Construction and measurement by Russian Sazhenami. Essence, meaning and practice. How to make the simplest surveying tool with your own hands? Rules for designing a house by sazhens

This statement by B. A. Rybakov is confirmed by his published series of “Babylons” - drawings by medieval architects, which depict squares and rectangles inscribed into each other.

Indeed, considering the drawing of the Dimensional Angel, we found that ABCD is a square with a side equal to the folk, or flyweight, fathom.

Diagonal of square ABCD with side a, equal to the people's sazhen, will be equal to the Pythagorean theorem √ 2 X a = 248.90 cm

We also established that the diagonal going from the feet of the dimensional angel to the upper left corner of the square ABCD, that is, the diagonal of the semi-square, gives us the expression a X √ 5 / 2 = 88 x 2 ,236 = 196,77 cm, which, with an accuracy of 0.4%, corresponds to the size of the royal sazhen.

If for A 2 i denote the national sazhen, then √ 2 x 176.00 there is an element of the table that is six steps to the right from the folk one, that is

BUT 2(i +6) = √ 2 x A 2 i .

In the figure, this is the segment OL = √ 2 x OF .

Accordingly, finding the royal sazhen is described by the relation

BUT 2(i +2) = 6 √2 x A 2 i\u003d Phi 6 / 16 x A 2 i,

that is, the royal fathom is 2 steps to the right from the folk one, and in the figure it corresponds to the segment OH.

Let us show in Table 3 the original sazhen and two sazhens derived from it.

Table 3

It is quite clear that similar constructions can be performed for all other known fathoms, and for each of them two more fathoms derived from it can be obtained. The fact that these architects used this method is clearly shown by their drawings that have come down to us, published by E. A. Rybakov.

In general, we have the following relations:

BUTk (i +6) = √ 2 x Aki , wherek = 1, 2, 3,i - any natural number;

BUTk (i +2) = 6 √2 x Aki\u003d Phi 6 / 16 x Aki , wherek = 1, 2, 3,i - any natural number.

Let's show you what happened. Green shows those elements in which the derivative of a fathom from the known one coincides with the already known one. We will not perform any actions with the city sazhen, since it is a double small sazhen, that is, the process of multiplicity from a small sazhen.

Table 4

The next very interesting topic is the arshin and the three-arshin or one and a half sazhen.

The word "arshin" has its root "arsh", which means "determining measure". Through the concept of "arshin" another of the most important properties of the Golden system of sazhens is manifested.

Let's take a look at Vladimir Dahl's Explanatory Dictionary of the Living Great Russian Language.

ARSHIN - ... four quarters (spans), four inches each ...; a third of a sazhen; the length of the entire arm from the shoulder; free step of a person, ... 0.711 meters.

So, arshin defines the "reach zone" - everything that is at arm's length or one step. Symbolic, isn't it? And each of us lives according to his own yardstick, and not according to someone else’s - “everyone measures by his own yardstick”, that is, he measures it with himself, with his internal energy device, chooses what exactly is consonant with him - the only true process.

And now, placing objects on my desktop so that it is convenient for me to work and easy to reach them, I use my arshin.

There are four spans, sixteen inches in an arshin, it is one third of a sazhen and is equal to 0.711 m.

Well, like this - 0.711 m and not a centimeter less or more? In such a “reach zone” I would have to stretch with all my might, and my long-armed and long-legged companion would be cramped - we have a difference of arshins - her step, mine is almost one and a half ...

Let's turn to another public source, the Internet contains a large number of this kind of reference tables:

But why an arshin a third of a sazhen? The fathom is not divided into three parts, only bifurcation or doubling - this is the algorithm for the formation of fathoms and their elements. But why is it necessary to share? Can't one fathom turn on into itself three elements of another fathom with a sufficient degree of accuracy? Of course it can. There are 16 vershoks in an arshin, which means that an arshin is half a sazhen, half of some sazhen - after all, there are 32 vershoks in a sazhen. This means that the fathom that formed the arshin - 2 x 71.12 cm = 142.41 cm - is a small fathom, the deviation is vanishingly small - 0.17 cm. Then three arshins - 213.36 cm - this is a fathom, which is one and a half times more than a small fathom.

A.F. Chernyaev in the book “The Gold of Ancient Rus'” wrote that the architects used not only single fathoms in their work:

“In the process of laying out, not only single fathoms were used, but also one and a half, double and 2.5-lengths. Doubled most often became smaller, small, simple and masonry. The most famous is the double small 2.848 m long, which has its own name - city.

Let's look at our table - one and a half, three-arshin fathom from a small one - this is the seventh element to the right of it.

Table 5

Let us write the manifested dependence in general form:

BUTk (i +7) = 3 x Aki / 2= 1.5 x Aki, wherek = 1, 2, 3,i - any natural number.

Let us show, as we have already done, in the table of sazhens the main sazhens and their three-yard correspondences.

Table 6

Comparing Table 4 and Table 6, we form Table 7.

We can clearly see that I use simple, well-known , and therefore the ratios that have come down to us, the architects of Rus' received and used in their work both the 14 basic fathoms, and other fathoms of the Golden System, obtained from the basic ones either completely accurately, or with a very high degree of accuracy.

Table 7

But one last element remained - the 12th in the first group, with its attractive whiteness saying that we have not yet received a complete picture.

The golden system of sazhens contains countless connections of one element with another and with others. What was revealed to me is a small drop, and by telling you about some of the interdependencies and complementarities that I was able to see, I sincerely hope that my story will also interest you, and together we can see more and more clearly.

The seven-partness, incorporated in the Golden System of fathoms, was not yet public knowledge, but quite the contrary, it belonged to sacred, hidden, stored and protected knowledge. But who took it upon himself to divide knowledge into available to everyone and, so to speak, knowledge for personal use ? And for what purpose?

So, Sevenfold.

The number 7 is the number of Truth. Christianity also manifested itself here in its own way, completely unfoundedly declaring that 7 is the number of Christ. This is the approach of any liar and thief - if a lie is repeatedly propagated in writing and repeated millions of times orally - there will be those who will believe simply because they have heard it often or read about it many times.

