seen one shred of evidence that this is the case. In point of fact, I have seen nothing whatsoever to suggest that he had any kind of contact with Spanish fencing at all.

      I find it much more likely that the mode of the time was to analyze and diagram and to render complex movements into geometric patterns and that led to the development of various floor diagrams across multiple systems and in varying geographic locations within a relatively short period of time. The similarities you note above could then be explained by the fact that most of the things that a sword and a human body can do are going to be fairly similar, so, while the diagrams for those activities may vary in complexity, they are likely to possess many common elements.

  2. Correction: I could be wrong about the location of the cross per se (the cross of course being where the quillions intersect the blade). The point in question could also be the location of the toe, or the shoulder as well, depending on the pedagogy.

  3. Hello, are there techniques with 2 swords per person?


    • Not in Thibault’s treatise, no. Giaccomo di Grassi and Jakob Sutor both address fighting with two swords.

  4. Just an observation – It is the opinion of several of my fencing masters and also of several SCA combat teachers, that both the floor diagram on the Leiden Salle engraving and Thibault’s ‘Mysterious Circle’ are actually used for directly teaching range and approaches (tactics).
    This would make them very similar in use to the ancient ‘sword stars’, used for teaching blade attacks. Thousand year old examples of awesome Spanish-stars can be found on the floors of the fencing courtyards (in tile mosaic) of the palaces of Alhambra and Granada.

    • Mr Steele,
      I agree; it is quite clear from Thibault’s book that his diagram is used to teach correct footwork and to clarify more complex actions. It is, if you will, a very elaborate form of graph paper. This is true of every combat floor diagram I have run across so far, at least within the Western European traditions.

      As to the ‘sword stars’ that you make reference to, I haven’t run across that particular term before. What, if I may ask is the source material that is coming from? Unfortunately my collection of combat treatises from the time of the Moorish occupation of Iberia is somewhat lacking. If you know of some that you could point me to, I would be most grateful.

  5. Dear Matthew:
    Your very interesting blog on the ‘Leiden circle’ makes jolly good read! Yesterday I saw the original engraving of the Leiden fencing school. I also made some comparisons with the Thibault circle and came to the conclusion that a better comparison can be made to turn one of the circles by 45°. Please see my blog (in Dutch). My conclusion: Willem Van Swanenburgh & Woudanus made a nice set of promotional folders for our university, but they were no photographers. While sketching Woudanus presumably made some errors. While engraving Van Swanenburgh didn’t have the slightest idea what he was interpreting.
    Best regards!

    • Professor,

      Thank you for the kind words. I agree with your assessment. The 45° rotation is certainly a tempting possibility. As I stated in the article above, it seems very likely that Thibault was exposed to something similar to the Leiden circle during his training in the Dutch school of fence and I keep hoping that I’ll run into another pre-Thibault source with similar diagrams. Unfortunately, I haven’t found anything yet.

  6. Dear Sir,
    this is a fascinating analysis indeed. But let me point to one essential error: This is not a book on handling a SWORD, which is a weapon to cut with its blade the body of the enemy, but on EPEE or RAPIR, whichs aim is to target the lung of the enemy with its top. Considering the period beeing the invention of the barometer und Rene Descartes essay on how to measure the air pressure, I think its not be chance, that even the oeconomical as well as the military use of this insights are represented in this book.

    • Professor Gerlach,

      First, how are any of the conclusions drawn in this analysis dependent on the sword being able to make cuts to the body? I certainly did not intend for any such correlation to be a factor in the analysis so, if it is there, I would be interested in seeing where.

      Second, epee literally translates to sword and that is the proper translation for the time period in question. The modern epee as a thrust only weapon doesn’t come about until the 19th century. This conflation is a common post Victorian error. As to the rapier not being a cutting weapon, I think Thibault would have disagreed with you on that. His system makes use of a number of very effective cuts and, given the effectiveness of his system overall, I find it unlikely that he would have advocated them had the weapon not been suited to the task.

      As to your final point regarding Descartes, the invention of the barometer, etc, I think something may be getting lost in translation. I can say that, as early as Camillo Agrippa’s ‘Trattato Di Scienzia d’Armes’ we begin to see a distinct theme of employing the so called “new sciences” in martial treatises. Thibault is certainly no exception here, but neither is that aspect of his text particularly revolutionary within the field. Quite to the contrary, by the time Thibault’s treatise was published it had become almost a requirement for combat systems to be described in terms of natural philosophy.

  7. Dear Matthew Howden,

    first of all I have to thank you for your formidable article about the Leiden circle.
    Secondly I have to admit that I cannot totally agree with your conclusion or maybe I misunderstood it.

    If I take your first Leiden circle diagram and compare it to your Thibault diagram, by turning one of them 45 degree so that they are
    aligned along the diameter and the inner square, ALL the lines of diagram 1 will fit exactly into the Thibault diagram.
    Only the “helping lines” are missing which mark the half intersections or the food lines for the starting positions.
    I’m studying Thibault in praxis for nearly 2 years now and and have to state that the missing lines are obsolete for training purpose.
    Our fencing salle has 6 Thibault diagrams drawn at the floor and I think the next will be like the Leiden circle because of its essential design.

    So for me, assuming that diagram 1 is more like the real physical Leiden circle, this is a 100% streamlined Thibault circle.

    I don’t know what this will mean for the 1610 dating of the engraving but since Pacheco probably invent the inner square in 1600 to Destreza (I may be wrong with that) it is amazing that van Ceulen could use such an advanced circle before 1610 for his teaching.

    Strongly hypothetical, since I think I am a little bit too familiar with Thibault’s Academy Of The Sword, the guy with the judging staff at the right corner looks a little bit like an aged Girard Thibault d’Anvers 😉

    With Best Regards

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