By G.J. Bath
'In one particular respect we can define Poussin's conception of Reason more precisely. It was closely bound up with mathematics, and especially with geometry. For the seventeenth century, mathematics was the supreme achievement of human reason because of the absolute certainty of its demonstrations, and it was also a symbol of clarity and order.' Anthony Blunt
So many people have claimed that they alone have solved the enigma of Poussin's Les Bergers d'Arcadie that one is forced to wonder if they can all be looking at the same painting.  Anyone who ventures a new approach to the subject, standing in the shadow of so many giants of research and reason, must do so with almost grovelling humility. Furthermore, mainstream thinking on the subject has become so rigid that to suggest there may be an alternative way to view the topic verges on anathema, even heresy.
Equally daunting to the investigator are the many who preach that no geometrical constructs underpin the art of the 16th and 17th centuries other, perhaps, than occasional glimpses of the Golden Section.  Some 'experts' seem to know that there is positively no geometrical foundation to, and certainly no 'key' embedded in, the works of Poussin and Teniers , as is suggested by the potentially fake or, at least, misleading Saunière cipher.
Such attitudes are, presumably, intended to convey to the observer that there is no point in looking any further, which would be either denying established fact or chasing after illusion. However, progress does not proceed from closed minds, any more than enquiry finds reasons to avoid searching for answers to questions unvoiced due to personal bias or lack of initiative.
This work does not claim to have any answers to the vexed question of the existence or not of geometrical formulae in art, it merely presents some observations that would not have surfaced had either of the above extremes of thinking held sway. It is merely a hypothesis for consideration, a suggestion that, perhaps, the Golden Section was not as supremely predominant in the art of the 15th to 17th centuries as has been supposed, and as is currently being insisted upon in certain quarters.
The work may prove to be an unproductive line of enquiry but some observations from a wider field of study are presented here to encourage further exploration and discussion should the subject of pentagonal 'signature' geometry, as outlined here, be considered of any relevance to the solution of this particular aspect of the Rennes-le-Château mystery.
Poussin Teniers Gardent la Clef?
One prominent element of the enigma of Poussin's Les Bergers d'Arcadie is the assumption that a key to the painting(s) exists but with no knowledge of its form, size and nature, and with nobody, other than Poussin, having seen the lock the key is supposed to fit.
However, if aficionados of the mystery are correct then this may not be altogether true. It is a widely-held assumption that the Shepherds Monument at Shugborough, Staffordshire , might bear upon the mystery but, apparently, without considering that the design of this monument may contain the same key as the painting. In this eventuality, the Shugborough tableau would merit careful analysis.
The Shepherds Monument features the central portion of the better-known version of Les Bergers d'Arcadie (hereafter, Bergers 2) but with elements of the earlier version (Bergers 1), in that the design is flipped horizontally, thus preserving the original order of the figures, and with the sarcophagus much as in the earlier painting. 
Preliminary analysis reveals that the ratio of the sides of the Shugborough monument approximates to 2:SQR3+1 (two to the square root of three plus one) and that the main feature of the design could, therefore, be a square of two units on the base. After drawing and developing this square, it becomes clear that there may be some potential for investigating the emergence of a surprising feature of the composition.
Figure 1: The geometrical design that emerges from the Shepherds Monument at Shugborough
It will be seen from Figure 1 that the centre of the square on the base lies on the hand of the kneeling 'blue' shepherd and that the diagonal passes through the top of the staff held by the standing 'white' shepherd. Furthermore, the line of this shepherd's staff is at roughly 75 degrees to the horizontal which, when mirrored, forms a trapezoid and, subsequently, a pentagon or pentagram.
An obvious step, thereafter, is to reverse the original painting (Bergers 2) to determine whether the same square overlay might fit. Initially, there is no obvious indicator as to what might be the common focal point, or the appropriate scale. However, it becomes immediately apparent that the major line through the 'white' shepherd's staff of the Shugborough monument runs almost parallel to the same shepherd's staff in Bergers 2. No surprise there, then!
As the square is tentatively scaled, it is noticeable that its centre moves closer and closer to the finger of the stooping 'red' shepherd, not the 'blue' one kneeling as in the Shepherds Monument. Roughly the same area of the painting as shown at Shugborough can be kept within the square but the centre draws closer and closer to the tip of the finger of the stooping 'red' shepherd, and towards the line marking the join in the masonry of the tomb. Moreover, the prominent trapezoid formed on the 'white' shepherd's staff of the Shugborough monument seems not to fit in this case.
