THE PYTHAGORAS_ THEOREM IN THE HIDDEN LAY

Autor
Waszlavik, L.
Publicado en
academia
Año
2024
Tema
ROSA
Idioma
English
Categoría
C3 Matemáticas
Número de archivo
2888

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The rigorg@&®but benecicent + transmitter of knowledge A Se LS PRE 5 e : ee mé ee ASE 2 "0 The "catching" of the" 7 action Pithagoras’ theorem à

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The painting was drawn to my attention by Zoltán Winkler, an educator and researcher, in November 2023, as a kind of riddle. I was required to identify the painting without the help of the Internet, which I could not do, but after he told me the title of the painting and that the central figure was Pythagoras, the next question to be solved was about the content. Later it turned out that Zoltán already had a solution, which I will come to shortly. I could only do one thing, I started on the more difficult way, which led to a result at about 100 pictures, based on a certain "EDM symbolism", which I published in 2021, and which seems to be the mainstream language of Western European Christian painting. It is identifiable from the early 6th century to essentially the present day, and has been inherited in part by classicist, historical and genre painting. In the meantime, I have been scouring the literature, where I have come across interpretations and theses that have proved to be both true and untrue. Some people see in the painting the legend of Pythagoras, a vegetarian and animal-loving scientist, who pays the fishermen for the fish he catches and then orders them to return them to the sea. I found a description of the painting as showing Pythagoras with a lance , but also a description describing a fish caught with a triangular mark on it. The latter statement, although perhaps not quite accurate and clear, and there are more substantial indications there, I was very pleased with because it provided the solution. Since one of the traditional meanings of the Milky Way is the life path, I concluded that the Pythagorean life path in the painting leads to the discovery of the Pythagorean theorem as a kind of "life goal", symbolized by the triangular sign, or in other words, the composition shows the "catching" of the Pythagorean theorem, which is the main moment of the scientist's life path. In a higher resolution image, I then saw that the fish was only faintly visible inside a large triangle (I will return to the contents of the net later), but at the same time I came across an earlier work by Salvator Rosa, where the painter had depicted this very Fig.2 [3] scene with a clearly visible right-angled triangle and obvious squares, which were a reference to the squares in the Pythagorean Theorem. So a weaker premise was dropped from a correct conclusion, but immediately replaced by a stronger one. From there, it was just a matter of refining the interpretation of the painting along the other components of the EDM ap paratus. As I sent Zoltan back the "solution", he sent me his article [1] published in the journal "Dobogó" in issue XXI. 4-5 of 2023 , where he had previously come to the same conclusion. I will briefly refer to this article. The work, entitled Deutsche Impressions, describes the painting in the context of an exhibition visit, drawing attention to its interdisciplinary pedagogical use, and then turns to the demonstration of the main content of the work, the Pythagorean theorem. On the left of the painting, a group of three and then a group of four fishermen are shown, in the latter group one of the fishermen is showing the number five with his palm open, so that a Pythagorean triple (3-4-5) is shown. What follows is the assignment of the 12 (13?) fig ures to the zodiacal signs. I would not rule out this possibility, although I see 13 or even 14 figures. The number of figures and the meaning of the number of figures would be worth further clarification, I would only add here that in my experience mythic painters often assign the number 12, typical for the Sun (solar calendar), to offensive themes, and the number 14, indicating the half of the "schematic" lunar cycle, or the number 15, approximating the synodic half-moon cycle from above, to sad, tragic, defensive themes in some form. Salvator Rosa is not very consequent in this sense, it is well known that his paintings are dark in tone and charged with stormy emotions. This 'inconsistency' is also evident here, where a discovery, an essentially positive act, is presented with a negative connotation. In relation to the numerosity of 12-13, the article raises the possibility of a Judas-type negative additional character - in a different sense, of course - referring to Py thagoras' legend about a murder, also referring to Salvator Rosa's painting Pythagoras Emerging from the Underworld. Finally, he gives an interesting literary analogy. In Rilke's poem Autumn Day, the number of lines in each stanza is 3, 4 and 5 (the smallest Pythagorean triple). The poem is written on the day of the au tumn equinox, the beginning of the darker half of the year (note that the darker half of the year is also an analogy for the underworld in astromythical language). *