Now I will quote A. F. Chernyaev. I do not doubt the sincerity of his statements, but I have a different point of view on the essence of the number 7. And another important addition from my point of view - A.F. Chernyaev, speaking about the construction of temple structures, implies the construction of Christian churches. I have a different point of view - that many of these great creations was built with a completely different purpose: as helping people to enter higher energy-informational layers, that is, as energy accumulators for the transition from interaction with the planetary volume of the Earth to interaction with the volume of the Cosmic Unity of Matter. These structures were simply captured by the Christian church after the violent and bloody Christianization of Rus' and reprogrammed in a special way - reconfigured to suit the tasks of the conqueror. To make my thought more understandable, I will briefly explain that modern chronology with its so-called " millennium the Baptism of Rus'" I consider it a conscious falsification and a lie, like all modern "history".

But this is a completely different topic ... Therefore, having made only the necessary explanations that determined the difference in views in the scope of the general topic, I turn to the book "Gold of Ancient Rus'".

“... The master is an architect, in a modern way - an architect, in Rus' he did not calculate the relationship and conjugation of sizes, did not calculate the golden proportions, because he did not know anything about them, and there was no need for this. Since, having “Semer”, he chose the commensurability of fathoms according to the rule of groups and according to the quality (significance of the church, for example) that the object required for its intended purpose. He did not even imagine, apparently, that something could be considered for an object, since he operated not with commensurable centimeters, but with incommensurable sazhens, and he knew that only by following the methodology - the canon, you can get a beautiful conjugation of proportions, harmony, object.

The proportions were not calculated because they were originally laid down in the lengths of fathoms, and a set of several fathoms, chosen according to the canon, always makes up a proportion ... a multiple of the golden number (Phi).

In addition, it seems that the sazhen was not a directive invariable tool, and the master, depending on his design and the status of the structure, had the opportunity to slightly change the length of the sazhen so that the harmony of the proportional division of the object into parts would pass from explicit to implicit, hidden, and the hidden harmony was not visible to the uninitiated. It must be assumed that the masters, if they did not know, then felt such an aesthetics of proportions, which Heraclitus fit into one sentence: "... the hidden proportion is stronger than the explicit one", and Plato described it as: "... similar is a thousand times more beautiful than unlike .. . . The relation of the part to the whole and the whole to the part can arise only when things are not identical and not completely distinguishable from each other.

A sazhen for an architect did not become a charter. It did not remain an immutable tool on maternity leave. He probably had the opportunity, even without understanding the reason for it, to change its length within 1%, which, as already mentioned, does not affect the proportioning, but “blurs” its boundaries, which, moreover, were deliberately made more “vague” ...

The sazhen as a latent process with a doubling of length changes its dynamics. The proportions displayed by it become, as it were, mobile. Dynamics of moving proportions plunges a true Master, a master with a capital letter, to create a harmonious object in co-creation with God. And the more spiritual the Master possesses, the more subtle his sense of the sublime and uplifting, the more impressive the product of this co-creation will be.

Here it should be noted that the importance (or significance) of objects in antiquity was emphasized by double, triple and even greater combination of commensurate instruments used to measure the same parameter (that is, the height, length or width of an object).

Let's also turn to the article "Gold of the Heavenly Account". In the article A. F. Chernyaev answers the questions of the journalist S. Kalenikin. I took the liberty of correcting the journalist's inaccurate wording by italicizing this passage.

- ...Let's clarify: what was taken into account during construction first of all? Did the ancient masters use any special principles when constructing objects?

“Of course, and there were a lot of them. So, if we now build anything from the ground, then in the past, on the contrary, any structure was built from a height. From God! That is, first of all, the architect figured out the height, which was determined from the top of the cross. And only then the width and length were set. Moreover, the sacred object had two sizes in height: one was mundane, and the other was hidden, sacred.

- That is, the same height was measured twice with different sazhens?

- Yes, but with the secular version (for the laity), an even number of some fathoms was taken into account. ... And the sacred height implied aspiration to God. And such a height should have had an odd number of sazhens, but at the same time their multiplicity was seven! Of particular importance for the masters was the display of a hidden proportion in the composition of spiritual structures. Let's say the church is the temple of God - the temple of Christ, an object of holiness for believers and even unbelievers. Holiness is the measure of the Church. And the measure is always expressed by a number. A number behind which quality can be hidden, including the significance of the object being built.

Seven is the number of Christ, a sacred, sacral number. And the qualitative composition of the church being built as a temple of Christ, as a spiritual structure in its hidden proportion included elements of sacredness, containing a combined number of dual measures: worldly, open to everyone, and hidden, a multiple of seven. However, those who were not initiated into the essence of the sacrament of Christianity did not notice either duality or multiplicity, just as they did not notice that the church had at least seven fathoms of various lengths.

These rules were so conspiratorial and followed with such care that even today, admiring, for example, the Great Pechersk Church in Kyiv, the Church of the Ascension in Kolomenskoye or the same Church of Paraskeva Pyatnitsa in Novgorod, even the major architects of today are not aware of the double dimensional structure of these masterpieces, nor about fathomed sacredness.

Can you give some explanation for clarity? In numbers

- When considering the plan of the Church of Paraskeva Pyatnitsa, it turns out that its length is 21.1 meters, or 12 folk fathoms (1.76 m each), and its width is 18.1 meters, or 12 simple fathoms (1.508 m each). This information is indicated in any reference book on ancient Russian architecture. But it turns out that 14 simple fathoms also fit in length (seven double fathoms of 1.508 x 2), and seven fathoms wide 2.587 x 7. As you can see, there is sacredness here too. And again "Vsemer". So it turns out that the plans of churches from the very beginning in a hidden form contained a certain mystery of sacred numbers.

And not only the Church of Paraskeva Pyatnitsa, but also, say, the Great Pechersk Church in Kyiv, the Church of the Ascension in Kolomenskoye, the Church of the Savior on Nereditsa in Novgorod were built taking into account the sazhen system of A. A. Piletsky's "Semer". Therefore, it was widespread throughout Rus' ... "

So, the algorithm is given as an example:

2110 cm = 12 x 176.00 cm = 14 x 150.87 cm or 2 (6 x 176.00 cm) = 2 (7 x 150.87 cm) is the length in the example.