By placing the centre of the square on the tip of the finger of the stooping 'red' shepherd it becomes clear that a trapezoid of a different shape is formed by the staff of the 'white' shepherd. Suffice it to say that there is a potential geometry underlying Bergers 2 sufficiently similar to that of the Shepherds Monument to suggest that the designer of the bas-relief was aware of the importance of the staff and of this particular square of the painting.
Figure 2: The two pentagonal schemas, Shugborough (left) and Bergers 2 (right)
Figure 2 presents the two schemas as they appear from the foregoing analysis.
The portion of the painting represented at Shugborough seems to be the inner square of a construction pertaining to Bergers 2. However, the side of this square cuts through the kneeling 'blue' shepherd's left foot in the painting, but at Shugborough the foot has, apparently, been redrawn so this fails to happen. At Shugborough, the intent seems more to enclose the figures within an arch formed by the lower semi-square and the upper semi-circle. In both, the standing 'white' shepherd's staff seems to be at 75 degrees but sourced at different points. The objective in both cases would seem, therefore, to be to outline a pentagon, but not of regular form.
Further analysis suggests that the perceived angle of the pentagon's left face would be correct at 105 degrees, as close inspection reveals that the top of the staff appears to have been painted to one side of the line and the bottom to the other. The fact that a similar device would seem to have been used in Bergers 1 hints at deception or, at least, an attempt to muddy the waters.
Figure 3: The major portion of the design showing the main and subsidiary squares and pentagons
The Shugborough pentagon has internal angles of (105, 105, 112.5, 112.5, 105 degrees, from base to apex) and Bergers 2 has two possible pentagons, one of (105, 105, 105, 105, 120 degrees) and the other of (105, 105, 108.75, 108.75, 112.5 degrees). The strange angles of the latter are due to this pentagon being in a circle perfectly inscribed within the former.
In order to recreate the design, it was found easier to work backwards from the assumed centre of the main circle (at the tip of the stooping 'red' shepherd's finger) than to attempt to move forward as if from a blank canvas. One of the major problems is the confusion over the size of the canvas and the availability of a good image of the painting out of its frame. Added to this, the canvas has been increased in size, and it is not known whether what we have at present is as Poussin originally planned it.
The pentagon is easily constructed, bearing in mind that the tips of the staff are at 142.5 and 232.5 degrees, the base angles being 105 degrees and the three 'containing' sides of the trapezoid the same length. The shepherd's staff provides a trapezoid into which a circle is introduced and another trapezoid within. The large dashed circle on the shepherd's staff in Figure 3 is extremely close to, if not matching, the inked line reported by Andrews and Schellenberger . Note that this lies between two significant horizontal lines of this construction.
The inner pentagon could have the function of linking the four figures of the painting at the main points of the trapezoid, marking shepherd 1 (white) on the left side, shepherd 2 (blue) on the right calf, shepherd 3 (red) on the left foot and the shepherdess also on her left side.
More on Composition
This leaves the problem of the 'red' shepherd's staff, which Poussin painted before the tomb. The staff must, therefore, be highly significant, but in what way? It is fairly easy to determine that it lies at some 85 degrees to the vertical, which suggests that a similar pentagonal construction might be possible based on this staff. 
A clue may be provided by another Poussin painting, Summer, or Ruth and Boaz. This depicts a guard with a lance at much the same angle - and a similar pentagon may be formed by matching the angle of the lance and the trunk of the tree about the vertical centre line. Note also the iindicator' of the pointing finger and the 'confirmers' of the line marking the chasm, upper right, and the bridge across it, the stone at bottom right and the 'correspondence' of the line of the uncut corn. 
Figure 4: Poussin's Summer, or Ruth and Boaz
In this painting the pentagon emerges, once more, from basic 'constructional' techniques, and the geometry is relative to the size of the canvas. The pentagon has internal angles of (95, 95, 112.5, 112.5, 125 degrees).
Returning to Bergers 2, by applying a process of pentagonal design similar to that employed with the standing 'white' shepherd's staff, and basing the construction upon a point on the horizontal 'centre' line directly below the tip of the staff, it will be found that a line projected at a right angle to the 'red' shepherd's staff passes across the tip of the kneeling 'blue' shepherd's finger. This point can also be seen to lie on the line from the bottom right point of the inner pentagon (formed indirectly from the 'white' shepherd's staff) to the centre. The point of intersection is on the letter 'R' of the inscription.