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downwards. The situation is rather unrealistic, as if he were standing behind a very steep hill or in a ditch, otherwise where would his legs fit? We can conclude that there may be a third side of the triangle, but that it intersects the man outside the picture, or that the third side is the ground level on which the man holding the rope is standing. Unfortunately, this is not straight - we often see such a white "omega" shape in this place in mythical paintings, this is usually the representative of Capricorn in the so-called wraparound zodiac, but this is not a matter important enough to go into here. The situation is similar for the part below the belt of the left male, where additional zodiacal representatives "interfere" with the depiction. The important point is that the three men are most likely related to the three sides of a triangle. The next thing that is worth looking at, is the actors' line of sight. The man on the left and the tall man are looking into each other's eyes, the third is looking perpendicularly out of the picture. This could be understood as two dimensions, which refers to the triangle already found as a 2D shape , but the line of sight of the two looking at each other is particularly interesting. If the two pupils are connected, they form an angle of exactly 60 degrees with the line from the tall man's eye to the button of the garment, and this line has also been highlighted by the painter as a crease in the garment. This line is exactly perpendicular to the rope branch on the left - I have taken the bottom line here (the rope is slightly wavy, and I have laid the line on the bottom edge running from the tall man's index finger to the common line of sight). This gives us a famous right triangle (marked in purple in the third panel) whose shorter leg is known to be half of the length of its hypotenuse. Thirdly, the upper arms and forearms of the two men on the left are worth noting. They form roughly a square, which may be a reference to the squares in the Pythagorean theorem (a 2+b2=c2). Not so obviously, but even in the third man, such a square detail at the shoulder on the right is interpretable. From what has been said, it is clear that the etching also refers to the Pythagorean theorem. The Pythagorean theorem embedded in the painting is most rigorously and obviously revealed by the EDM apparatus. On the one hand, "EDM" is an "exile-domicilemonogramed" axis system hidden in (sacral) paintings and used almost exclusively until the Parisian isms, but it is not a symbolic skeleton for its own sake, it is more than that, it allows painters to support the secret content of the paintings by several traditional methods, among which I would highlight the distribution of planets between the characters, the Milky Way symbolism and the place of the Jesus monogram. The description of the EDM system and the practical use of the EDM apparatus has been published in several works - I would recommend [4] as a starting point - but I will briefly describe it here too. In the oral and visual arts, the zodiacal structure is an imprint of the annual natural cycle (and the precessional cycle). In the Christian era, this can be dated to the period after the 'catacomb art', when representation moved from genre art to a more symbolic one. An example of this is the depiction of Jesus Pantocrator in the St Catherine's Monastery of Sinai, where I see a simple face with the 12 signs of the zodiac, the darker half of the year on one side and the lighter half of the year on the other, which can be interpreted as the earthly and heavenly faces of Jesus (I believe the heavenly-earthly interpretation comes from the Hungarian researcher Csanád Dobos). The zodiac symbolism is much older, but this may be the time when it became integral with Christian painting. A typical oral example might be the fourth-century legend of St. Paul the Hermit by St. Jerome, which traces the 12 stages of the zodiac from the Sun's rulership (Leo) to the Moon's rulership (Cancer) [5]. This principle coincides with the more "ancient" layer of EDM images, where a socalled wraparound zodiac is always observed, where the zodiacal signs are hidden roughly in order along the circumference of the painting, similar to the 12 numbers on a clock face. Typically, Aries is at 9 o'clock and the zodiac rotates to the right, so Cancer, corresponding to the highest solar position, is at 12 o'clock, Libra, corresponding to the autumn equinox, is at 3 o'clock, and Capricorn, corresponding to the lowest solar arc, is at 6 o'clock. The Ptolemaic principle of planetary dignities is likely to have influenced the relationship between the planets and the zodiacal signs in both the oral and visual arts, above all in the form of the exil and domicil dignities of the planets. In paintings, this can be seen in the way that, in addition to the wraparound zodiac mentioned above, the seven astrological planets are represented in the picture, each of which is strictly aligned with the exil and domicile signs of the planet in question, of which there may be one or two (see Figure 5).

