Ministry of Education and Science of the Russian Federation

State educational institution

higher professional education

"Tver State Technical University"

(GOU VPO "TSTU")

in the discipline "History of Science"

on the topic: "Leonardo da Vinci - a great scientist and engineer"

Completed: 1st year student

FAS AU ATP 1001

Ivanova Tatyana Lyubomirovna

Tver, 2010

I. Introduction

II. Main part

1. Artist and scientist

2. Leonardo da Vinci - a brilliant inventor

. "It is better to be deprived of movement than to be tired of being useful"

3.1 Aircraft

3.2 Hydraulics

3 Car

4 Leonardo da Vinci as a pioneer of nanotechnology

5 Other inventions of Leonardo

Conclusion

References

Application

I. INTRODUCTION

Renaissance (French Renaissance, Italian Rinascimento) is an era of great economic and social transformations in the life of many European countries, an era of radical changes in ideology and culture, an era of humanism and enlightenment.

During this historical period, favorable conditions for an unprecedented rise in culture arise in various areas of human society. The development of science and technology, great geographical discoveries, the movement of trade routes and the emergence of new trade and industrial centers, the inclusion of new sources of raw materials and new markets in the sphere of production significantly expanded and changed man’s understanding of the world around him. Science, literature, and art are flourishing.

The Renaissance gave humanity a number of outstanding scientists, thinkers, inventors, travelers, artists, poets, whose activities made a tremendous contribution to the development of universal human culture.

In the history of mankind it is not easy to find another person as brilliant as the founder of High Renaissance art, Leonardo da Vinci. The phenomenal research power of Leonardo da Vinci penetrated into all areas of science and art. Even centuries later, researchers of his work are amazed at the genius of the insights of the greatest thinker. Leonardo da Vinci was an artist, sculptor, architect, philosopher, historian, mathematician, physicist, mechanic, astronomer, and anatomist.

II. MAIN PART

1. Artist and scientist

Leonardo da Vinci (1452-1519) is one of the mysteries in human history. His versatile genius of an unsurpassed artist, a great scientist and a tireless researcher has plunged the human mind into confusion in all centuries.

“Leonardo da Vinci is a titan, an almost supernatural being, the owner of such versatile talent and such a wide range of knowledge that there is simply no one to compare him with in the history of art.”

For Leonardo da Vinci himself, science and art were fused together. Giving the palm in the “dispute of arts” to painting, he considered it a universal language, a science that, like mathematics in formulas, displays in proportions and perspective all the diversity and rational principles of nature. The approximately 7,000 sheets of scientific notes and explanatory drawings left by Leonardo da Vinci are an unattainable example of synthesis and art.

Long before Bacon, he expressed the great truth that the basis of science is, first of all, experience and observation. A specialist in mathematics and mechanics, he was the first to expound the theory of forces acting on a lever in an indirect direction. Studies in astronomy and the great discoveries of Columbus led Leonardo to the idea of ​​​​the rotation of the globe. Specifically studying anatomy for the sake of painting, he understood the purpose and functions of the iris of the eye. Leonardo da Vinci invented the camera obscura, conducted hydraulic experiments, deduced the laws of falling bodies and motion on an inclined plane, had a clear understanding of respiration and combustion, and put forward a geological hypothesis about the movement of continents. These merits alone would be enough to consider Leonardo da Vinci an outstanding person. But if we consider that he did not take everything except sculpture and painting seriously, and in these arts he showed himself to be a real genius, then it will become clear why he made such a stunning impression on subsequent generations. His name is inscribed on the pages of art history next to Michelangelo and Raphael, but an impartial historian will give him an equally significant place in the history of mechanics and fortification.

With all his extensive scientific and artistic pursuits, Leonardo da Vinci also had time to invent various “frivolous” devices with which he entertained the Italian aristocracy: flying birds, inflating bubbles and intestines, fireworks. He also supervised the construction of canals from the Arno River; construction of churches and fortresses; artillery pieces during the siege of Milan by the French king; Seriously engaged in the art of fortification, he nevertheless managed to simultaneously construct an unusually harmonious silver 24-string lyre.

"Leonardo da Vinci is the only artist about whom it can be said that everything that his hand touched became eternal beauty. The structure of the skull, the texture of the fabric, a tense muscle... - all this was done with an amazing flair for line, color and illumination are transformed into true values" (Bernard Berenson, 1896).