A similar procedure can then be applied to the staff of the kneeling 'blue' shepherd, which is found to bear at some 110 degrees to the horizontal. The centre of the enclosing circle is, once more, at a right angle to the staff on the 'centre' line (and passing through the point of intersection of the 'blue' shepherd's finger, as above). The radius in this case is determined by the 'constructed' base of the third staff. The resulting pentagon has internal angles of (110, 110, 105, 105, 110 degrees).
Figure 5: The positioning of the 'white' staff (left) and the 'blue' staff (right) in Bergers 2
The centres of all three circles defining the staffs lie on the 'centre' line, and it may be appreciated how the three interact. The 'white' staff, on the left, effectively sources the other two, both of which are pinned by the two lines that define the location of the 'R' under the kneeling 'blue' shepherd's finger. This point determines the line of the middle staff and, by extension, that of the right-hand staff, this pentagon having internal angles of (95, 95, 117.5, 117.5,115 degrees).
Figure 6: The placing of the 'red' staff in Bergers 2 (left) and the location of the main points and features of the design (right)
It should be noted that the constructional lines are slightly longer than the staffs, and that the origin of the top of the 'red' shepherd's staff is at the same level as that of the 'white' shepherd.
I have attempted to determine what dimension might form the basis of the painting and conclude that this could be an outer square of 30 pouces (the French inch) on the base or, perhaps, a corresponding inner square of 28 pouces (possibly with SQR2 as 10:7). One pouce is 27.07 mm, or about 1.066 inches. The width and height of Bergers 2 can be variously constructed and determined but in Figure 7 the canvas size is calculated at 34.86 x 44.68 pouces (944 x 1210 mm) based on a square of 30 pouces.  The 'viewing' frame is assumed to be 31.59 x 44.68 pouces (855 x 1210 mm) having the ratio of 1:SQR2 in line with the main construction. Needless to say, the suggested canvas size and viewing frame are inconsistent with the Cornford pentagon.
Figure 7: A potential design framework for Bergers 2 based on SQR2 (ad quadratum)
The height here is merely a suggestion, as there are a number of ways to derive the assumed measure of around 94 cm. Any analysis is hampered by the lack of a clear statement of the actual size of many paintings, both in and out of the frame, with official and accurate images - and no knowledge of what Poussin intended! 
Figure 8: Bergers 2 with the overlay of significant compositional features derived geometrically
It may be appreciated that, as in Figure 8, it is unnecessary to complete the three pentagons because the line of each staff is the first face to be produced, or 'constructed'. The inked line on the 'white' shepherd's staff, as marked upon the original painting, is shown here in white.
"The idea of connecting painting with mathematics was not, of course, new - it had been one of the foundations of Renaissance aesthetics - but Poussin believed in it with such fervour that it produced new and astonishing results in the paintings of the 1640's, of which the most striking example is the Holy Family on the Steps." Anthony Blunt
Figure 9: Poussin's Holy Family on the Steps, National Gallery of Art, Washington
The analysis in Figure 9 is, assuredly, not specific to any geometry Blunt had in mind but is certainly a demonstration of what he intended to convey. It is unnecessary to search for a constructional geometry here because the eye provides both the framework and the focus in any event. Of a certainty, it's there, but is it as formal as suggested, and is the setting of the staff and the derivation of the 'platform', both arising from the geometry, purely accidental? Am I, perhaps, reading too much into this? Further analysis of other paintings connected with the mystery may reveal some common features and could, perhaps, assist in developing a testable hypothesis vis-a-vis the Saunière cipher and Rennes-Le-Château.
The Chatsworth View of Arcadia
The suggestion that the key to the layout of the Louvre version of Les Bergers d'Arcadie (Bergers 2) might lie in the design for the Shugborough monument is somewhat confused by the fact that the pentagons in each are of a different form. However, it has already been noted that, although the scene depicted by the Shugborough monument is that of Bergers 2, the reversal of the figures and the tomb design seem to point to the Chatsworth version (Bergers 1) as a foundation.