For the width in the example: 1810 cm = 12 x 150.87 cm = 7 x 258.67 cm = 14 (258.67 cm / 2),

that is, 2 (6 x 150.87 cm) \u003d 2 (7 x 129.34 cm), where 129.34 cm is a half fathom.

To complete the picture, let's take 2 more sazhens:

breech fathom 217.52 cm: 6 x 217.52 cm = 7 x 186.47 cm;

and a smaller sazhen 134.42 cm:

6 x 134.42 cm \u003d 7 x 115.21 cm, where 115.21 cm is a half fathom Greek.

This algorithm can be called "transition of 6 elements to 7". Let us show in Table 8 the elements of this transition.

For elements of groups 3 and 2, this algorithm is expressed by the relation:

6 x A ki = 7 x A (k-1)(i+1), where k = 3, 2 andi - any natural number.

6 x A 1 i = 7 x A3(i-10), wherei - any natural number.

Table 8

In addition to the seven-part “transition of 6 elements into 7”, another seven-part transition appears in the Golden fathom system. - "transition of 8 elements to 7".

Let's take a few fathoms again:

breech fathom 217.52 cm: 8 x 217.52 cm = 1,740.16 cm = 7 x 248.90 cm;

folk fathom 176.00 cm: 8 x 176.00 cm = 1408.00 cm = 7 x 201.39 cm;

small fathom 142.41 cm: 8 x 142.41 cm = 1 139.28 cm = 7 x 162.95 cm.

For elements of groups 3 and 2, this algorithm has the relation:

8 x A ki = 7 x A ( k-1)(i+6) , for k = 3, 2 andi - any natural number.

For elements of group 1 we have the relation:

8 x A 1 i \u003d 7 x A 3 (i-5), wherei - any natural number.

Table 9

What is the sacred meaning of 7? What is the essence of the sevenfoldness, manifested in the Golden system of fathoms? Through the seven-partness, the Unity of the three spirals, the mutual connection of their elements, is manifested. In other words, the sevenfold unites the three into the Trinity. This is the essence of the number 7 - it manifests the Unity of all things.

Now about the last element of our table - the 12th in the first group. The existence of the 11th element of the 2nd group 296.00 cm programs, determines and manifests, according to the law of seven-partness, the existence of an element interconnected with it and complementary to it - the 12th element in the 1st group.

One does not exist without the other: 6 x 296.00 cm = 7 x 253.74 cm.

Table 10

And here is the answer: the architects of Rus' in their work freely owned all the countless, that is, endless, set of Golden fathoms and their elements, choosing for their creations those of them that were proportionate to the one for whom they created.

The golden system of sazhens was used not only by architects, but by all the Masters of Rus': they plowed and built, weaved, sewed and forged, it was used to make a lumberjack's ax, a farmer's plow and a warrior's sword. Caftans and shirts were sewn on it, so they never sat like a "caftan from someone else's shoulder." Each person was a Master, showing through the fruits of his labor a sense of proportion, Unity with the world in which he lived, bringing his complementary melody to the overall coordinated sound of the World and the Universe.

The conscious process of the destruction of the system of commensurations, which manifested in everyone human action and everyone object created by him, his proportionality , consonance with the world in which he incarnated began through pulling fathoms out of the Golden system one element and its absolutization by giving it only measuring qualities. This was done by force, through legislative pressure on people, through the destruction and prohibition of seditious "other" arshins, except for the permitted one, under the false slogans of progress, enlightenment, and development.

What does the saying "Caftan from someone else's shoulder" mean? This caftan is for another person, not for you, because it is sewn on a different arshin. On the introduction of a single arshin, a proverb arose: “ It is a sin to carry away (measure) on an arshine, but God commanded (in a cut) on scissors. What are you talking about? Now buying material, person used alien, imposed him an arshin, and the material was always bought with excess than the tailors used.

To live according to someone else's yardstick means to lose your system of proportionality to the World, to measure not by your own measure, not to hit all the time, remeasure, try on and miss ...

In the understanding of our ancestors, Measure is proportionality, not measurement. The destruction of the Golden system of fathoms took away from a person his proportionality to himself and the World, replacing by force proportionality by measurement, comparison.

Proportionality is a manifestation of the feeling of Unity, the feeling of the Primordial. Measurement - a comparison with a certain standard, to which YOU HAVE NO RELATIONSHIP - which of us feels our attitude to the meter? How do you feel the meter today? - even the question is strange. Measurement is a mental process, each measurement-comparison that a person makes in his life increases the area of ​​his mind in him and infringes on the volume of feeling. Mind chamber - the chamber of weights and measures. The destruction of the Golden System of Fathoms put a person in conditions in which he began to live according to his mind, and not according to his original feeling.

For today, I say goodbye to you. See you soon!

Practical guide to
work with saphens

WORKSHOP PLAN

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5.
6.

Basic design principles for fathoms
human proportion system
Outlines of residential buildings
Room dimensions
Wurf relations and facade proportions
Plot proportions

1. BASIC PRINCIPLES
DESIGN BY FATHS
A sazhen meant the distance from the end of the fingers of one
hands to the end of the fingers of the other.

The very word "sazhen" comes from the verb "squeeze"
(get to something, grab, reach - cf.
also "reach", "reachable").

In the understanding of our ancestors, Measure is proportionality, and not
measurement.
The destruction of the Golden System of fathoms took away from man his
proportionality to oneself and the World, replacing forcibly proportionality
measurement, comparison.
Proportionality is a manifestation of the feeling of Unity,
feelings of the Primordial.
Measurement - comparison with a certain standard, to which he himself
the person is not related.

2. System
human proportions

According to 3 parameters (span
hands, arm height,
2 steps or length
outstretched hand from
shoulder joint)
received complex
from 3 sazhens characteristic
for a person
medium height -
Treasury - 2,176m
Folk - 1.76m
Smaller - 1,344m

Fathoms unfolded
phi number series

Table of fathom groups according to Chernyaev A.F.