In his works, issues of art and science are practically inseparable. In his “Treatise on Painting,” for example, he conscientiously began to outline advice to young artists on how to correctly recreate the material world on canvas, then imperceptibly moved on to discussions about perspective, proportions, geometry and optics, then about anatomy and mechanics (and to mechanics as animate , and inanimate objects) and, ultimately, to thoughts about the mechanics of the Universe as a whole. It seems obvious that the scientist is striving to create a kind of reference book - an abbreviated presentation of all technical knowledge, and even distribute it according to its importance, as he imagined it. His scientific method boiled down to the following: 1) careful observation; 2) numerous verifications of observation results from different points of view; 3) a sketch of an object and phenomenon, as skillfully as possible, so that they can be seen by everyone and understood with the help of short accompanying explanations.

For Leonardo da Vinci, art has always been science. To engage in art meant for him to make scientific calculations, observations and experiments. The connection of painting with optics and physics, with anatomy and mathematics forced Leonardo to become a scientist.

2. Leonardo da Vinci - a brilliant inventor

Leonardo da Vinci enriched the Renaissance worldview with the idea of ​​the value of science: mathematics and natural science. Next to aesthetic interests - and above them - he placed scientific ones.

At the center of his scientific constructions is mathematics. "No human research can claim to be a true science unless it makes use of mathematical proof." “There is no certainty where one of the mathematical sciences does not find application, or where sciences not related to mathematics are applied.” It was no coincidence that he filled his notebooks with mathematical formulas and calculations. It is no coincidence that he sang hymns to mathematics and mechanics. No one sensed more keenly than Leonardo the role that mathematics had to play in Italy in the decades that elapsed between his death and the final triumph of mathematical methods in the works of Galileo.

His materials were collected and largely scientifically processed in a wide variety of disciplines: mechanics, astronomy, cosmography, geology, paleontology, oceanography, hydraulics, hydrostatics, hydrodynamics, various branches of physics (optics, acoustics, theriology, magnetism), botany, zoology, anatomy, perspective, painting, grammar, languages.

In his notes there are such amazing provisions that, in all their conclusions, were revealed only by mature science of the second half of the 19th century and later. Leonardo knew that “motion is the cause of every manifestation of life” (il moto e causa d "ogni vita), the scientist discovered the theory of speed and the law of inertia - the basic principles of mechanics. He studied the fall of bodies along a vertical and inclined line. He analyzed the laws of gravity. He established the properties of the lever as a simple machine, the most universal.

If not before Copernicus, then simultaneously with him and independently of him, he understood the basic laws of the structure of the universe. He knew that space is limitless, that the worlds are countless, that the Earth is the same luminary as the others and moves like them, that it “is neither in the center of the circle of the Sun, nor in the center of the universe.” He established that “the sun does not move”; This position is written down by him, as especially important, in large letters. He had a correct understanding of the history of the Earth and its geological structure.

Leonardo da Vinci had a very solid scientific background. He was, without a doubt, an excellent mathematician, and, what is very curious, he was the first in Italy, and perhaps in Europe, to introduce the signs + (plus) and - (minus). He was looking for the squaring of a circle and became convinced of the impossibility of solving this problem, that is, to be more precise, of the incommensurability of the circumference of a circle with its diameter. Leonardo invented a special tool for drawing ovals and for the first time determined the center of gravity of the pyramid. The study of geometry allowed him to create for the first time a scientific theory of perspective, and he was one of the first artists to paint landscapes that were somewhat consistent with reality.

Leonardo da Vinci was more interested in various branches of mechanics than other areas of science. The scientist is also known as a brilliant improver and inventor, equally strong in theory and practice. Leonardo da Vinci's theoretical conclusions in the field of mechanics are striking in their clarity and provide him with an honorable place in the history of this science, in which he is the link connecting Archimedes with Galileo and Pascal.

With remarkable clarity, the scientist-artist sets out in general, large terms, the theory of leverage, explaining it with drawings; Without stopping there, he gives drawings related to the movement of bodies on an inclined plane, although, unfortunately, he does not explain them in text. From the drawings, however, it is clear that Leonardo da Vinci was 80 years ahead of the Dutchman Stevin and that he already knew the relationship between the weights of two weights located on two adjacent faces of a triangular prism and connected to each other by means of a thread thrown over a block. Leonardo also studied, long before Galileo, the length of time required for the fall of a body descending an inclined plane and along various curved surfaces or cuts of these surfaces, that is, lines.