Bergers 1 has some obvious geometrical properties already presented by previous researchers, and it is possible to build upon this.  In the light of the apparent discoveries in the design of Bergers 2, it is a simple matter to investigate whether there might be a similar underlying geometry, and an associated pentagon, present in Bergers 1.
The key to this painting seems to lie, once more, in the angle of the shepherds' staffs. That of the bearded shepherd (with the crook) appears to be at 75 degrees from the horizontal, and the other at 120 degrees. The line of the sarcophagus seems to lie at 30 degrees, at a right angle to the aforementioned staff and forming a cross with it, with an implied vanishing point off the left edge of the painting. Once more, a significant problem is to identify what size of original to use in the reconstruction, as there are suggestions that the canvas of this painting may also have undergone some alteration. Although published images vary slightly in width and height there is, nevertheless, potential for developing a basic construction.
Figure 10: Poussin's Les Bergers d'Arcadie (Bergers 1) with pentagonal overlay
Figure 10 shows the construction by which one particular pentagonal form emerges. The pentagon is the same as that of the Shugborough monument, perhaps indicating the designer's knowledge of the original geometry. As in Bergers 2, the central trapezoid links the four figures but, in this case, the use of the centre to mark one of these provides a vacant fifth point upon the tomb. The centre of the pentagon identifies the bearded 'pointing' shepherd, the bottom right the 'reclining' shepherd, the bottom left the 'standing' shepherd and the top left the shepherdess. The rightmost point indicates the space preceding the letter 'R' of the inscription, perhaps confirming its significance in both paintings and explaining the somewhat contrived positioning of the legend in this one.
Note that the shepherdess has her own linked pentagon with its centre above her belly, coincidentally or not, perhaps reflecting a suggestion made of Bergers 2 that she is pregnant although, if this is at all significant, it may point to her being a fertility figure. The geometry builds up as seven linked pentagrams connected by a major 'shepherds Star' within the larger circle shown.
No discussion of Poussin's Les Bergers d'Arcadie should ignore the bas-relief commissioned in the 19th century and placed as a central feature on Poussin's tomb by Chateaubriand and associates. Were they aware of the underlying geometry of the painting? The evidence is inconclusive, but I suggest not.
Figure 11: Poussin's tomb, Basilica Lorenzo in Lucina, Rome
While there seems to be an appreciation of the function of the staff, the key positions of the two shepherds' hands are ignored. The designer may have recognised that a trapezoid is present in the painting but failed to emphasize the key element of the design - the centre of the circle and its relationship with the pointing fingers. However, the pentagon seems to be the same as the outer of Bergers 2 from which the bas-relief was taken.
The Teniers Connection
Because the reference to a shepherdess in the Saunière parchment cipher seems particularly relevant to Poussin, it has been conjectured that the text 'pas de tentation' refers to Teniers, particularly in view of his many paintings on the subject of the temptation of St. Anthony.
When deciding upon the selection of St. Anthony and St. Paul in the Desert as the relevant Teniers painting, Andrews and Schellenberger wrote, "Stupefaction best describes our reaction on recognising, prominently displayed in the painting, the occult geometry."  As 'occult' implies 'hidden' or 'not easily understood' Teniers proved incompetent in achieving the key objective of secrecy! Perhaps such pointers were never really a secret but an outward expression of a symbol only fully understood by initiates.
The text continues, "The two saints had obligingly arranged their staffs so as to cross each other at an angle of 60 degrees and, furthermore, had oriented them to produce angles of 75 degrees and 45 degrees to the horizontal." In view of a similar situation appearing in Poussin's Bergers 1 this would certainly seem promising. However, the two authors have their own particular axe to grind and their investigation is directed towards tilted designs culminating in sloping polygons "confirmed by various correspondences."
The painting in question depicts the occasion of the two saints meeting at which the raven that normally brought half a loaf of bread to feed St. Paul carried a full loaf to feed them both. I have nowhere seen an image of this painting out of its frame, which renders analysis difficult. However, the observation concerning the staffs seems to be correct, and a vertical line through the crucifix produces a trapezoid and pentagon of the same pattern as in Bergers 1. The continuation of the left upper side of the pentagon passes through the loaf and the raven. The second bird is approximately 30 degrees from the true centre of the painting and the large book forms part of the design, perhaps as a 'confirmer'.
Figure 12: St Anthony and St. Paul in the Desert, Teniers the Younger, private collection.
