Edited by Nan Nan
Preface
Vitruvius's Ten Books of Architecture is the only surviving architectural book from the Western classical era, and it has the evaluation that "a history of Western architecture is a history of Vitruvius's reception".
The history of the development of architecture is also a history of human life and culture, and a history of the accumulation of architectural art and theoretical knowledge.
Looking at the masterpieces of thousands of years of architectural art in ancient and modern China and foreign countries, and experiencing the rich architectural theories and experiences of the architectural masters of the past dynasties, you will find a living building, which contains a wealth of anthropology, philosophy, aesthetics, mathematics and mechanical knowledge.
An introduction to Vitruvius and his Ten Books of Architecture
Vitruvius, lived in the 1st century BC at an important transition from a Roman republic to an imperial state.
He was a "conservative" who spared no effort to uphold the humanistic values and architectural ideals inherited from ancient Greece.
His parents gave him a broad education in the "liberal arts", as well as vocational education that he needed to earn a living.
But his knowledge depended on his lifelong Xi, or by his own collection, or by the libraries of the rich and powerful.
Vitruvius shows Octavian the Ten Books of Architecture
Thus, the curriculum of Vitruvius included painting, geometry, arithmetic, optics, history, philosophy, music, medicine, law, astronomy, classical linguistics, writing, and paleography.
He emphasized that it is impossible for one person to be an expert in all disciplines, but it is essential to master the fundamentals of these subjects.
Vitruvius believed that in order to be an ideal architect, one should have an insight into the physical nature and the true meaning of life, and should have a wide range of knowledge.
The impact of his ideas on future generations was far-reaching.
Such as the Renaissance "literary giant" ——— Leonardo da Vinci.
With his erudition and talent, Vitruvius provided the world with a model of the ideal architect.
The Ten Books of Architecture is the only architectural monograph left over from Europe before the Middle Ages.
The book continues to have a profound impact on the world of architecture today.
Mathematical Culture in the Ten Books of Architecture
The ancient Greek philosopher Plotta Gaures once said, "Man is the measure of all things." ”
The concern and research of human beings themselves is the premise of design, and the concept of "people-oriented" is the primary concept of Vitruvius's architectural design.
Surveying, as one of the indispensable steps in engineering construction, is very important in architectural design.
Vitruvius drew on the Pythagoreans and other mathematicians to believe that the units of measurement were derived from the human body, such as fingers, palms, feet, elbows, etc.
The mystical number theory of the Pythagoreans held that "ten" was a perfect number, because the perfect fingers of both hands were ten.
Ten is made up of the addition of the original one, two, three, four.
In ancient Greece, ten was derived from the addition of four elements called units, and once eleven or twelve was obtained, it exceeded "ten" and exceeded the four of a group of four, and it ceased to be a perfect number until the next ten, and the first four numbers were the constituent units of perfect numbers.
However, there are also some mathematicians who believe that "six" is the perfect number because it contains six units, and their ratio matches the number six.
For example, one-sixth of six equals one, one-third of six equals two, one-half of six equals three, two-thirds of six equals four, six-sixths five-sixths equals five, and the perfect number is six.
Another explanation for the perfect number is that 6 is 1+2+3=6 and 1·2·3=6.
Vitruvius, after observing common things, studied Xi previous research, and added up the two perfect numbers six and ten to arrive at the most perfect number sixteen.
This invention originated from the foot, according to the observation of the ancients, the elbow is made of six palms or twenty fingers, if two palms are deducted from one elbow, the remaining four palms are equal to one foot, and each palm is composed of four fingers, from which one foot is sixteen fingers.
Thus, Vitruvius pointed out that according to nature's arrangement of the size of the human body, the commonly used units in measurement are: four fingers for one palm, four palms for one leg, six palms for one cubit, and four cubits for human height.
Geometry ——— a compulsory course for architects
Geometry is a great help to architecture, as it inherits the techniques of compasses and rulers, and helps to implement the layout of the site, drawing right-angled, horizontal, and straight lines.
As the sacred abode of the immortal gods of the West, the temple occupies an important place in the history of Western architecture, and Vitruvius explains its design method in Book 3.
The basic principles of temple design determine its planar form, most of which are mainly expressed in the form of columns, so the column becomes the main design in most temples.
The column groove of the cylinder is 24, it is concave inward, if the ruler is placed in the groove and rotated, the angle of the ruler will touch the left and right edges of the column groove.
This design by Vitruvius was an application of a corollary of the "Thales theorem" of the early 6th century BC, when Thales of Miletus proved what is now known as the "Thales theorem": the circumferential angle on a semicircle is a right angle.