Even more curious are the general principles, or axioms, of mechanics that Leonardo is trying to establish. Much here is unclear and directly incorrect, but there are thoughts that are positively amazing from a writer of the late 15th century. “No sensually perceived body,” says Leonardo, “can move by itself. It is set in motion by some external cause, force. Force is an invisible and incorporeal cause in the sense that it cannot change either in shape or in tension. If a body is moved by a force at a given time and passes through a given space, then the same force can move it in half the time through half the space. Every body exerts resistance in the direction of its movement (Newton’s law of action equal to reaction is almost guessed here). a falling body at each moment of its movement receives a certain increase in speed. The impact of bodies is a force acting for a very short time.”

Leonardo da Vinci's views on wave-like motion are even more distinct and remarkable. To explain the movement of water particles, Leonardo da Vinci begins with the classical experiment of modern physicists, that is, throwing a stone, producing circles on the surface of the water. He gives a drawing of such concentric circles, then throws two stones, gets two systems of circles and wonders what will happen when both systems meet? “Will the waves be reflected at equal angles?” asks Leonardo and adds. “This is a most magnificent (bellissimo) question.” Then he says: "The movement of sound waves can be explained in the same way. Air waves move away in a circle from their place of origin, one circle meets another and passes on, but the center always remains in the same place."

These extracts are enough to convince oneself of the genius of the man who, at the end of the 15th century, laid the foundation for the wave theory of motion, which received full recognition only in the 19th century.

3. "It is better to be deprived of movement than to be tired of being useful."

Leonardo da Vinci is a genius whose inventions belong entirely to both the past, present and future of humanity. He lived ahead of his time, and if even a small part of what he invented had been brought to life, then the history of Europe, and perhaps the world, would have been different: already in the 15th century we would have driven cars and crossed the seas by submarines.

Historians of technology count hundreds of Leonardo's inventions, scattered throughout his notebooks in the form of drawings, sometimes with short expressive remarks, but often without a single word of explanation, as if the inventor's rapid flight of imagination did not allow him to stop at verbal explanations.

Let's look at some of Leonardo's most famous inventions.

3.1 Aircraft

“The great bird begins its first flight from the back of a gigantic swan, filling the universe with amazement, filling all the scriptures with rumors about itself, filling the nest where it was born with eternal glory.”

The most daring dream of Leonardo the inventor, without a doubt, was human flight.

One of the very first (and most famous) sketches on this topic is a diagram of a device that in our time is considered to be a prototype of a helicopter. Leonardo proposed making a propeller with a diameter of 5 meters from thin flax soaked in starch. It had to be driven by four people turning levers in a circle. Modern experts argue that the muscular strength of four people would not be enough to lift this device into the air (especially since even if lifted, this structure would begin to rotate around its axis), but if, for example, a powerful spring were used as an “engine” , such a “helicopter” would be capable of flight - albeit short-term.

Leonardo soon lost interest in propeller-driven aircraft and turned his attention to the flight mechanism that had been working successfully for millions of years - the bird's wing. Leonardo da Vinci was convinced that “a person who overcomes air resistance with the help of large artificial wings can rise into the air. If only its members were of greater stamina, able to withstand the swiftness and impulse of descent with ligaments made of strong tanned leather and tendons made of raw silk. And let no one fiddle with iron material, because the latter quickly breaks at bends or wears out.”

Leonardo thought about flight with the help of the wind, that is, about soaring flight, rightly noting that in this case less effort is required to maintain and move in the air. He developed a design for a glider that was attached to a person's back so that the latter could balance in flight. The drawing of the device, which Leonardo himself described as follows, turned out to be prophetic: “If you have enough linen fabric sewn into a pyramid with a base of 12 yards (about 7 m 20 cm), then you can jump from any height without any harm to your body.” .

The master made this recording between 1483 and 1486. Several centuries later, such a device was called a “parachute” (from the Greek para - “against” and the French “chute” - fall). Leonardo’s idea was brought to its logical conclusion only by the Russian inventor Kotelnikov, who in 1911 created the first backpack rescue parachute attached to the pilot’s back.