A similar format to that appearing in Poussin's work, as previously discussed, seems to be present here in the use of an angle of 22.5 degrees, perhaps together with 120 degrees, to determine the size of canvas (that is, employing SQR2 and SQR3). Note that this is not the only painting by Teniers the Younger portraying St. Anthony that contains pentagonal geometry.
It certainly looks as if this painting and the two versions of Poussin's Les Bergers d'Arcadie could have much in common, and that what is being postulated in this article may constitute part or all of the 'key' mentioned in the Saunière cipher as this relates to compositional geometry.
Pentagonal Signature Geometry
In my discussions elsewhere, I refer to the various pentagonal forms shown above as 'signatures' and note that these seem to be found in many paintings by Poussin and Teniers (although not all) and perhaps those of other notable artists throughout the period covered by the late Gothic, Renaissance, Mannerist and Baroque. The technique, if it really existed as a compositional 'style', may have been considered outmoded, and gone underground, during the Age of the Enlightenment, to make a re-appearance in the Romanticism of the late 19th century. Space prevents my discussing the topic here but some examples can be found on my web site:
The potential use of the points of the pentagonal signature to connect figures in paintings as, perhaps, in Bergers 1 and Bergers 2, may also be seen in Poussin's Time Revealing Truth with Envy and Discord, A Dance to the Music of Time, The Adoration of the Shepherds and The Plague of Ashdod. It may also be present in Leonardo da Vinci's Virgin of the Rocks (both versions), Raphael's Triumph of Galatea, Grünewald's Crucifixion , Rubens' Adoration of the Magi and the Delacroix mural Heliodorus Chased from the Temple, in the church of St. Sulpice, referred to in the Serpent Rouge.
Figure 13: Poussin's Adoration of the Shepherds (National Gallery, London) showing a linked double pentagonal signature: one pentagon marks each of the five cherubs (via the trapezoid) and the other the three shepherds - upon a major radius of the containing circle - and the Holy Family on the opposite and matching key arc of the circumference.
Figure 13 provides an example of a more advanced geometrical structure in two parts, a technique apparently also employed by Raphael, Rubens and Michelangelo. The pentagonal signature in its simplest form, seemingly present in Raphael's Allegory: A Vision of a Knight (Dream of Scipio), may have developed into a full geometrical framework of which the pentagonal signature eventually forms a central but fairly insignificant compositional part, for which see Teniers' A Barn Interior.
Figure 14: A Barn Interior, by Teniers the Younger, private collection, illustrating the application of 'indicator', 'confirmer' and 'correspondence'.
In this painting we see 'indicators' of, or 'pointers' to, the presence of an underlying geometry - such as the rather strange curved post to the right of the cattle, suggesting arcs of concentric circles, and the peasant's finger pointing off-canvas (marking the diameter of the major circle). This may also be a 'confirmer' of the geometry, along with the broom in the bottom right corner, the line of the peasant's stick (all popular with Teniers) and the owl on its perch by the door, eventually found to be sitting within its own square and circle.
As an aside, the rather strange angle of Poussin's head in his earlier self-portrait seems to be a consequence of a construction developing a pentagonal signature, which is slightly modified in the later version. This tilt, the pen and the book are the pointers to the particular geometrical form employed.
The pentagonal signature in A Barn Interior emerges mainly because of the circle formed from initial constructions employing the angles of the regular pentagon, with the signature seemingly confirmed by the 54 degree arc of the post. So, the signature is indicated in much the usual way by the presence of staffs, sticks, arrows, ladders and such, forming straight lines, but in this case by an arc. As an aside, Teniers seems to employ the regular pentagon more frequently than Poussin whose Triumph of Neptune and Time Revealing Truth with Envy and Discord are the only potential examples I have yet found.
"I want the painter, as far as he is able, to be learned in the liberal arts, but I wish him above all to have a good knowledge of geometry. I agree with the ancient and famous painter Pamphilus - that no one could be a good painter who did not know geometry." Leon Battista Alberti
No Stone Unturned
Of some significance to this work is the possible appearance of the pentagonal signature in works commissioned by Saunière at Rennes-le-Château, and further instances at other locations in the region. Might he, and others of his time, have been aware of the device, and how widespread was this?