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In principle, each planet can have a hidden axis, which I have called the exile-domicile (ED) axis of the planet, and since there are seven astrological planets, the number of these is seven by default. However, Table 5 shows that where Mercury is in exil dignity, Jupiter is in domicile, and vice versa. This means that the exile-domicile axes of Jupiter and Mercury can be conjunct such that the representatives of Jupiter and Mercury and their common exile-domicile signs lie on it. Such merging is often used by painters, and thus the number of hidden ED axes in a painting may be fewer. The same is true for the Mars-Venus pair, and even for the ED system of Saturn, which includes the ED systems of the Sun and Moon. It can be seen that the number of secret axes associated with the planets can vary between 3 and 7. This number can be increased by one by the Milky Way, which painters can include as an additional secret axis. In the sky, the Milky Way is fixed to the zodiac, with its upper stem running between Taurus and Gemini and its lower end splitting into two branches, one running into Scorpio and the other into Sagittarius. This allows for several two- and three-point codings, which are used in tradition, but most often the Milky Way is coded for the Sagittarius-Gemini axis. The number of secret axes can thus vary between 3 and 8, including the Milky Way. This exile-domicil axis system corresponds to the ED component within the EDM acronym. The "M" refers to the Jesus - monogram, since in paintings with the EDM system there are always 3 ED axes that intersect at a point, one being the exact angular bisector of the other two, and on which an arc is written as visible in the picture, giving a 4th century Jesus monogram where the "X" and "P" that make it up, have the "P" headline running into the intersection of the "X". All in all, each EDM picture shows a rather complex and unique astromythical system, with the exile and domicile signs of the planets partly taken from the wraparound zodiac, but to create the right composition, the painters add a large number of additional exile and domicile signs. So far this is the EDM system itself, but what do painters use it for? Analysis of a large number of paintings has shown that if there is hidden content in the painting, this line system tends to support it. The painters refer to the hidden content mainly using three components that can be identified from the EDM system (of course there are more). 1. Allocation of planets in paintings with several actors. The principle is that the planetary character is transcribed to the character in which the representative of the planet is hidden. For example, the Sun is the main character, the Moon is a supporting character, etc. The identification of planets is greatly facilitated and confirmed by the precise definition of the EDM axis system. 2. The Milky Way symbolism. The Milky Way has traditional meanings. As one of the most luminous paths in the night sky that cannot be trodden - and is therefore not of the thisworld - it has long been associated with the idea of a path connecting the thisworld and the afterworld, on which a person or a human community (e.g. dynasties) is born from the afterworld to the thisworld, or on which they return to the afterworld. It has also been given a "reincarnation" meaning, when it is the common path of actors born into the same role. It can mean the transcendent, but also, in certain contexts, the ordinary path of life, and sometimes also a heavenly providence or nourishing force (such as the spouting of Hera's milk in Greek mythology, from which the Milky Way takes its name). Painters use all the meanings listed. 3. The location of the Jesus monogram. The character or situation on which the Jesus monogram is placed receives divine protection. In the case of a secular subject, this can mean fateful favoritism, election, or even simple luck There are other aspects arising from the traditional astromythical language, such as the many "rebirth" analogies associated with the Pisces-Aries transition (so-called End-Beginning coding: foundation, resurrection, healing, restoration, etc.), but the three points listed are sufficient to examine this painting. We will begin our detailed exposition of the EDM system by showing the so-called wraparound zodiac, which runs clockwise, roughly along the circumference of the painting (thin white polygon - Figure 6). To identify each zodiacal sign, we need to know that it can be represented by: 1. A direct representation of the animal or animal head representing the western zodiac sign or the nonanimal sign; 2. The graphic symbol of the western zodiac sign, whether in handwritten, stylized or other recognizable form; 3. A representation of the animal or animal head of the Eastern Zodiac; 4. A depiction of the lunar mansion's animal or the head of the animal associated with the sign of Zodiac; 5. Depicting other established analogies, such as the middle-aged female head for Cancer, or the young boy's head and young girl's head side by side for Aquarius . There is a fixed symbolic correspondence between the signs of the western and eastern zodiac and the groups of two and three of the 28 Chinese lunar mansions, which was published in Hungary in 1985 (the so-called Pap-Kustár circle). This is a triple correspondence system specific to Europe, and it differs from the