Fathom ratios
2,176/1,345 = 1,618
2,176/1,76 = 1,236
1,76/1,345 = 1,309

Algorithm for obtaining the divine proportion

Comparison of the obtained functions in
given series

Numerical ratios of fathoms

Addition of a number of functions "golden
proportions"

3. Outlines
residential buildings

Proportionation of the building is carried out according to external dimensions,
taking into account ideologically important elements
(the height of the temple, taking into account the height of the cross, a residential building up to the ridge of the roof).

The length, width and height of an object, its main parameters, are determined by:
adjacent sazhens, interconnected by the relation
f =1.618, 1/2φ =0.809 and f2/2 = 1.309;
or in a geometric way - through the diagonal of the square
(silver section) = 2.414

The plan was formed on
function base
silver proportion.
Width ratio
buildings to length - through
square diagonal.

Building height with roof
formed through
9th step in
relation 1x2

The plan was formed on
function base
silver proportion
(deviation 0.9%).
Width ratio
buildings to length - through
square diagonal.

Building height with roof
formed through
golden feature
proportions - 1.236.
Division of the facade according to
vertically done according to
wurfu 1,309.

The number of fathoms must be even and whole.
View of fathoms in the main shaping dimensions of the structure
corresponds to the purpose of the structure and is determined from the status and
purpose of the object for public buildings and based on growth
house owner for private houses.

The proportions of a residential building are tied to the growth of the owner of the house
and are made up of fathoms of one group,
where the first is, for example, "Treasury",
corresponds to the size of a person with a raised arm (2.176m)
and tied to the height of the building,
the second - "Folk" - the height of a person (1,760m) and is tied to the width
building,
the third - "Small" - 2 steps (1.424m) and is tied to the length of the building.

When building multiple floors
different sazhens were used for each floor
(from different groups of "Semera" 1 step lower
for each next floor or according to the wurf rule).
The vertical articulation of the facade is carried out through the whirl
relations.

4. Room dimensions

The breakdown of the internal parts and axes of the building was carried out
fathoms different from those used on external structures,
integer lengths-quanta:
fathoms, half fathoms, cubits or smaller parts.

It should be noted that in all dimensional operations, we took
the dimensions of the premises in cleanliness - without taking into account the thickness of the walls,
those. the dimensions of only functionally used areas.
The thickness of the structures seemed to be ignored, although the internal
transverse walls, unlike modern partitions
were very massive.

By doubling the number of fathoms, a proportion is established between
person and space. This alignment is called
the scale of the elements of the structure in relation to a person. That is
the height of the room must be at least 2 heights.
For different in their meaning and position in the hierarchical ladder
people, rooms are created, measured accordingly by different
types of saplings.

outlines
residential
at home -
17th century drawing

Architecture is anthropomorphic, any thing or object that comes into contact
with a person, usually does not equal a person, but is performed either more,
or less than a person.
Doorway, bed - more than a person, and the top shelf
should be smaller than a person with a raised hand so that he can
reach out.
The size of the object, element of the structure is made one step larger
or a step below the model of the corresponding person.

The internal heights of the floors and the attic are made different,
but harmonious to each other fathoms,
may coincide with those used for outdoor measurements.
If there are 3 internal heights, for example, 1st, 2nd floors and attic,
then the consistency check is carried out
according to the wurf ratio: a-1st floor, b-2nd floor, c-3rd floor.
W(a,b,c)=(a+b)(b+c)/b(a+b+c)=1.3-1.33.
In practice, three adjacent sazhens participate in this ratio.
For a more accurate calculation, use the Novgorod
slide rule."

Division into isolated
compartments - cages dictated
only functional
the need to share
living area (heated) from
economic
(unheated).
The set of such compartments was dictated
vital
parameters - provision
food and labor
activities.
To the list of premises
included: common residential
room, canopy
(communication zone),
business premises,
cold areas - rooms
for livestock and a "latrine" place.

Reconstruction of a residential building in Trypillia

5. Wurf relationships and
facade proportions

In living nature, in biological bodies,
in the structure of the human body tripartite
division is constantly observed.
Member parts
tripartite division of the body (wurf)
form a system
mutual proportioning and
therefore they are inseparable.
For a block with three elements
with lengths a, b, c
wurf relation W(a, b, c)
calculated by the formula:
W(a,b,c)=(a+b)(b+c)/b(a+b+c).
By means of transformations such blocks
can be combined with one another
complete coincidence of all their points.

Wurf meanings vary slightly,
averaging W = 1.31.
In the ideal case, V. Petukhov indicates W = 1.309,
that when expressed in terms of the golden ratio
W = φ2/2.
He calls him "gold wurf"
If the construction has a wurf relation of three-term division,
then no matter how the observer moves relative to it,
the angle of view will always have the same wurf value,
and a moving observer will perceive
constantly changing
but remaining aesthetically perfect,
harmonious design.

6. Proportions of plots

Not so long ago, land was measured all over Russia
not by a meter, but by sazhens.
There was a square sazhen, something more than a square meter.
There was a tithe equal to 109 acres, or 10,900 square meters.
There is evidence that 2,400 square sazhens fit into a tithe.
Based on this information, we find out the size of a square sazhen. 10900:
2400 \u003d 4.542 - more precisely 4.548 sq.m.
It should be borne in mind that the length and width of the land plot
cannot be the same.
When proportioning and determining the size of allocated land
plots you can use fathoms as follows:
Width

masonry

policeman

Folk

Church

Greek

Treasury

The resulting size of a square sazhen and the tithe itself
have the Golden Ratio property.
Moreover, they are most harmonious for those
according to whose height plots are measured by a square sazhen
and will give a greater harvest than measured by the meter,
for they form the space of the volume of the harvest.
Examples of yield increase noted
in the diary of M.V. Lomonosov
and in the settlements of the Kirov and Krasnoyarsk regions.

Increasingly, in the scientific literature, the fruitful influence on a person of structures proportional to the golden section is noted. Moreover, we mean any structures and objects created by man. From a primitive spoon to a grandiose palace.