For example, a version of the Rennes-les-Bains 'Le Christ au Lièvre' at "un petit village du Hainaut", based on Van Dyck's Lamentation Over Christ, contains a more explicit statement of the pentagonal signature than the original.  However, in this case, it is the former painting that provides the key to the Van Dyck which, otherwise, has no obvious indicators of an underlying geometry or pentagonal signature.
The angels above the stoup at the church of Rennes-le-Château seem to be placed upon a regular pentagon linking the figures, perhaps with the intention that it is by this particular sign, rather than the Cross, that thou shalt conquer (him or it). The design of the tympanum of the porch above the church door potentially contains two pentagonal signatures and the layout of the park and gardens the same.
It is possible that the design for the Tour Magdala contains the fundamental elements of the pentagonal construction and its associated geometry (as a square containing a rectangle with sides of 2:SQR2+1 standing upon an inverted trapezoid, with the staircase tower perhaps featuring ratios of 1:SQR3) although this does not seem to have been the case with the tower at Girona, or Saunière's orangery.
Another example may be seen in the date inscribed in the commemorative stone of the bell tower at Rennes-le-Château - specifically the numeral '4' - which is likely to pre-date Bigou. 
Figure 15: The date on the bell tower at Rennes-le-Château (left) and a design by Boudet (right) drawn from images using geometrical constructions forming pentagonal signatures, only parts of which have been inscribed
A design said to have been incorporated into the pediment of the church at Quillon, at the behest of Boudet , also seems to have been based on pentagonal signature geometry, as might that of the Coume-Sourde Stone (if and when this can be proved to have existed and to be genuine.) This leads naturally to the possibility of a pentagonal geometry in the landscape, not necessarily based on the regular pentagon, and thoughts of a possible map, or overlay. However, the introduction of an even greater range of circumscribed pentagons into an already highly fraught debate (une folie anglaise!) is likely to result in anarchy if not outright rebellion!
Figure 16: A possible source outline for the Coume-Sourde Stone based on a claimed fake (left) and a potential map overlay based on a pentagonal signature (right) drawn upon Wood's Circle of Churches
Suffice it to say that the pentagonal signature may have been a symbol, device or talisman, much as the Masonic square and compasses. That such a signature could be acceptable in 17th century Italy and 18th century England (as evidenced by Shugborough) may suggest an association that is either hermetic or humanist rather than purely religious - unless Anson was a Jacobite! He may, of course, have been a Freemason or, perhaps, subscribed to l'Écossais or one of the more esoteric early Masonic 'side' degrees. In this way, the signature could have belonged to a proto- or quasi-Masonic group with a tradition dating back to the 15th century (but not necessarily Gothic in origin) that may even have survived to the present day.
As to the way the Rennes-le-Château mystery was launched upon the world, one should perhaps not exclude the possibility that someone may have gleaned an insight into a possible underground movement, and its outward signs, and is fishing for information, or an answer to the key that they know to be present in certain works of art.
Figure 17: The Altar, La Chapelle Saint Pierre, Jean Cocteau: "Un ... style purement décoratif, fait de géométries ornamentales..." 
So, from Sandro Botticelli to Jean Cocteau and, perhaps, beyond, many artists may have introduced a pentagonal signature into their works. However, this may well owe more to an esoteric tradition than to membership, or even leadership, of an underground organisation such as the Priory of Sion.
Perhaps the real conundrum relating to a possible 'key' underlying the works of Poussin and Teniers is how the perpetrators of the potentially faked Saunière parchment cipher came to learn of such a thing in the first place. After all, given that there is any substance to this or any similar hypothesis, the traces of an underlying geometry would not have been so diligently searched for had it not been for the message of the parchment cipher - if not the wider trappings of the Rennes-le-Château mystery.
Or is the real puzzle of the paintings more mundane than this - that the human mind can find traces of anything in nothing and, thereby, has the capacity to mould fantasy out of coincidence? After all, how can anyone actually prove there is such a geometrical foundation to any work of art? The process is fraught with dangers; the possibility of forming patterns out of random lines and, once drawn, any number of symmetrical or regular forms may be inscribed within a circle. Much will depend upon a subjective interpretation of 'pointers', 'confirmers' and 'correspondences' and more than one design may be possible from any single painting.
This said, pentagonal signature geometry is as likely to be present in Poussin's Les Bergers d'Arcadie as are the Cornford and Rigby pentagons - and the Shepherds Star formed within the pentagonal signature must be as viable as the Grail Star - if not arguably more so!