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u6)UINVIuooabbeiidg “FX|ınına9DIA|o¡eyng‘xO Aayuowsnruvndv$ 3YM3V1NSS0OOYN SJlNa‘Jq=i9uItaeSigHe=s¡UNpOeAr|‘ALDVIONDOOdWI3SNd3AYUHDNSOSVDIISd=0*<Se= The Hungarian triple animal wheel system of the Astral mythica symbols. G ©iva u/14091I0uU3NS Yo NOSvud NUODIUdVI ‘3u8q9ex oP9yUeIuOsH ULIOM oxeus ‘3d2o09us Bid ‘m118o9934eg o‘s1no2yH co N

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corresponding to the vernal equinox and is usually located around 3 o'clock. Figure 8 shows that on the headlines of the two men on the left side of the painting, the graphic symbol of Aries can be written. This is a familiar solution, as we see in Leonardo's Last Supper, for example, on the two apostles to the right of Jesus. The painter can use it to assign 12 signs to the 13 people behind the table. The second sign of the zodiac (from the vernal equinox) is Taurus, which can be represented in many ways. Here the painter has favored the two possible Chinese lunar mansions These are the Dove (Pigeon) and the Pig, the Pig being also a zodiac sign. These representations of Taurus can be recognized in the head of the green-clothed disciple holding the book. Roughly speaking, the hair of the disciple already forms a rightfacing dove, especially the tail, although the head is not visible and therefore is not a perfect representation, but rather a reference to the Dove. With a good imagination, a Fig. 8 [3] pigeon with extended wings en face can be seen inside the head of the disciple, here the man's ear can be the head of the pigeon. The most reliable code, however, is the pig's head, which can be seen on the left side of the face, showing the pig's round nose, two round cheeks and the left ear (Figure 9). Fig. 9 [3] I have also included the representation of the next sign, Gemini, in Figure 9. Two figures talking and facing each other can bring Gemini, and this is what we see in the figure, but there is also a smaller Gemini representation. Over the green-clothed disciple's ear looks an owl, which is the lunar mansion of Gemini (see table). For better perception, I also bring this owl head in the upper right corner of Figure 9, contrasted and enlarged, in a yellow frame. This owl, by the way, is not only the Gemini's representative of the wraparound zodiac, it is also part of the Sagittarius-Gemini coded Milky Way, where it brings the sign of Gemini. Fig. 10 [3] As a rule, the representative of Cancer corresponding to the summer solstice is at the top center. Here, in landscapes, there is usually a cloud, and in our case, this is also where the head of the woman with which the painter has encoded the sign is to be found. We search in vain for this representation in the table.