3.2 Hydraulics

Leonardo da Vinci began to become interested in hydraulics while working in Verrocchio's workshop in Florence, working on fountains. As the Duke's chief engineer, Leonardo da Vinci developed hydraulics for use in agriculture and to power machinery and mills. “Water moving in a river is either called, or driven, or moves itself. If it is driven, who is the one who drives it? If it is called or demanded, who is the demander.”

Leonardo often used wooden or glass models of canals, in which he painted the created flows of water and marked them with small buoys to make it easier to follow the flow. The results of these experiments have found practical application in solving sewerage problems. His drawings include ports, closures, and sluices with sliding doors. Leonardo da Vinci even planned to dig a shipping canal diverting the river. Arno to connect Florence with the sea through Prato, Pistoia and Serraval. Another hydraulic project was conceived for Lombardy and Venice. He assumed the flooding of the Isonzo Valley in the event of a Turkish invasion. There was also a plan for draining the Pontine swamps (which Medici Pope Leo X consulted with Leonardo da Vinci about).

Leonardo da Vinci created lifebuoys and gas masks for both military and practical needs. Imitating the outlines of a fish, he improved the shape of the ship's hull to increase its speed; for the same purpose, he used a device on it that controlled the oars. For military needs, Leonardo da Vinci invented a double hull for the ship that could withstand shelling, as well as a secret device for anchoring the ship. This problem was solved with the help of divers who went underwater in special suits or in simple submarines.

To speed up swimming, the scientist developed a design of webbed gloves, which over time turned into the well-known flippers.

One of the most necessary things for teaching a person to swim is a lifebuoy. This invention of Leonardo remained virtually unchanged.

3.3 Car

It was in the head of Leonardo da Vinci that the idea of ​​a car was born. Unfortunately, the body drawings were not fully drawn out, because during the development of his project the master was very interested in the engine and chassis.

This famous drawing shows a prototype of a modern car. The self-propelled three-wheeled cart is propelled by a complex crossbow mechanism that transmits power to actuators connected to the steering wheel. The rear wheels have differentiated drives and can move independently. In addition to the large front wheel, there was another small one, rotating, which was placed on a wooden lever. This vehicle was originally intended for the entertainment of the royal court and belonged to the range of self-propelled vehicles that were created by other engineers of the Middle Ages and the Renaissance.

Today, the word “excavator” will not surprise anyone. But hardly anyone thought about the history of the creation of this universal machine. Leonardo excavators were designed more for lifting and transporting excavated material. This made the workers' work easier. The excavator was mounted on rails and, as work progressed, moved forward using a screw mechanism on the central rail.

3.4 Leonardo da Vinci as a pioneer of nanotechnology

artist screw hydraulic saw

A group of researchers from the laboratory of the Center for Research and Restoration of Museums in France, led by Philippe Walter, once descended on the Louvre and, pushing the museum workers aside, conducted an X-ray fluorescence analysis of the works of Leonardo da Vinci. Seven portraits by the great master, including the Mona Lisa, were exposed to the rays of a portable X-ray machine.

The analysis made it possible to determine the thickness of individual layers of paint and varnish in the paintings and to clarify some features of the sfumato painting technique (sfumato - “vague, blurred”), which made it possible to soften the transition between light and dark areas in the picture and create believable shadows. Actually, sfumato is da Vinci’s invention, and it was he who achieved the greatest heights in this technique.

As it turned out, Leonardo used varnish and paint with unique additives. But most importantly, da Vinci was able to apply glaze (glaze) in a layer 1-2 microns thick. The total thickness of all layers of varnish and paint in portraits by Leonardo does not exceed 30-40 microns; however, the refraction of light rays in various transparent and translucent layers creates a powerful effect of volume and depth. It is curious that modern screen coatings that create a stereoscopic effect are designed according to the same principle (see Appendix).

The study left open the question of how Leonardo managed to apply paint and varnish in such a thin layer (up to 1/1000 of a millimeter!). An additional intriguing fact is that no traces of brush strokes, much less fingerprints, were found in any layer of the paintings.