It becomes clear that the proportioning of parts of buildings and structures, corresponding to the natural proportions and proportions of a person, his perception of reality and sensations, is the most important factor in the normal functioning of the human body. But how to calculate the "golden sizes"? Due to the fact that in golden proportions all numbers are irrational, it is difficult or impossible to calculate them in the mind or even on a calculator. Only a modern computer can handle it. But it is not yet possible to write a program for a computer, since the principles of applying the golden ratio are just beginning to emerge from the fog. But how did our ancestors get out of the situation? An analysis of absolutely all ancient structures, starting with the Egyptian pyramids, shows the presence of the Golden Ratio, and the versatility of its application is confusing. And the most "fresh" of the surviving gold-cut structures are ancient Russian churches and temples !!! Since ancient times and right up to the 18th century in Rus' they built according to the golden proportions! Only Peter I put an end to the "mess", equating the official sazhen (217.6 cm) to 7 English feet (213.360 cm). In 1835 Nicholas I generally banned the remaining sazhens, and in 1924 the metric system was introduced.

This means that it is much easier to try to restore the ancient Russian measuring system than to compose fancy programs for a computer and carry it around with you. It is not clear yet how this “invention of the bicycle” will end.

To understand the essence and meaning of measurement in ancient Russian sazhens, you have to plunge a little into mathematics and geometry. Quite a bit, look at least diagonally all the formulas.

The existence of the mysterious "Golden Number" by F.

Practical acquaintance with the Golden Ratio begins with dividing a straight line segment in the golden ratio using a compass and ruler. From a point AT a perpendicular is restored equal to half AB. Received point FROM connected by a line to a dot BUT. A segment is drawn on the resulting line sun, ending with a dot D. Line segment AD transferred to a straight line AB. The resulting point E divides the segment AB in the golden ratio.

The exact value of Ф is found mathematically as the root of the quadratic equation obtained by dividing the segment in extreme and average ratios, that is, in the golden ratio:

(a+c)/c=c/a=Ф This is the golden ratio. There are an infinite number of solutions for the numbers a and c, and all of them will be irrational (although one number can be an integer). But there is only one solution for the number F:

F \u003d (1 + V5) / 2 \u003d 1.6180339887498948482045868343656 ... (V5 is the square root of 5)

True, the above quadratic equation has one more root (1- V5) / 2 \u003d - 1 / Ф, but since it is negative, and both numbers a and c are positive, we discard this solution.

F-number irrational infinite.

Reciprocal value 1 / F \u003d 0.6180339887498948482045868343656 ...

Square F 2 \u003d 2.6180339887498948482045868343656 ...

All decimal places are the same... That's a mysterious number, isn't it? But that's not all.

The well-known Fibonacci number series (opened in the 13th century), where each subsequent member of the series is equal to the sum of the two previous ones, has the form:

1,2,3,5,8,13,21,34, 55, 89,... 377, 610,987,1598,2885,...

It is easy to see that with an increase in the serial numbers of members, the division of the next member by the previous one is increasingly approaching the golden number Ф:

3:2=1,5; 5:3=1,666; 21:13=1,615; 55:34=1,617; ...610:377= 1,618037... .

The golden irrational number Ф was known in ancient Greece as the basis for the formation of an infinite series of quantities that have the properties of Fibonacci numbers obtained by multiplying or dividing the basic unit 1 by the golden number Ф. The branch of the series formed by successive multiplication by Ф is called ascending:
one; 1.618; 2.618; 4.236; 6.854; 11.090; 17.944; 29.034 ... and the other part of the series, formed by successive division by Ф, is called descending:
1; 0,618; 0,382; 0,236; 0,146; 0,090; 0,056; 0,034 ... .

The number 1 itself, the first three members of the ascending series and the seven members of the descending series constitute the Greek series of numbers, called "golden ratio" or "golden section".

golden ratio- the only geometric progression (of course, you can take any basic number instead of 1 and there will be a different series, but the factor is 1.618 ... the only one), which also has the properties of the Fibonacci series: each subsequent member of the series is obtained, like the Fibonacci numbers, by adding the two previous members, and the entire series, with the exception of the base 1, consists of irrational numbers. Moreover, the series is infinite in both directions, unlike the classic Fibonacci series, which have a beginning.

Where did the idea of ​​dividing the segments in the extreme and average ratios come from, which makes it possible to obtain the golden number Ф and the proportion called by Leonardo da Vinci the "golden section", we do not know.

So, the mysterious number Ф is calculated. But why do we need it?

It turns out that everything in nature, including humans, is created according to the proportions of the golden section.

We love beauty. Our body intuitively feels the golden ratio. Everything that seems beautiful to us has the properties of the golden ratio. Whether it's a natural landscape, an artist's painting or the human body. Why this is so, there is no definite answer yet. Esotericists immediately cite as evidence the “frequency of vibrations” created by different bodies, and it seems to be the same for gold-cut bodies. Some argue that gold-cut bodies, on the contrary, absorb (or pass) all frequencies equally, due to which they have balanced information. There was also such an expression about modern buildings: “they give rise to standing waves that have a detrimental effect on the consciousness and human body.” Scientists from science are still completely silent on this matter.

Over the past decades, numerous researchers have established ubiquitous manifestations of the law of golden proportions from the Cosmos to the Microworld.

In the Universe, all galaxies known to mankind and all bodies in them exist in the form of a spiral, corresponding to the formula of the golden section. The Russian astronomer Butusov in 1978 established that the ratio of the periods of revolution of neighboring planets around the Sun is equal to either the golden ratio 1.618 or its square 2.618.

Researchers find the ratios of the golden ratio in the morphological structure of plants, birds, animals, and humans.

The patterns of the golden ratio are also found in the organization of inorganic nature, for example, the structure of melt water, practically corresponds to the triangle of the golden ratio.

Thus, the manifestation of the principle of golden proportions is observed everywhere in nature from infinitely large galaxies to infinitely small cells and atoms.