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This coding habit of the painters probably stems from the fact that the mother (the old family in general) belongs to the fourth house of the horoscopes, and in the zodiacal circle analogous to it, Cancer is also in the fourth position, i. e. from the vernal equinox. Numbering from the vernal equinox is the most typical, and mythical numbers in fairy tales are often derived from this principle. It takes a lot of practice to identify the figures written in the clouds, so I've also contrasted the image a bit, but it's also worth looking at a larger enlargement of a given motif, sometimes it's clearer that way. Whether or not a particular representation has been correctly identified can usually be confirmed by referring back to the complete EDM system already determined in cases where that representation is required for an ED axis. In this case the representative, in our case the female head, either must enclose the axis together with another representative or the axis must pass through the eyes, nose or mouth of the animal or human. For some of the representations resembling mainly graphic symbols (Libra, Scorpio, Virgo, Mercury, Aquarius, Moon), the axis usually passes through the corner of the representative, but the axis passes through the circle representing the Sun, and for Jupiter and Saturn it passes through the cross. The representation of Leo of the wraparound zodiac is shown in Figure 11. Fig. 11 [3] Identifying the representative is also a difficult task here, I have indicated two possibilities. I also drew the end of Saturn's ED axis, which confirms that the motif is worth looking here (Leo is the exil sign of Saturn). The sixth sign from the vernal equinox is Virgo. It is represented by animals (cat, bear), a young girl's head, a female head with coif (nun's head), but often by the stylized graphic symbol of the sign. The latter consists of three vertical lines, similar to the graphic symbol, and a short section at the bottom of the three lines, pointing inwards into the block, which can be seen as a loop 'pointing back on itself'. A similar solution is also used for Scorpio, except that there it should be an arrow pointing outwards. The left half of Figure 12 shows the corresponding detail of the painting, here the three verticals are formed by three sail poles, the backward pointing section being part of one of the boat hulls. It is also worth mirroring the figure, so that the third sail appears to be a loop of the graphic symbol. It is possible that

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two other ED axes. As shown in Figure 1, the Jesus monogram is placed on the head of a man sitting on the ground, with one arm of the "X" on the ED axis of the Sun, the other arm on the ED axis of Mars and Venus, and the angular bisector (the stem of the "P") on the ED axis of Mercury and Jupiter. Mythic painters also like to form multiple nodes, which can be a confirmation that we have the system correctly revealed. Such is the fact that a fourth line, the ED axis of the Moon, passes through the triple node of the Jesus monogram. Let's start with the Sun's ED axis (Figure 15), on which only the Sun, the Sun's domicile sign (Leo) and exile sign (Aquarius) should lie, as the Sun has only one exile and one domicile sign. Fig. 15 [3] I have marked the ED axis of the Sun with a translucent white line. The lower end starts from the eye of the recently identified representative of the Aquarius. The line is touched from the left by the lion's head inscribed in the hair of the low disciple facing right, but this is only for confirmation. The regular display of the domicile sign is the lion's head en face in the hair of Pythagoras, with the axis passing through the corner of the eye. This is shown enlarged in the right panel of the figure. The Sun is represented by Pythagoras' round head. The head of the man sitting on the ground also lies on the axis, but it is not so round. Hidden in his face is a right-facing Moon, and we will see from the fuller context of the work that Pythagoras is playing the role of the Sun. The Moon, like the Sun, has only one domicile and one exile sign, Cancer and Capricorn. Here, the painter has taken both signs from the wraparound zodiac of the painting. The Moon's ED axis, marked in turquoise, runs from the upside-down goat's eye (Capricorn) to the eye of the cloud-mother (Cancer). As mentioned, the Moon is represented by the right-facing face of the man sitting on the ground, touched by the Fig. 16 [3] axis. This is an established custom. The fact that the seated man is encoded for the Moon is no coincidence. We mentioned that the character of the planets written in the figures is transmitted to the person. We will return to this point in the interpretation of the painting. Let's continue our study of the ED system with the common ED axis of Mars and Venus (Figure 17).