Est-ce-Que Poussin Teniers ne gardent plus la clef?
Or is the key, perhaps, an entity of divers parts, both visible and invisible? If so, we may yet find the former. Adrian Lodge has suggested that compositional geometry may indicate those paintings that contain non-compositional elements, and that this may well be the actual key being sought. However, the key referred to may just as easily relate to secrets lying behind the visible symbols, the sacred to the profane - unwritten or indecipherably cryptic - carried forward much as by the Widow's Son. This might be borne in mind with respect to Abbé Louis Fouquet's comments after his meeting with Poussin:
"He and I discussed certain things - which, according to him, perhaps nobody else will ever be able to rediscover in the centuries to come; and, what is more - these are things so hard to come by that nothing now on earth can prove of better fortune nor be their equal."
Nec mysteria quae non occulta.
Figure 18: Derivatives of pentagonal signatures: Linked pentagons and the Shepherds Star, W Cassiopeia, and the Masonic Square & Compasses
Identifying works of art that might contain a pentagonal signature relies heavily upon indicators, confirmers and correspondences, generally in the form of straight edges. However, not every painting with a staff will necessarily have such a signature, and chance will no doubt play a part in the erroneous selection of some examples, perhaps in my identification of works by the artists below (23 paintings by Poussin and 10 by Teniers) which include four painting of 'Shepherds in Arcadia' and three of St. Anthony and St. Paul.
The earliest work I have found with a potential pentagonal signature is Luis Dalmau's Virgen de los Consejeros (c.1445, Barcelona) which contains pointers provided by the cross of St. Andrew and the staves accompanying Sta. Eulalia, which seem to generate a regular pentagon (perhaps accidentally). Signatures may also be present in the work of Bosch (1450-1516).
The source of a potential pentagonal technique in Valencia would seem not to be Flanders, so any such influence on Hispano-Flemish art may have derived from Moorish sources or, more likely, Italy in the early 15th century. The Council of Florence (1438-39) may have had some bearing upon the transmittal of such a schema if hermetic in origin (as this seems an unlikely device for Orthodox iconography) and its assumed appearance at this time. However, the scheme is essentially Pythagorean, if not also Platonic, in outlook - the four of the trapezoid crowned with the One, the quintessence, producing the first 'obvious' pentagonal number (22 being the third, although actually the fourth.) Where else, and when, would such a marriage have come about, a concept as comfortable in the Medieval Roman world as in the Byzantine?
It is possible that Fra. Filippo Lippi (1406-69) employed the pentagonal signature in his work but, thereafter, Botticelli (1444-1510), Leonardo da Vinci (1452-1519), Castiglione (1478-1529) and Raphael (1483-1520) seem to have used it and, possibly, Michelangelo (1475-1564). The technique may have been taken up by Veronese (1528-1588) and others through to Guercino (1591-1666) and Poussin (1594-1665). Van Dyck (1559-1641) may have discovered the technique while in Italy and communicated it to Teniers the Younger (1610-1690) upon his return to Flanders (1627). The link could also have been provided by Rubens (1577-1640) who travelled to Italy in the first decade of the 17th century. Velasquez (1599-1660), who befriended Rubens in Spain, is also known to have spent some time in Rome to benefit from the advances and techniques of Italian art.
Traces of pentagonal geometry in the work of Grünewald (1470-1528) may derive from Dürer (1471-1528) who worked and studied in Venice in the last decade of the 15th century, although the two had very different styles and outlooks. In fact, so many artists visited Italy at this time that it would hardly be surprising that any influence introduced there would spread rapidly throughout Europe.
1. For example, see Andrews and Schellenberger The Tomb of God (1996, Little Brown and Company), David Wood's Genisis (1985, The Baton Press) and Wood and Campbell's Poussin's Secret (1995, Genisis Trading Co. Ltd.), not forgetting a host of works by the most famous populariser of the mystery, Henry Lincoln. Similar claims are made by Blake and Blezzard in The Arcadian Cipher (2000, Sidgwick & Jackson). Humility and diffidence do not sell books!