The human figure, studied by the German researcher prof. Zeising in 1855 was a prime example of golden proportions.

For a block consisting of three elements with lengths a, b, c, the wurf relation W(a, b, c) is calculated by the formula:

W(a,b,c)=(a+b)(b+c)/b(a+b+c).

At the same time, another block - with other sizes and other ratios of elements - a", b", c" will be conformally symmetrical to it if the values ​​of their wurfs are equal, i.e. if:
W(a, b, c)=W(a", b", c").

By means of transformations, such blocks can be combined with one another with the complete coincidence of all their points.

In the process of growth, the sizes of parts of the human body and their ratios change all the time. Moreover, these changes follow the principles of conformally symmetric transformations. For example, if we take the ratio of the foot, lower leg and thigh at the age of 1 year, 10 and 20 years, then the changes look like this: 1:1.27:1.40; 1:1.34:1.55; 1:1.39:1.68.

The growth of different parts of the body does not proceed evenly. The lower leg and thigh increase much more than the foot, the proportions of the human body change all the time. Wurf ratios for any age are calculated with the same value (W(1;1.27;1.40)=1.30; W(1;1.34;1.55)=1.30; W( 1;1.39;1.68)=1.30) and remain unchanged throughout the growth period. The constant and unchanging value of the wurf testifies to the transformation of the forms of our body according to the principles of conformal symmetry. The same picture opens for other blocks: shoulder - forearm - hand; phalanges of fingers; torso, upper and lower limbs of the body, etc.

Wurf values ​​vary slightly, averaging W = 1.31. In the ideal case, V. Petukhov indicates W \u003d 1.309, which, when expressed through the value of the golden section, is equal to Ф 2 /2. He calls him "golden wurf".

Wurf proportions make it possible, therefore, to identify conformally symmetrical groups, in other words, groups of kinship relations with a single initial beginning. Ordinary two-term proportions show only differences, while wurf proportions show the commonality of a certain set of three-term ratios.

If the proportions of the works of architecture around us belong to random groups, as in most modern buildings, then a person finds himself in an environment whose proportional structure, in its symmetry, is not characteristic of him. Such an Environment, which does not have any of the characteristic symmetry groups of a person, is most often not perceived by him, and is often rejected. This is where the root of the unfavorable psychophysical impact of the Environment on a person lies, and not only in the fact that residential buildings are a set of the same type of "boxes". The same can be said about the attractiveness and beauty of any objects that surround us.

Many scientists have been working diligently for 100 years to decipher and restore the lost Russian sazhens. A significant breakthrough occurred after 1970, when a fragment of the measure of the Novgorod architect was found near the church of Paraskeva Pyatnitsa in Novgorod. In the process of researching the yardstick, first A.A. Piletsky, and then A.F. Chernyaev, managed not only to restore it completely, but also to show that it was both a measuring and co-measuring tool. On one side, measurements of all fathoms were applied, and the remaining three sides, in combination with the first, were a kind of slide rule, which makes it very easy to select the golden proportions! At the same time, the missing fathoms were calculated and the sizes of the known ones were specified. The list of sazhens is given below. Many names could not be restored, many had several names, so new ones were invented or one of the old names was used.

There were also smaller measuring values: half a sazhen (1/2 sazhen), cubit (1/4 sazhen), span (1/8 sazhen), metacarpus (1/16 sazhen), vershok (1/32 sazhen). On the basis of sazhens and their shares, as well as successive multiplication by 2 of all sazhens, a matrix called "Russian Semer" was compiled:

The dimensions of all fathoms are given in cm, highlighted in red. At the top of the table are the names of fathoms. It turned out that all the diagonals from left to right from bottom to top represent the Fibonacci series and the Golden Ratio at the same time. For example, let's take the diagonal of the People's fathom:

67,2+108,8=176,0; 176/108,8=1,618; 108,8/67,2=1,618.

In the rows, the coefficient is everywhere 2/Ф = 2/1.618 = 1.236.

If the fathoms are arranged in ascending order of length, then the neighboring ones will relate to each other with the same coefficient 1.059 ... - just like the frequencies of neighboring semitones in the musical series.

Idea! Since fathoms correlate with each other in the same way as the frequencies of notes, you can try to “lose” the design of the house, having previously coordinated the table of fathoms with the notes, and the dimensions of the house with the duration of the notes. Perhaps a house with harmonious dimensions will “sound” pleasantly. Musicians check it out!

The matrix can be continued indefinitely in all directions - left and right, up and down.

It is easy to see that a matrix containing the diagonal of the Greek series, the golden ratio, would look more logical (from our point of view):

…0,382; 0,618; 1; 1,618; 2,618; 11,090; 17,944; 29,034 …122,97; 198,96…

Then one of the vertical columns would look like this:

…0,25; 0,5; 1; 2; 4; 8; 16; 32; 64; 128; 256; 512; 1024…

And one could choose a very similar set of fathoms, in the same range. They are highlighted in bold.

The answer is that in Ancient Rus' they did not know such a matrix, and it was more logical for them to choose the correspondence of sazhens to the size of a person. If we accept the people's sazhen as equal to the height of the architect, then everyone could calculate the remaining sazhens in proportion to it. This was done by various very simple methods, without the use of numbers and calculations at all (geometrically). Several of these methods can be found in the sources (links at the end of the article). Well, numbers are closer to us, we will rely on them.

Apparently, over time, for convenience, they adopted a single sazhen system, focused on the growth of an average person - 176 cm, he was equated with a national sazhen. That's just how this "standard" was stored is still unknown. It is possible that it was one of the royal relics in the form of a rod or cane. In order not to mess things up, for the time being we will also rely on this “fat standard”.

The system of Russian sazhens is a legacy of an ancient civilization that developed according to the principles of interconnection of everything around. We, the descendants of a technocratic civilization who have lost touch with Nature, cannot understand the essence and meaning of the subtle processes taking place in the Universe, as well as the structure of it itself. We are used to dividing everything into components, disassembling it in order to understand the device. On the contrary, it is necessary to unite in order to understand the whole, to create harmony. The system of Russian sazhens allows you to calculate proportions that are harmonious for Nature and create harmony without delving into the process of proportioning according to the Golden Ratio. At the moment, not all principles of building by sazhens have been restored. But what is already there is quite enough for the construction of simple buildings.