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On the common ED axis of the two planets, in addition to the representations of the planets, the representatives of Aries, Taurus, Libra and Scorpio must lie, because Aries and Scorpio are the domicile signs of Mars, and exile signs of Venus, while Taurus and Libra are the exile signs of Mars and domicile signs of Venus respectively. Although the axis in red is close to the two heads representing Aries in the wraparound zodiac, the Aries of the ED axis is represented by the "V" composed by the book in the hand of the green-clothed disciple and the hand of the disciple, whose corner lies on the axis. The solution is not very elegant, because it does not bring the outward bending shape of the Aries symbol. Venus is most often encoded by painters with a pentagon, less often with a five-pointed star, and even less often with a curved "V". In our case, the group to the left of Pythagoras shows a darker pentagon (see Figure 1), intersected by the ED axis. The other planet, Mars, is represented by its graphic symbol. Its circle can be traced on the thigh of a fisherman climbing into a boat. Attached to the circle is the 'arrow' of the graphic symbol in the form of a long line on the thigh. This and the upturned dove inscribed in the lower leg enclose the end of the axis (this detail is framed in yellow in the top right corner of the figure). The Dove is the lunar mansion of Taurus, so we have that sign. The fisherman itself, with its shape, gives Libra, and the axis passes regularly at the corner of the graphic symbol of the sign ("capital omega"). The only sign missing is Scorpio. It is often represented in mythical representations by a human or animal arm or foot system, and as mentioned above, it consists of three vertical lines and an arrow pointing away. I have marked this representation in turquoise. The three vertical lines are the fisherman's two legs and one arm, the arrow pointing forward is his other arm. The Scorpio's representative touches the axis regularly from above (the axis essentially passes through the corner of the graphic symbol).

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Figure 18 shows the common ED system of Jupiter and Mercury. The handwritten graphic symbol of Jupiter can be recognized on Pythagoras. The arc of the graphic symbol starts from the round head of the scientist, and the cross is formed by the horizontal forearm and a vertical wrinkle of cloth. Mercury is represented by its most common symbol, an arched 'M', which appears on Pythagoras' chest. The ED axis of the two planets, marked in yellow, passes, as a rule, through the cross of Jupiter's graphic symbol and the corner of the "M". In addition, the axis must also pass through the representatives of Sagittarius, Gemini, Virgo and Pisces. Sagittarius is represented by the figure of the horse outlined in purple in Figure 18, as the Horse is the eastern counterpart of Sagittarius. This enclose the ED axis with the head of the rooster (=Pisces) written on the knee of the green-clothed disciple. Gemini is often represented by two heads or persons facing each other, or two heads or persons facing in opposite directions. Note that the hair of the man sitting on the ground contains a backward-looking face, which, together with the forward-facing face, gives Gemini code. I have enlarged this head at the bottom center of the figure and outlined the backward-facing face in yellow. This Gemini code lies also on the ED axis. All that is missing is the representation of Virgo. There are two of these. There is a cat's head (=Virgo) hidden under the horse's head, and another to the left of Jupiter's cross. These are shown at the bottom left and right of the figure, both in the original and outlined, marked A and B. This provides all the necessary representatives. Fig. 19 [3] Saturn's ED system is illustrated in Figure 19. The planet is represented by its graphic symbol, with the cross inscribed on the horizontal forearm and the vertical edge of the cloak. The possible curve of the skirt of the graphic symbol is clearly visible, the horizontal section of the skirt can be drawn with a certain degree of freedom, but only the position of the cross is really important, because it must lie on the axis. On the axis, marked in gray, should be the signs of Capricorn, Aquarius, Cancer and Leo. The lower end of the grey ED axis is enclosed by the familiar goat's head (marked in green) and young face (marked in yellow), which are the Capricorn and Aquarius representatives. The other end of the axis ends at the mouth of the wraparound zodiac's Lion, but before that it passes through a cloud-mother, which brings Cancer. This is not the same as the Cancer representation of the wraparound zodiac, the latter lies further out. The two eyes of this "secondary mother" are quite visible. This gives us the four signs we need.