2. The Golden Ratio has been studied from the days of Ancient Greece, and probably before. Leonardo da Vinci wrote of it in De Divina Proportione, although whether or not he employed it in his art is open to question - although it is reasonable to assume he did. The ratio came into vogue last century through Le Corbusier and Salvador Dali, and commentary on its place in Renaissance art and architecture is widespread. The thoughts of Charles Funck-Hellet (Compositions et Nombre D'Or and De La Proportion: L'équerre des Maîtres d'Oeuvres, éditions Vincent, Freal & Cie, Paris, 1950 and 1951) are widely referenced in popular works on Sacred Geometry.
3. I am indebted to Adrian Lodge's Arcadia article The Curious Case of Mr. Rigby's Pentagon, which presents a separate but complementary analysis, for a most apposite (although surprising) quote by an academic and expert in the history of art, Prof. Martin Kemp: "... we have hundreds and hundreds of drawings by Poussin - thousands and thousands including his contemporaries - now, not in one of those is there any evidence of a geometrical armature, of angles, of precise proportions being laid down - either at the deeper level or at the top level. It's not there."
4. According to the Shugborough Guide, the Shepherds Monument is believed to have been instigated by Thomas Wright (1711-1786) from an idea in his Six Original Designs for Arbours (1755), and was carved by the Flemish sculptor Peter Scheemakers (1691-1781). The guide gives a date for the monument of 1748-1758.
5. The earlier version (Bergers 1) is dated c.1630 and is located in the Duke of Devonshire collection at Chatsworth, Derbyshire. Bergers 2 is given a date of c.1640 and can be found at the Louvre, Paris.
6. Andrews and Schellenberger op cit Plate 11.
7. This angle cannot, of course, be created by construction (that is, with compasses and an unmarked straight edge) but there are mechanism employing measured lengths by which it can be achieved. There is also a construction that derives an acceptable approximation to within 18 seconds of arc (0.005 degrees).
8. Summer, or Ruth and Boaz is the second of four paintings depicting the seasons through the illustration of passages from the Bible. Despite being the same size, each canvas depicts a different geometry and pentagonal form of increasing complexity in tune with expressions of light and colour reflecting the time of year. All four paintings are at the Louvre, Paris.
9. The ratio between the sides of images of this painting out of the frame vary. There is certainly a discrepancy between the version published by Andrews and Schellenberger and those in the photographic analysis provided by RLC Archive. I have used the latter as my guide - the former seems to be a parallelogram, as if both leaning and taken slightly off-centre - but the image I use here is taken from The Tomb of God.
10. Geometrical analysis such as employed here can be applied to other paintings to assess possible units of measure. For example, the dimensions of the canvases for Poussin's Seasons may have been based on a square of 36 pouces. A particularly interesting case is Dürer's Melancolia, where the results differ in scale and import from those of Deckwitz and others (see John Michell, The Dimensions of Paradise, 2008, Inner Traditions, pp 89-97).
11. For example, Andrews and Schellenberger op cit pp.139-146.
12. ibid pp.119-120.
13. Source: RLC Archive: Un autre Christ au lièvre (artiste inconnu). "On retrouve cette allusion dans une autre toile d'un petit village du Hainaut et d'un artiste inconnu. La tête d'un lièvre est effectivement visible sur le genou gauche du Christ." Site © 2004-2007, last accessed February 2008. There are no further details to pin down the location. The 'hare' isn't at all obvious in the painting by Van Dyck but assuredly is in the apparent derivatives.
14. Source: RLC Archive: Le haut du clocher sud. "Mais le plus surprenant est la forme du 4 exagérément incliné comme pour le rapproché d'un trace qui rappelle d'autres signes analogues ..." Site © 2004-2007, last accessed February 2008.
15. Source: Rennes le chateau: Pierre gravée par Boudet. "Cette pierre fût gravée a la demande de Boudet sur le fronton de l'église de Quillan. Est-ce une nouvelle clé pour l'énigme de Rennes le Château? Document appartenant à Jean-Claude Daniel." Site © 1997-2007, last accessed February 2008.
16. Jean Cocteau: La Chapelle Saint Pierre, Villefranche sur Mer, 1957, Editions du Rocher, Monaco. "L'autel, où sont gravés les armes de l'Apôtre, taillé dans un seul bloc des rochers de la Turbie, est l'oeuvre du jeune tailleur de pierres, Giovanni ..." For more images, and a discussion of associated pentagonal features, refer to the Arcadia article Last Message of the Initiate Jean Cocteau by Corjan de Raaf and Henry Lincoln's Holy Place.
© G.J. Bath 2008.
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