3.5 Other inventions of Leonardo

Leonardo's theoretical contributions to science are contained in his studies of "gravity, force, pressure and impact... the children of motion...". His drawings of the components of mechanisms and devices for transmitting motion remain. Five main types of mechanisms have been known since ancient times: winch, lever, block (gate), wedge and screw. Leonardo used them in complex devices that automate various operations. He paid special attention to screws: “On the nature of the screw and its use, how many eternal screws can be made and how to supplement them with gears”

The problem of motion transmission is closely related to friction research, which led to the appearance of bearings that are still used today. Leonardo tested bearings made of antifriction material (an alloy of copper and tin), and ultimately settled on a variety of ball bearings - the prototypes of modern ones.

Let us also mention Leonardo’s most famous inventions: devices for converting and transmitting motion (for example, steel chain drives, still used in bicycles); simple and interlaced belt drives; various types of clutch (conical, spiral, stepped); roller bearings to reduce friction; double connection, now called "universal joint" and used in cars; various machines (for example, a precision machine for automatic marking or a hammering machine for forming gold bars); a device (attributed to Cellini) to improve the legibility of coinage; bench for experiments on friction; suspension of the axles on movable wheels located around it to reduce friction during rotation (this device, reinvented by Atwood in the late 18th century, led to modern ball and roller bearings); a device for experimentally testing the tensile strength of metal threads; numerous weaving machines (for example, shearing, twisting, carding); power loom and spinning machine for wool; combat vehicles for waging war (“the most severe insanity,” as he called it); various intricate musical instruments.

Oddly enough, only one invention of da Vinci received recognition during his lifetime - a wheel lock for a pistol that was wound with a key. At first, this mechanism was not very widespread, but by the middle of the 16th century it had gained popularity among nobles, especially in the cavalry, which was even reflected in the design of the armor: for the sake of firing pistols, armor began to be made with gloves instead of mittens. The wheel lock for a pistol, invented by Leonardo da Vinci, was so perfect that it continued to be found in the 19th century.

But, as often happens, recognition of geniuses comes centuries later: many of his inventions were expanded and modernized, and are now used in everyday life.

Archimedean screws and water wheels

Hydraulic saw

CONCLUSION

In the history of science, which is the history of human knowledge, people who make revolutionary discoveries are important. Without this factor, the history of science turns into a catalog or inventory of discoveries. The most striking example of this is Leonardo da Vinci.

Leonardo da Vinci - Italian artist, sculptor, architect, scientist, engineer, naturalist. His extraordinary and versatile talent aroused amazement and admiration of his contemporaries, who saw in him the living embodiment of the ideal of a harmoniously developed, perfect person. In all his endeavors he was an explorer and pioneer, and this had a direct impact on his art. He left behind few works, but each of them was a stage in the history of culture. The scientist is also known as a versatile scientist. The scale and uniqueness of Leonardo da Vinci’s talent can be judged by his drawings, which occupy one of the honorable places in the history of art. Not only manuscripts dedicated to the exact sciences are inextricably linked with Leonardo da Vinci's drawings, sketches, outlines, and diagrams. Leonardo da Vinci owns numerous discoveries, projects and experimental studies in mathematics, mechanics, and other natural sciences.

The art of Leonardo da Vinci, his scientific and theoretical research, the uniqueness of his personality have passed through the entire history of world culture and science and have had a huge influence on it.

The legendary fame of Leonardo has lived for centuries and has not yet faded, but is still burning brighter: the discoveries of modern science again and again fuel interest in his engineering and science fiction drawings, in his encrypted notes. Particularly hotheads even find in Leonardo’s sketches almost a prediction of atomic explosions.

Leonardo believed in the idea of ​​homo faber, man - the creator of new tools, new things that did not exist in nature. This is not man’s resistance to nature and its laws, but creative activity on the basis of the same laws, for man is the “greatest instrument” of the same nature. River floods can be counteracted by dams, artificial wings are destined to lift a person into the air. In this case, it can no longer be said that human strength is wasted and drowns without a trace in the stream of time, the “destroyer of things.” Then, on the contrary, it will be necessary to say: “People unfairly complain about the passage of time, blaming it for being too fast, not noticing that it is passing quite slowly.” And then the words of Leonardo, which he wrote on the 34th sheet of the Codex Trivulzio, will be justified:

A life well lived is a long life.

La vita bene spesa longa`e.

REFERENCES

1. Arshinov, V.I., Budanov V.G. Cognitive foundations of synergetics. Synergetic paradigm. Nonlinear thinking in science and art. - M., 2002, pp. 67-108.