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The last secret axis, the Milky Way, is of great importance for the interpretation of the painting. The most common encoding of this is Sagittarius-Gemini. The Milky Way lies on the two hands of Pythagoras, and even on the index finger of the left hand, with the familiar little owl at the ear of the green-clothed disciple, representing Gemini, and two Sagittarius representatives. One of these is the bow-shaped back arch of the fisherman bending forward in the boat, with the 'arrowhead' ending in the darker-toned, protrusion of the garment. The other representation is inscribed on the branches of the rope and on the fisherman's hand pulling out the net. One of the traditional meanings of the Milky Way is the path of life, and here, as clarified earlier, it leads to the place of the " catching of the Pythagorean theorem ", which can be interpreted as the end point or result of the scientist's life. This conclusion corresponds to the second paragraph mentioned in the evaluation mechanism of the EDM analysis ("Milky Way analysis"), but it is also confirmed by the analysis according to the first and third paragraphs (according to the planetary assignment and the Jesus monogram). Let's look at the position of the planets. Mars, which is on the thigh of the fisherman climbing into the boat, is of minor importance. Mars is the planet of action, and in our case it is in the part of the painting where the actors are acting, pulling out the net, rowing, or filling the baskets with the loot. The other planet of lesser importance is Venus, which can be recognized in the group of disciples close to the master, otherwise adjacent to the sign of Taurus in the wraparound zodiac. This may represent music, dance, ritual meals, which may be related to the lifestyle of the Pythagorean sect and the music theory of the scholar. It is important to note that Pythagoras represents the Sun, Mercury, Jupiter and Saturn, while the man sitting on the ground represents the Moon. The Sun is typically the protagonist and the Moon a supporting character, the latter being a kind of subordinate to the Sun. Pythagoras is essentially pointing to his own theorem with both hands, but he is looking into the eyes of the seated man, who is looking back at him, and so he is explaining to him. This means that there is a kind of master-disciple relationship between them, which is confirmed by the Sun-Moon coding. Mercury often indicates some kind of mediating, transmitting role. In our case, Pythagoras is clearly giving mathematical knowledge to the recipient. Jupiter is the planet of wise old men, and in this context it gives Pythagoras a pedagogical character, while Saturn in this context may represent a kind of teacher's rigor, tutoring, orientation. Finally, let us evaluate the position of the Jesus monogram. The arc of the P of the monogram is written on the head of the recipient. This means that the seated man is a "beneficiary", lucky, he benefits from knowledge. It is worth taking a closer look at the recipient of the knowledge in Figure 21. His figure forms a right-angled triangle (marked in translucent green), and his right (for us) arm together with his torso forms a square (marked in translucent yellow). It is as if he has stepped off the print we examined at the beginning of our study. But the most interesting is the triangle obtained by connecting the prey embodying the Pythagorean theorem, the scientist's head vertex, and the sitting point of the triangle pupil (the latter I have considered to be the center of the goat's head). This is a right-angled triangle with a 3:4:5 aspect ratio, which brings the smallest so-called Pythagorean triple. The number triple that Zoltán Winkler observed in the painting...

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Literature and illustrations 1. Winkler Zoltán: Német benyomások, Dobogó folyóirat, Két Hollós kiadó, 2023 XXI. 4-5-ös szám; (Winkler Zoltán Deutsche impressions, Journal Dobogó, Két Hollós Publishing, 2023 Issue XXI. No. 4-5) 2. A man pulling a net with two figures behind him, from the series 'Figurine', ca. ..., ca. 1656-1657. .CC0 Public Domain Designation 3. https://commons.wikimedia.org/wiki/File:1662_Rosa_Pythagoras_und_die_Fischer_Kat._Nr._59.1_anagoria .jpg; public domain, 4. Waszlavik László: The zodiac as a hidden ABC of painting... Demonstration of the "EDM" coding system on the painting "The nativity" from the Belvedere gallery in Vienna, Academia. edu, 2023 5. Waszlavik László: The life of Paul of Thebes, the hermit – as a Zodiac tale, Academia Letters, 2022 6. Irina Palagina: Зодиакальный круг в китайской астрологии The illustrations also include processed images