Vitruvius, on the other hand, demonstrated the corollary of Thales' theorem in his design of the groove in a cylinder.
That is, "all triangles that are attached to a circle, with hypotenuse diameters, are right-angled triangles." ”
There is a square piece of land, full of length and width, with an area of 100 square feet.
If necessary, double its area to a 200-square-foot piece of land, while keeping the sides equal.
The question is, what should be the length of the sides of the square, so that the doubling area is equal to 200 square feet.
As mentioned earlier, Vitruvius said that it was impossible to find it by calculation, so he gave a geometric solution according to Plato's method of doubling the area.
Apparently Vitruvius applied two diagonals of a square to divide it into four isosceles right triangles of equal size, and then doubled the area of the original square by reducing the triangle to a square with fifty square feet.
In addition, after the Pythagoreans discovered and proved the "principle of the ruler" (i.e., the Pythagorean theorem), Vitruvius faced the imprecise rulers made by the craftsmen, and according to the theorem discovered by Pythagoras, he made a ruler in the following way: he first took three rulers, one was three feet long, the other was four feet long, and the third was five feet long, and put them together so that their ends touched each other to form a triangle, and then made a perfect ruler board.
At the same time, Vitruvius found that the sum of the areas of two squares with a side length of three legs and a four-legged side is equivalent to the area of a square with a side length of five legs.
These principles were useful in many measurements, and Vitruvius applied them to calculate the angle of inclination when building stairs.
One of the sources of the study of proportional thought
Architectural design has its inherent, innate approach to proportion.
Vitruvius's Ten Books of Architecture deals with the basic principles and methods of drawing in architecture, and the idea of proportion is the most widely used of them.
The problem of proportionality is dealt with in both books 3 and 4, and Vitruvius begins by giving a definition of proportion:
"Proportion is a check of the relationship between each component of a building and with the whole. ”
Since there was no unified unit of measurement in the ancient West, the application of proportion in architecture was extremely important, and Vitruvius mainly involved two aspects of proportion, one was to apply the natural proportions of the human body to the measurement of architecture, and the other was to produce equilibrium from proportion in temple architecture.
In Book 3, Vitruvius mentions that a building should reflect the proportions of the human body.
He believed that nature constructs the human body in such a way that the face is one-tenth of its height from the chin to the crown of the forehead and the hairline, as is the palm of the hand from the wrist to the tip of the middle finger, the head is one-eighth from the chin to the top of the head, from the top of the chest with the hairline including the lower end of the neck to one-sixth of the head, and from the middle of the chest to the top of the head one-fourth.
The face itself, from the base of the chin to the bottom of the nose is one-third of the height of the whole face, from the lower end of the nose to the midpoint between the eyebrows is another third, and from this point to the frontal hairline is also one-third.
The length of the foot is one-sixth of the height, the forearm is one-quarter, the chest is also one-quarter, and the other limbs have their own proportions.
These proportions are widely used in architecture, occupy an important position, and have been deeply influenced in later research, such as painting, in Leonardo da Vinci's body painting, he emphasized the use of Vitruvian proportions, pointing out that the architect Vitruvius arranged the size of the human body in nature as follows:
Four fingers are one palm, four palms are one foot, six palms are one wrist ruler, four wrist rulers are the height of people, four wrist rulers are one step, and twenty-four palms are combined with the whole body.
He also used these measurements in architecture, if you spread your legs apart, reduce your height by a fourteenth, raise your arms so that the tips of your middle fingers are level with the top of your head, and link the ends of the stretched limbs to form a circumscribed circle, and the navel happens to be in the center of the whole circle.
The space between the legs forms an equilateral triangle.
And the width of a person's arms when he stretches out his arms is equal to his height.
When a person kneels, his height is reduced by a quarter of a degree.
These proportions were widely used in Leonardo da Vinci's paintings, among which the famous "Vitruvian Man" is a perfect human body based on the description of the proportions of the human body in the Ten Books of Architecture, which depicts the "cross" and "fire" posture of a man in the same position, embedded in a rectangle and a circle, respectively.
Vitruvius' proportions of the human body laid the foundation for many of Leonardo da Vinci's works of perfect and harmonious figures.
epilogue
As an "encyclopedia of ancient culture", the Ten Books of Architecture are known as the source of Western architectural theory.
It contains a wealth of philosophical, astronomy, geography and other knowledge, making architectural art one of the treasures in the treasure house of human art.
bibliography
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