2. Voloshinov, A.V. Mathematics and art. - M., 1992, 335 p.

Gasteev A.A. Leonardo da Vinci. The life of wonderful people. - M.: Young Guard, 1984, 400 p.

Gnedich P.I. History of art. High Renaissance. - M.: Eksmo Publishing House, 2005, 144 p.

Zubov V.P. Leonardo da Vinci. - L.: Publishing House of the USSR Academy of Sciences, 1962, 372 p.

Cuming R. Artists: the life and work of 50 famous painters. - M., 1999, 112 p.

7. COMPULENT. Science and Technology / Applied Research / <#"526349.files/image003.gif">

Leonardo da Vinci was born on April 15, 1452 in the village of Anchiato near the city of Vinci (hence the prefix to his surname). The boy's father and mother were not married, so Leonardo spent his first years with his mother. Soon his father, who served as a notary, took him into his family.

In 1466, da Vinci entered as an apprentice in the studio of the artist Verrocchio in Florence, where Perugino, Agnolo di Polo, Lorenzo di Credi also studied, Botticelli worked, Ghirlandaio and others visited. At this time, Leonardo became interested in drawing, sculpture and modeling, studied metallurgy, chemistry , drawing, mastered working with plaster, leather, and metal. In 1473, da Vinci qualified as a master at the Guild of St. Luke.

Early creativity and scientific activity

At the beginning of his career, Leonardo devoted almost all his time to working on paintings. In 1472 - 1477 the artist created the paintings “The Baptism of Christ”, “The Annunciation”, “Madonna with a Vase”. At the end of the 70s he completed Madonna with a Flower (Benois Madonna). In 1481, the first major work in the work of Leonardo da Vinci was created - “The Adoration of the Magi”.

In 1482 Leonardo moved to Milan. Since 1487, da Vinci has been developing a flying machine that was based on bird flight. Leonardo first created a simple apparatus based on wings, and then developed an airplane mechanism with full control. However, it was not possible to bring the idea to life, since the researcher did not have a motor. In addition, Leonardo studied anatomy and architecture, and discovered botany as an independent discipline.

Mature period of creativity

In 1490, da Vinci created the painting “Lady with an Ermine”, as well as the famous drawing “Vitruvian Man”, which is sometimes called “canonical proportions”. In 1495 - 1498 Leonardo worked on one of his most important works - the fresco "The Last Supper" in Milan in the monastery of Santa Maria del Grazie.

In 1502, da Vinci entered the service of Cesare Borgia as a military engineer and architect. In 1503, the artist created the painting “Mona Lisa” (“La Gioconda”). Since 1506, Leonardo has served under King Louis XII of France.

Recent years

In 1512, the artist, under the patronage of Pope Leo X, moved to Rome.

From 1513 to 1516 Leonardo da Vinci lived in the Belvedere, working on the painting “John the Baptist.” In 1516, Leonardo, at the invitation of the French king, settled in the castle of Clos Lucé. Two years before his death, the artist’s right hand became numb and it was difficult for him to move independently. Leonardo da Vinci spent the last years of his short biography in bed.

The great artist and scientist Leonardo da Vinci died on May 2, 1519 at the castle of Clos Luce near the city of Amboise in France.

Other biography options

Biography test

An interesting test for knowledge of the biography of Leonardo da Vinci.

Teacher - Somko E.V.

Slide 2

Many outstanding scientists valued art and admitted that without studying music, painting, and literary creativity, they would not have made their discoveries in science. Perhaps it was the emotional upsurge in artistic activity that prepared and pushed them for a creative breakthrough in science.

Slide 3

"For Pythagoras, music was derived from the divine science of mathematics, and its harmonies were strictly controlled by mathematical proportions. The Pythagoreans maintained that mathematics demonstrates the precise method by which God established and established the Universe. Numbers, therefore, precede harmony, since their immutable laws govern all harmonics." proportions. After the discovery of these harmonic relations, Pythagoras gradually initiated his followers into this teaching, as into the highest secret of his Mysteries. He divided the multiple parts of creation into a large number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color. and form. He then proceeded to demonstrate the accuracy of his deductions, demonstrating them on the various planes of reason and substance, from the most abstract logical premises to the most concrete geometrical solids. From the general fact of the consistency of all these different methods of proof, he established the absolute existence of certain natural laws. "

Slide 4

Einstein was passionate about music, especially the works of the 18th century