So, the general rules for the use of Russian sazhens (mainly with regards to the construction of houses):

1. To divide a sazhen and the resulting shares to calculate smaller sizes is possible only by 2. When building houses, the minimum share is 1/32 - an inch. Further, the sazhen is not divided. A vershok can be divided by any number. If you make small objects in fathoms, you can divide by 2 to infinity.

2. Any object was designed using at least 3 different harmoniously connected fathoms: separately in height, width and length. Most often, their number was 5-7, that is, the internal dimensions were made according to other harmoniously connected fathoms.

3. All parameters of objects were measured only by a whole, as if quantized, number of measuring instruments - sazhens, cubits, vershoks, etc. For example, the length of the building was equal to 12 sazhens small by 142.4 cm, which is equal to 17.088 m in a meter measurement. the height is equal to two simple sazhens of 150.8 cm or 3.016 m. Thus, the parameters of objects, measured by an integer number of sazhens, always turn out to be fractional when measured with a standard meter. This feature is systematically recorded when measuring all ancient Egyptian structures with a meter. Therefore, it can be repeated that it is impossible to achieve an understanding of the structure of dilapidated pyramids without knowing the harmony of the measuring instruments that gave rise to them.

4. It is permissible to enter coefficients of 1.5; 2; 2.5 to the fathom value, and measure all axes respectively by one and a half, double, two and a half fathoms, but this method is not used in residential construction.

5. When constructing residential buildings along all axes, an even integer number of fathoms is taken from the outside, for sacred structures (temples, chapels, churches, tombs) an odd number, and preferably a multiple of 7 or 11.

6. Inside buildings, it is permissible to measure in fractional parts of fathoms, respectively, an even or odd number.

7. First, the height is selected, then the width harmonious to it, then the length harmonious to the height and width (more on the selection methods below).

8. All dimensions are measured by protruding parts: an extension, steps, a canopy, a drainage system, a cross on a temple, a weather vane on a roof, etc. - everything is taken into account. The height is determined by the highest point of the house, for example, a ridge, and if a rooster is built at the end of the ridge, then according to it. If a tower adjoins the house, the height of which exceeds the height of the house, then the height of Creation is determined by the highest point of the tower. Chimneys and ventilation pipes are not taken into account.

If the plinth is more than 20 cm, then the height is measured in 2 different fathoms: separately from the plinth and separately from the ground. If the house is on a slope, then on both sides the height is measured in different fathoms. If the height difference is less than 3%, ignore it. Internal height is measured from the finished floor to the ceiling. With an inclined ceiling - to the highest point.

It is also better to make the length of the roof slope according to the fathom. It does not affect changes in calculations. But when the roof overhang extends more than 1/3 of the height of the building, the width of the building must already be measured by the width of the overhangs, and the distance from the overhang to the ground (zero mark of the building, foundation or basement) must also be taken into account by the fathom.

9. Errors and size changes up to 1/32 (3%) in relation to this size - do not matter. For example, with a house length of 6 royal fathoms 6x197.4 cm = 1184.4 cm, protruding parts and errors within 37 cm can be ignored.

10. The internal heights of the floors and the attic are made different, but harmonious to each other, sazhens, may coincide with those used for external measurements. If there are 3 internal heights, for example, the 1st, 2nd floors and the attic, then the harmony check is carried out according to the wurf ratio: a-1st floor, b-2nd floor, c-3rd floor. W(a,b,c)=(a+b)(b+c)/b(a+b+c)=1.3-1.33 External dimensions are not checked by the wurf ratio.

11. In round buildings (six-eight-polyhedral) - the diameter (of the circle in which the polyhedron is inscribed) is measured with a sazhen. And height, of course.

12. If the roof overhangs are up to 30 cm, the size is taken according to the roof overhangs. If more than 30 cm, 2 different fathoms are used - one measures the walls, the second is the full width (length) along with the overhangs.

13. In general, in absolutely all options not mentioned above, everything must be measured in sazhens, a meter should be used only for the convenience of transferring sazhen sizes to reality. This applies to doors, windows, distances between windows, wall thicknesses.

14. Doors and windows along the top within the same room must be at the same level.

Now in detail about the calculation of sazhens harmonious to each other.

Here is the entire list of restored ancient Russian sazhens:

1st group:

1 Pilecki 205.5 cm

2 Egyptian 166.3 cm

3 Smallest 134.5 cm

2nd group:

4 Breech 217.6 cm

5 Folk 176.0 cm

6 Small 142.4 cm

3rd group:

7 Greek 230.4 cm

8 Church 186.4 cm

9 Simple 150.8 cm

4th group:

10 Great 244.0 cm

11 Royal 197.4 cm

12 Masonry 159.7 cm

5th group:

13 Large 258.4 cm

14 Pharaoh 209.1 cm

15 Chernyaeva 169.1 cm

Without a group:

16 Policeman 284.8 cm (equal to double the small 2x142.4 cm)

Basic rules for using sazhens:

1. Fathoms that are in the same group (total 5 groups of 3 fathoms) are inharmonious to each other, and they cannot be used together. That is, when determining the triple height-width-length, even 2 sazhens from one group are not allowed. Or, if any size is measured by more than one fathom at a time (for example, the height of a house on a slope), it is also necessary to take fathoms from different groups.

2. City fathom as an independent one is not used in the construction of houses.

4. If you arrange the fathoms in increasing length, then they are grouped in 3 rows of 5 pcs:

small fathoms: smaller, small, simple, masonry, chernyaeva;

medium fathoms: Egyptian, folk, church, royal, pharaoh;

big fathoms: Pilecki, state-owned, Greek, great, big.

This is just first the first in each of the 5 groups, then the second and third. Fathoms in the same row are harmonious with each other, and you can use them without restrictions.

Using these rules, it is already possible to calculate harmonious combinations of proportions. But these combinations are often not enough, and here the Russian Semer comes to the rescue - the same restored commensurate instrument of the Novgorod architect.

