Architectural mathematics of ancient Russian architects

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

The buildings of ancient Russian architects still delight with thoughtful proportionality, amazing harmony of their parts, strict logic of architectural design.

The methods of architectural calculations of the XI-XIII centuries are almost unknown to us. Approaching their disclosure with our modern standard, considering ancient architecture from the point of view of Euclidean geometry, we can discover and mathematically substantiate the proportional relationships contained in it. An interesting and valuable work in this direction has been done by K. N. Afanasyev.

However, we are not at all certain that the ancient Russian architects followed the same path in their calculations, starting from the theoretically irreproachable positions of the great Greek geometer.

On the contrary, the evidence of medieval mathematicians speaks of their contemporaries using approximate, practically convenient, but theoretically unjustified calculations.

For example, the famous Persian mathematician Abul-Wafa, a contemporary of the most ancient Russian church buildings, translator of Euclid and Diophantus, wrote in the preface to the collection of geometric problems compiled by him: “In this book we will deal with the decomposition of figures. This question is necessary for many practitioners and is the subject of their special research … In view of this, we will give the basic (theoretical) principles that relate to these issues, since all the methods used by workers, not based on any principles, are not trustworthy and are very erroneous; meanwhile, on the basis of such methods, they perform different actions."

Unfortunately, these "methods used by workers" in architecture and craft remain unknown to us.

The mystery of calculations and recipes was characteristic of all medieval craftsmen; even passing on the legacy of teachers and their experience to students, they tried to encrypt their advice, hiding, for example, under the name of the "yellow lizard" gold. Probably, the mathematical calculations condemned by Abul-Wafa were also the architects' secret.

In Russian medieval literature, there are several interesting records that highlight certain details of the calculation and construction process. In the well-known story of the Kiev-Pechersk Paterik about the construction of the Assumption Church in 1073, attention was usually paid only to how the church was measured with a golden belt: “20 in width and 30 in length, and 30 in height; walls with a spacing of 50.

But it should be noted that, in addition to these valuable data, the Paterik's story gives an almost complete description of the process of preparing a construction site: choosing a dry, elevated place where morning dew does not lie, leveling the site ("valley") to designate ditches on it ("like a ditch like "), Making a wooden standard to the extent of the golden belt (" … the tree is a creature "), marking first the width and then the length of the building in certain measures, digging ditches, and, finally," setting up roots ", that is, laying a stone foundation.

Historians of architecture have never paid attention to the most interesting information about the calculated work of the architect, contained in the Slavic "Legend of Solomon and Kitovras", which is a fabulous reworking of the stories about the construction of Solomon's temple (XII century).

King Solomon needed a wise centaur - Kitovras to draw the plan of the temple he had planned.

In Russian applied art and architectural ornamentation, images of the centaur-Kitovras are quite common. Mention should be made of the centaurs with rods on the walls of the St. George Cathedral in Yuryev-Polsky (1236).

The image of a wise centaur with a finger at his forehead (gesture of reflection) on the sash of a silver bracelet of the 12th-13th centuries. from the so-called Tver treasure of 1906. The wise Kitovras is depicted here surrounded by three elements (water, earth and air) and representatives of two kingdoms of nature - animal (beast) and vegetable (fruit-bearing tree) (Fig. 1).

"The Legend of Solomon and Kitovras" has preserved for us the ancient Russian name of the architectural plan - "outline"; Solomon says to Kitovras: "I didn’t bring it to my needs, but to simplify the outline of the holy of holies."

The most important thing in this episode is that Kitovras, knowing in advance that he was called by the king to make a plan for the future temple, came to him with wooden yardsticks, standards of some measures: “He (Kitovras) dying a rod of 4 cubits and entered tsar, bow down and lay down the rods before the tsar in silence …"

It is especially interesting for us here that the main tools of the architect, which he needs to create the "outline", are wooden yardsticks (described in the plural), 4 cubits each. An appeal to ancient Russian metrology shows the complete reliability of the Legend's messages: firstly, in ancient Russia several types of fathoms were used simultaneously, and secondly, each fathom was subdivided into 4 cubits; this division existed until the 16th century.

Obviously, the magical architect Kitovras was endowed by the author of the legend with the real accessories of the Russian architect in the form of fathoms made of wood, subdivided into 4 cubits.

These two references in the literature of the XII-XIII centuries. about the initial stage of construction of buildings - in the Patericon and in the "Legend of Solomon and Kitovras" - they speak alike about the significance of the established measures, their portable standards and the very process of measuring the "outline" of the temple on the leveled "valley".

All this makes us pay special attention to the issue of ancient Russian measures of length and their application in architecture; this will help reveal the working methods of ancient architects. We know some architects by their names preserved in chronicles.

The only image that is supposedly associated with the Russian architect Peter, known from the annals, was found in the tower of the Antoniev Monastery in Novgorod.

In 1949, I made an attempt to revise the Russian medieval metrology in order to use measures of length in the analysis of architectural structures.

The main findings are:

1. In ancient Russia from the XI to the XVII century. there were seven types of fathoms and cubits that existed at the same time.

Observations on Russian metrology showed that very small and fractional divisions were not used in ancient Russia, but a variety of measures were used, using, say, "elbows" and "spans" of different systems.

Old Russian measures of length can be summarized in the following table:

2. There are a number of cases when the same person measured the same object at the same time with different types of fathoms.

So, during the repair of St. Sophia Cathedral in Novgorod in the 17th century, measurements were carried out with two types of fathoms: “And inside the head, there are 12 fathoms (152 cm each), and from the Spasov image from the forehead to the church bridge - 15 measured fathoms (176 cm each).) , During the construction of the notch line in 1638, “a rampart 25 fathoms wide was felled and 40 fathoms for simple ones”.

Analysis of architectural monuments of the XI-XV centuries. made it possible to assert that ancient Russian architects widely used the simultaneous use of two or even three types of fathoms

3. The simultaneous use of different measures of length, which is incomprehensible to us, is explained by the strict geometric relations incorporated in these measures during their creation (Fig. 3).

The geometric conjugation of the Old Russian fathoms is especially clear in the naming of "straight" and "oblique" fathoms. It turned out that the straight fathom is the side of the square, and the oblique is its diagonal (216 = 152, 7). The same ratio exists between “measured” and “great” (oblique) fathoms: 249, 4 = 176, 4.

"Fathom without fathom" turned out to be an artificially created measure, which is the diagonal of half a square, the side of which is equal to the measured fathom.

4. The graphic expression of these two systems of measures of length (one based on "simple" fathoms, and the other based on "measured" fathoms) are well-known from ancient images "Babylon", which is a system of inscribed squares. The name "Babylon" is taken from Russian sources of the 17th century. (see fig. 3).

New archaeological finds of mysterious drawings - "Babylon" - at the Taman settlement (ancient Tmutarakan) and the Old Ryazan settlement, dating back to the 9th-12th centuries, make it possible to significantly deepen the analysis of these drawings and establish their close connection with the process of architectural calculation.