The design and manufacturing technique of the Russian Semer.

The Russian semester is a wooden block with a section of 20x40 - 35x70mm and a length of a city sazhen - 2848mm.

The figure shows the seven in expanded form.

And this is the enlarged central part.

Side C is divided into 34 equal parts, side A into 48 parts, side B into 39 parts. On the fourth side, the lengths of all sazhens are plotted (in the figure, Chernyaev's sazhen from the small row is missing - 1691 mm). The lengths of sazhens are drawn through all sides of the seven measures.

Since we will still not use seven measures as a measuring tool, but only as a commensurate one - to search for a harmonious proportion, for convenience, we can reduce all dimensions by a factor of 2-4. I reduced it by 2. As a result, the length of the seven came out 1424mm, equal to a small sazhen. Next, find out the lengths of the cells of all sides. 1424/34=41.882mm - cell length on side C, 1424/39=36.513mm - B; 1424/48 = 29.667 mm - A. It is not advisable to set aside the length of the cell sequentially according to the template. An error will accumulate, which in the end can be a third of the cell. It will be much more accurate to add the size of the cell sequentially with all the signs on the calculator, and mark it on the Semere without taking away the tape measure. For example, for side C, this would be the number 41.882; 83.76; 125.6; 167.5; 209.4; 251.3…1382.1; 1424.0 mm.

Here is a photo of the Russian Semer that I took:

On the fourth side, we mark all 15 sazhens, taking into account the coefficient (if any). In my case, all sazhens must be divided by 2. Near the mark of each sazhen, we write its name and real length in meters, accurate to the 4th digit. We transfer marks of fathoms to all faces. Near the names of fathoms we also write the number of its group (1-5). And in any way we designate fathoms belonging to one row (3 rows in total). I connected them with arcs on sides B and C. On one side it gets confusing - the rows intersect. At the beginning of seven, we will inscribe the letter designations of the sides. Next, we cover the finished Semer with colorless varnish in 2 layers. For marking cells and inscriptions, it is better to use a simple pencil, it is the most light-resistant. The marks of fathoms can be colored with a dark pencil so that they differ. Markers with a marker, felt-tip pen, ballpoint pen disappear over time, especially in the sun.

Algorithms for selecting harmonious fathoms usingRussian Allmeasure.

It all starts with choosing the height of the house. For example, we have a 2-storey house with an attic. The basement is 0.5 m, the floors are 3 m each (including ceilings), the attic is 2.5 m. The total is about 9 meters.

Approximately 9 meters we can get in several ways: 4 fathoms of Greek 2.304x4 = 9.216m; 4 fathoms of state-owned 2.176x4 \u003d 8.704m; 6 simple sazhens 1.508x6=9.048m; 6 fathoms small 1.424x6=8.544m; 6 fathoms of masonry 1.597x6 = 9.582m. There are many options. We will choose 6 simple sazhens (9.048m), which is closest to 9 meters. And since the height without a plinth must be measured with another fathom, we take a small fathom (8.544m). Small and simple fathoms in one row, harmoniously connected. The height of the base will be 9.048-8.544 = 0.504m. Until everything is on point.

Here are some algorithms:

1. We look in which cell on side C the original fathom is located. This is a cell with the number D. We look at what fathom is in the cell with the number D on side B. This will be the required fathom.

2. The original fathom on side C is in cell D. In cell D on side A is the required fathom.

3. The original fathom on side C is in cell D, and on side B in cell F. In the cell with the number F on side C, we are looking for the required fathom.

4. The original fathom on side C is in cell D. Cell D on side B corresponds to cell E on side A. In cell E on side C is the desired fathom.

5. The original fathom on side A in cell E. In cell E on side C, the required fathom.

The list of algorithms is not yet complete, I am searching for the missing ones. Therefore, for some sazhens it is impossible to choose harmonious ones. I would appreciate the help if anyone knows other algorithms.

So, a simple sazhen is on side C exactly on the border of 18 and 19 cells. Therefore, we choose algorithm 3. On side B, a simple fathom falls into 21 cells. 21 cells on side C are Chernyaev's fathoms - 1.691m. We choose a width of 4 sazhens Chernyaev 4x1.691 = 6.764m.

We are looking for a sazhen of length. According to the algorithm, 3 sazhens of Chernyaev correspond to the royal sazhen of 1.974m. And according to algorithm 4, a state sazhen is obtained, but it is in the same group with a small sazhen, which measured the height without a base. This means that the treasury fathom cannot be used. We leave the royal sazhen for length, take 6 sazhens. Total 6x1.974=11.844m - the length of our house.

To measure the outer dimensions, we selected 4 sazhens: small, simple, chernyaev, royal. All of them are from different groups, the main rule is observed.

Features of the proportioning of land plots.

Not so long ago, all over Russia, the land was measured not by a meter, but by sazhens. There was a square sazhen, something more than a square meter. There was a tenth equal to 109 acres, or 10,900 square meters. There is evidence that 2,400 square sazhens fit into a tithe.

Based on this information, we find out the size of a square sazhen.

10900: 2400 \u003d 4.542 - more precisely 4.548 sq.m.

It should be borne in mind that the length and width of the land plot is measured in different fathoms. Based on this, we determine which sazhens participated in the formation of a square sazhen. To do this, we divide a square sazhen sequentially into all sazhens, starting with large ones. So:

Table for determining the participation of fathoms in the formation of a square fathom

As you can see, a square sazhen can be measured by five different pairs of sazhens. A simple sazhen participates alone in the formation of half a square sazhen.

Width Length

City Masonry

Bolshaya Narodnaya

Great Church

Greek Royal

State Pharaoh

The resulting size of a square sazhen and the tithe itself have a golden-cut, moreover, the most accurate holiness, "sacredness" for those inhabitants of the Earth who process it. It should be expected that plots measured by a square sazhen will yield more than those measured by a meter, because they form the space of the volume of the crop. Examples of increased yields have already been noted in the settlements of the Kirov and Krasnoyarsk regions.

Mandatory literature: