Download a treatise on cardano gambling. The life and discoveries of Gerolamo Cardano, or the secrets of one formula
Which of today's schoolchildren, and especially motorists or automakers, does not know what a driveshaft is? However, this phrase is well known to everyone, even those far from the automotive industry, because the advent of the cardan mechanism revolutionized technology.
In any encyclopedia you can read: “The driveshaft is a structure that transmits torque from the transmission to the wheel drive. It is used in various means movement. A characteristic feature is the cardan drive, invented by Girolamo Cardano, which allows the transmission of torque between non-parallel axles."
You can read it, but few people know about the fate of its inventor Girolamo Cardano (1501-1576). At one time, he was not only a great engineer, mathematician, mechanic, physicist and doctor, but also a major occultist. To understand this, it is enough to mention just one fact: he made all important decisions based on the interpretation of his own dreams.
Girolamo Cardano was an absolutely fantastic man, encyclopedically educated. He stands on a par with such figures as Saint Germain, Cagliostro, Swedenborg. From birth to death, Cardano knew the other world, was known as a powerful magician, healer and deep expert in the secret sciences.
In fact, his abilities were truly immense - and not only in the occult and magical field. Those involved in intelligence services, for example, no matter which country, honor him for developing an outstanding encryption system, which was named in his honor as the “Cardano lattice.”
This same outstanding person invented the famous method of secretly opening mail, that is, perlusration: it does not even occur to the final recipient that the message addressed to him had already been read by someone else. The technique of such an opening is very unusual.
A thin rod is inserted into the envelope through a gap in the glue and the letter is carefully wound onto it, then removed through the same gap and read.
After reading the message, it is returned to its place in the same way. Many people know this method: using it, many scammers have been taking money out of bank packages since Soviet times. Of course, the method requires a certain dexterity and experience, but any experience can be acquired.
Girolamo Cardano was the illegitimate son of Milanese lawyer Fazio Cardano. Fazio was well versed not only in law, but also in medicine and mathematics.
He even advised his friend, the great Leonardo da Vinci, on geometry issues. As contemporaries write, Cardano’s father and son had personal spirits (or demons) that helped them in life. They warned them of the dangers. Most often in a dream.
Cardano claimed that he himself was guided by dreams in the most important cases of his life: during marriage and in his medical practice. As a man, he was absolutely insolvent until he was thirty.
In a dream he was informed that he would gain male strength, and even his future wife was named, whom he had never seen before.
Cardano's dreams also suggested treatments that were best suited for a given disease and a given patient. And people thought that he was healing with the help of magic or evil spirits.
In addition to the ability to interpret dreams, Cardano had three more remarkable abilities that helped him solve life and scientific problems.
He fell into a trance any time he wanted. He could see what he needed using his imagination. He knew how to find out about upcoming events by looking at his nails.
In 1524, Girolamo Cardano's father died, leaving him a house and a small inheritance. The young heir decided that dice, chess and cards would help him quickly increase his fortune.
He was a hot-headed man, he always carried a knife with him and, when he felt that the enemy was cheating, without hesitation, he used it. His uncontrollable temper and aggressiveness got him into a lot of trouble.
In addition, his life was darkened by another point: Cardano was not accepted into the medical corporation not only because of his unbearable character, but also because he was illegitimate. However, without permission to practice medicine, Cardano still treated - and very successfully.
So, for ten years, John Hamilton, Archbishop of Scotland, suffered from asthma. The best doctors could do nothing to help him and considered the archbishop's position completely hopeless. Meanwhile, the patient’s torment became more and more unbearable every day.
It was then that his entourage remembered the Italian doctor Cardano, who, as they said, was subject to any disease. Cardano, who never turned down the opportunity to earn big money, immediately hit the road.
In 1552 he arrived in Edinburgh and immediately examined the archbishop. And two weeks later Cardano was already leaving the city, having received 2 thousand gold crowns and many expensive gifts.
By this time, his high-ranking patient’s illness had completely disappeared. This fact is recorded in numerous documents. But asthma is not a disease that can be cured in one day, any doctor knows this.
Rumors of miraculous healings forced wealthy people to turn to Cardano, and he soon acquired many influential patrons: among them were cardinals, senators, and patricians. In 1537 Cardano became the personal physician of Senator Sfrontati.
Among his patients were also the senator's son, the quiet and sickly Niccolo, the future Pope Gregory XIV. Cardano's fame grew quickly, and he began to be called the best doctor in the world. He received invitations to enter permanent service from the German Emperor, the French King, the Queen of Scotland and the Pope.
Cardano was offered the most favorable conditions, but he rejected all offers, valuing his independence above all else. The mystical scientist spent his time on teaching, medical practice, research and gambling.
He wrote about everything in the world: about miraculous cures, about water, air, poisons, plague, urine, wisdom teeth. Many of his books became bestsellers.
In 1543, Cardano published a treatise on astrology, highly appreciated by his contemporaries. By the way, among his astrological predictions were prophecies about the great changes that would occur in the Christian world around 1800. Many historians and occultists believe that he was talking about the coming French Revolution. Most likely, they are right, because nothing larger and more significant than the French Revolution happened on the planet in those years.
In fact, Cardano wrote many books on astrology. His works such as “On the restoration of celestial times and movements, as well as 47 horoscopes, remarkable because of the events that they predict” (Cardano’s first major astrological work), “On questions”, “On annual, monthly and daily circulations”, “Examples of one hundred genitura”, “Book of twelve genitura”, comments in 4 books to Ptolemy’s “Tetrabiblos”, “Astronomical aphorisms in seven parts”, etc.
Cardano compiled horoscopes of his most famous contemporaries - Petrarch, Durer, Vesalius, Luther. Reviews say they were surprisingly accurate.
A pious believer in astrology, he nevertheless, in his work Geniturarum exempla (1554), gives examples of twelve unsuccessful horoscopes to show how easy it is for an astrologer to fall into error.
Using astrology and magic in his medical practice, Cardano developed astrological metal therapy and the octatope system (an eight-part scheme for constructing horoscope houses). He was also the founder of metoposcopy, a system of divination based on the lines of the forehead.
Cardano wrote a lot about various types of magic. Some, this genius believed, are based on the use of the hidden powers of things, others on the influence of the stars, some on the separation of the soul from the body, on the relationship between man and nature, etc.
Cardano created an original cosmology, according to which primordial matter consists of three elements - Water, Air and Earth, and Fire is only a form of existence of all-pervading celestial heat.
Cardano's astrological analysis of religions is also of great interest. Following Pomponazzi, he explained the emergence, flourishing and decline of religions by the influence of celestial bodies.
In addition, Cardano specifically dealt with the problem of the influence of stars on precious stones. Stones, as this great Italian taught, have special forces that they don't have soft fabrics plant or animal. Thus, hyacinth worn by a person affected by the evil eye turns pale and loses its shine.
There's no such thing gemstone, which would not have great merits. Some help prolong life, others gain wealth, physical strength, health, love, luck.
However, stones can make a person lazy, timid, and sad. It is important at what position of the stars the jewelry with stones is made, since the stone takes on the power of the heavenly bodies. It is curious that everything that Cardano spoke about in relation to stones is confirmed not only by modern esotericists, but also by scientists.
Cardano himself had a wonderful emerald that protected him, revealed many secrets to him, but at the same time did not teach him how to help himself and his sons. The fact is that Cardano’s firstborn was executed, and youngest son- Aldo, like his father and grandfather, became a passionate player. So passionate that one day he lost everything he had, including his clothes.
To pay, he stole money and jewelry from his father. Aldo was imprisoned many times, but Cardano always rescued his heir. He knew that he would not have another. Cardano was, so to speak, a classic illustration of the expression: “A shoemaker without boots.”
Cardano associated his own troubles with the fact that he too often used the help of spirits. They never provide this help disinterestedly, and the payment for their services is always immeasurably more than the help. (I wish modern experts in magic and occultism would remember this!) However, the gift of making contact with spirits is given to few people, so almost no one is able to refuse the help of the rulers of the other world.
In 1570, Cardano, despite his extensive connections in the Vatican, was arrested on charges of heresy. The reason for his imprisonment was his insatiable scientific curiosity. Cardano's heresy was that he compiled a horoscope not of anyone, but of Jesus Christ himself (and then Muhammad), and argued that all the events of their lives were determined by the influence of the stars.
Cardano spent only a few months in captivity, but in the end he suffered seriously: he was prohibited from holding a post at the university and publishing his works.
Then Cardano went to Rome, where his old patient Niccolo Sfrondati, now Pope Gregory XIV, sat on the throne of St. Peter. Dad forgave the scientist, because from childhood he knew that he did everything sincerely, following his passion. The Pope allowed Cardano to resume medical practice and even gave him a small pension.
Girolamo Cardano died on September 21, 1576, three days before his 75th birthday, as he predicted in his own horoscope.
The lunar crater Cardanus is named after Cardano.
Gerolamo(Girolamo, Jerome) Cardano(lat. Hieronymus Cardanus, Italian. Girolamo Cardano, Gerolamo Cardano; September 24, 1501, Pavia - September 21, 1576, Rome) - Italian mathematician, engineer, philosopher, physician and astrologer. The formulas for solving the cubic equation discovered by Scipio del Ferro (Cardano was their first publisher), the gimbal suspension and the cardan shaft are named in his honor.
Biography
Gerolamo Cardano was the natural son of the lawyer Facio Cardano; his father legitimized him only shortly before his death in 1524, by marrying Clara Micheri, his mother. The boy was often sick, once he was even close to death, but miraculously recovered. From the age of seven he worked for his lawyer father as a servant, carrying a bag of papers and books.
Over time, Facio began to notice the boy's intelligence and his thirst for knowledge, so he taught him reading, writing and arithmetic. His father told him different stories, gave books, which the boy read greedily, increasingly thinking about the meaning of existence. Gerolamo later writes about his youth in his autobiography:
In 1520, Cardano entered the University of Pavia to study medicine, but due to the closure of the university in 1524, he completed his studies at the University of Padua. In 1526 he received a doctor's degree and at first studied medicine exclusively (he taught in Pavia and Padua). In 1534 he became a professor of mathematics in Milan, and in 1539 he was admitted to the Milan College of Physicians. In 1562, he was forced to leave Milan and began teaching medicine in Bologna, gaining a reputation as one of the best European doctors, but did not abandon his studies in other sciences. He also worked part-time by compiling astrological almanacs and horoscopes. For compiling and publishing the horoscope of Jesus Christ (1570), he was accused of heresy, spent several months in prison and was forced to go to Rome to ask the Pope for absolution.
In 1531, Cardano married 15-year-old Lucia Bondareni. His wife died in 1546, leaving Cardano with two sons and a daughter. Cardano's eldest son was convicted of murdering his adulterous wife and executed, and the youngest son became a gambler and stole money from his father, as a result of which he was expelled from Bologna.
According to legend, Cardano predicted the day of his death and, in order to justify his prediction, committed suicide. In fact, he was mistaken by 3 years, setting the day of his death for December 1573.
Scientific and engineering activities
Despite the fact that Cardano practiced medicine almost all his life, he left his mark in many areas of science, which was typical for encyclopedist scientists of the Renaissance.
Cardan shaft, cardan clutches, gimbal suspension - these things are well known today, especially to auto mechanics and inertial navigation specialists. Mathematicians still know the Cardano formula, encryption specialists know the “Cardano lattices”. All this is the work of the hands, or rather the mind, of the great mathematician, mechanic, engineer, geologist, astronomer - in a word, the Renaissance encyclopedist Gerolamo Cardano. However, he considered himself, first of all, an outstanding doctor - in his autobiographical book “About My Life” he even compared himself with Hippocrates, Galen and Avicenna!
Origin
He was born on September 24, 1501 - exactly 510 years ago - in the ancient city of Pavia, in northern Italy. 510 years is, of course, not a “round” date, but even 10 years ago, almost no one seemed to remember the half-millennial anniversary of one of the most notable representatives of the Renaissance. Probably, the temporal distance had an effect: we willingly celebrate centenary, even bicentennial dates, but we hardly look further into the depths of history. Perhaps because people who lived so long ago seem to us to be semi-mythical creatures, even despite their accomplishments and achievements. But they lived, and we know quite a lot about the lives of some of them, such as Cardano.
So, Gerolamo Cardano's father was a famous lawyer, whose name is found even in the notes of Leonardo da Vinci, but the boy was born out of wedlock. This greatly hindered him in the future, because when, after graduating from the University of Padua in 1526, he tried to obtain medical practice in Milan, he was not accepted into the city college of doctors as an illegitimate. However, he still began treatment, but in the provincial town of Gallart. At the same time, he selflessly continued to explore the mysteries of medicine and even began to write treatises on medical topics. However, not only medical, he was also interested in philosophy, astrology, and much more. Around the same time, he began his career as a lecturer in mathematics: this science attracted him from childhood, and already in his youth he achieved success in it no less, and perhaps greater, than in medicine. He also constantly improved his skills in gambling, which he joined back in teenage years. And he not only played, but also tried to find certain patterns in the game, which ultimately resulted in one of his completely scientific works- “The Book of Dice,” which contained the beginning of probability theory, some questions of combinatorics and even psychology (of course, the game and the players). Note that the book was written when he was still a very young man - in 1526, but he published it only in 1563.
Renaissance polymath
In general, he wrote a lot of books during his life. After all, he studied not only medicine and mathematics, but also philosophy, chemistry, geology, mineralogy, drawing up calendars, astronomy and astrology and, of course, inventing and designing various technical devices. There are 138 known printed works with a total volume of approximately 7,000 large format pages - in folio. He was even the author of original encyclopedias - the books “On Subtle Matters” and “On the Variety of Things.” In addition, he destroyed about 100 (!) of his own creations himself in anticipation of arrest several years before his death.
In all the industries in which Gerolamo Cardano was involved, he achieved considerable success. It is known, for example, that even the Pope resorted to his services as an astrologer (in those years, compiling horoscopes was considered a completely charitable activity). There is even a version that his death was not accidental: he allegedly committed suicide in order to confirm his own horoscope. Information about the peculiarities of his character that have survived to our time, if they do not make us believe in this gloomy legend, then at least explain a lot in his life.
Gambling, vindictive, desperate, sharp-tongued, ready to do anything to achieve a goal, and at the same time noble and faithful in friendship, Cardano was, of course, an extraordinary person. It is not for nothing that the great German mathematician and philosopher Gottfried Wilhelm Leibniz later remarked: “Cardano was a great man with all his shortcomings; without them he would have been perfect.” In fairness, it is worth noting that these shortcomings were a consequence difficult childhood: his mother considered him a burden, was embarrassed as if it were a disgrace, and often took out her anger on him by beating him; the father lived separately and during meetings also limited educational influence to spanking; Moreover, Cardano could not boast of good health either in childhood or in adulthood. Therefore, what others received without any effort, he had to snatch in life. It is quite obvious that in many ways it was the early experiences of survival that ultimately shaped both positive and negative traits his character and desire for recognition.
The latter was extremely important in his life. It is known, for example, that even the famous device that received his name and is now known as the cardan shaft or gimbal, appeared in 1541 as a result of the fact that Cardano (then rector of the city college of doctors) was given the honor of being one of the most respected citizens of Milan to meet Spanish King Charles V. He even walked near the royal canopy. Touched by this display of respect, he proposed to equip the crowned carriage with a suspension of two shafts, the mutual rotation of which would not remove the carriage from a horizontal position. True, the idea of such a suspension was known for quite a long time and even found a place in Leonardo da Vinci’s Codex Atlanticus, however, educated people were able to become acquainted with this collection of a wide variety of information from almost all then known fields of knowledge only two centuries later. And this design began to be used more and more widely in various variants and used in technology precisely after the unveiling of Cardano.
The mystery of cubic equations
Around the same years, Cardano was actively involved in mathematics. Back in the thirties, he began working on a large treatise on arithmetic, the first edition of which was published in 1539. “The Practice of General Arithmetic” brought him recognition among mathematics experts, but the author himself was not too pleased with it. The reason was that it did not reflect the solution to one of the then mathematical secrets, which, although he owned, he could not make public due to a circumstance associated with the author of this discovery.
We are talking about a way to solve cubic equations. Or, rather, about the recipes for their solutions, because the introduction of algebraic symbolism was still more than a hundred years away, and mathematicians explained how to find the roots of equations with descriptions of the necessary actions, often in poetic Latin.
European and Arab mathematicians have been trying to solve this problem for several centuries. In 1494, the famous Italian scientist Luca Pacioli, in the book “Summa of Arithmetic” - one of the first printed mathematical treatises, written, moreover, not in Latin, but in Italian, even authoritatively stated that in order to solve cubic equations “the art of algebra still there is no given method, just as there is no given method for squaring a circle, and therefore they should be classified as “impossible.” This statement distracted many mathematicians from further attempts to find such a way.
Many, but not all.
Around 1515, Professor University of Bologna Scipio del Ferro (1456-1526) had already invented a way to solve cubic equations of the form x3 + ax = b. Before his death, Ferro revealed his secret only to his son-in-law Annibal della Nava and also to his student Antonio Mario Fiore. The latter decided to use the acquired knowledge in tournaments to solve various mathematical problems, which were then common in Europe. Victories in such tournaments brought respect, monetary awards and the opportunity to get a decent position at one of the universities.
Tartaglia and his victory
At the same time, a young mathematician from Verona, Niccolo Fontane, known in the history of science under the nickname Tartaglia, which translated from Italian meant “stutterer,” began to solve the problem of solving cubic equations. He owed this nickname to injury from a saber wound to his face and palate, received in childhood from a French soldier - one of his conquerors hometown Brescia during the war with the Venetians. After that he could not speak freely. But the injury did not stop him from studying and doing science. This was a real feat, because his family was very poor: his father, who worked as a postman, died when he was only six years old, besides him his mother had two more children. He even attended school for only 15 days, and then he had to work and study while other children were playing on the street. And yet, his success in mathematics was so significant that he soon began to make a living by teaching and consulting engineers, artillerymen, merchants, architects and builders. Moreover, he translated alive Italian works of Archimedes and Euclid and wrote his own books devoted to the practical application of mathematics and mechanics.
Once, a teacher from Brescia, where Coi, turned to him for help in solving problems that boiled down to cubic equations. Tartaglia refused indignantly, saying that he didn’t even want to take on obviously unsolvable tasks. However, the problems interested him, and after some time Tartaglia managed to find a way to graph a cubic equation of the form x3 + ax = b and he began to declare that he had mastered a great algebraic secret. Rumors about this also reached Antonio Fiore, who took them for simple praise of an ignoramus. By the way, Fiore and Tartaglia thought the same thing, who somehow learned about del Ferro’s will.
However, confident in his " secret weapon", del Ferro challenged Tartaglia to a competition in 1535, under the terms of which the rivals exchanged thirty problems through a notary, the solution of which was given fifty days. The winner was the one who solved large quantity tasks. Of course, all 30 problems that Fiore came up with were cubic equations with different coefficients. To find the key to their solution, Tartaglia had to make every effort. In the end, eight days before the deadline when the decision had to be handed over to the notary, a way was found. Therefore, he solved the proposed problems within two hours. The next day, he found a way to solve cubic equations of the form x3 = ax + b, which, due to the fact that negative numbers were not yet used at that time, were considered different from the one given above. As for Fiore, he failed to cope with most of the problems selected by Tartaglia in various sections of algebra and geometry.
The rumor of Tartaglia's brilliant victory not only over Fiore, but over the mathematical riddle of the centuries, quickly spread throughout Italy. Cardano, who cherished ambitious dreams that the mathematical treatise he was then just writing would replace classic book Luca Pacioli, lost his peace. He began to literally pursue Tartaglia with a request to reveal his secrets to him. He stubbornly refused, even suspecting that Cardano was a figurehead that the above-mentioned mathematics teacher where Koi had filmed. However, oddly enough, after some time Cardano still achieved his goal! How he forced Tartaglia - a man who, according to contemporaries, was far from angelic in character - to part with his secret is not entirely clear. But the fact remains that he told Cardano about his recipe in Latin verse, although without indicating any hints about its derivation. In exchange, Cardano was forced to swear that he would never reveal it to anyone else. Therefore, he simply had no right to publish the decision in his book!
"Great Art"
Cardano spent several years carefully testing and justifying the resulting rules. Be surprised by this for a long time it’s not worth it: there was no algebraic symbolism at that time, and even using ready-made methods, not to mention their derivation, was a very difficult matter. But Cardano succeeded; moreover, he also found a way to solve equations of the form x3 + b = ax, and then complete cubic equations. He solved these equations using, if necessary, reasoning that played with negative roots. He allowed their existence, although he called them “fictitious” or “less pure.” Thus, it was Cardano who was the first among mathematicians to begin, albeit very carefully, to operate with negative numbers. Moreover, Cardano even allowed the possibility of using in calculations complex numbers, thanks to which it is ultimately possible to obtain real roots of the equations.
In 1543, Cardano, together with his best student Luigi Ferrari, visited the son-in-law of the late professor Scipio del Ferro, Annibal della Navi, in Bologna (as already mentioned, della Navi was one of two people to whom the professor entrusted his secret). Without much objection, he allowed them to familiarize themselves with his father-in-law’s papers, in which they found a description of a method for solving a cubic equation that was already familiar to them. Now nothing connected Cardano - another source was found from where the treasured formula could be obtained, so the path to its publication was open! At that time, Gerolamo Cardano had already begun work on a systematic presentation of what was then known from algebra, so without further ado, he included in his book “The Great Art, or On the Rules of Algebra” (in the history of mathematics it is more often called simply “The Great Art” ") section on cubic equations with a preface outlining the history of the issue.
The book was published in 1545 and caused a frenzy in Tartagli. He tried to take revenge, distributed insulting letters, and in his book “Problems and Various Inventions” (1546) attacked Cardano with reproaches. Instead of Cardano, his already mentioned student Ferrari, also an outstanding mathematician, entered the quarrel, the results of whose research, with appropriate references to the author, were also included in “Big Art”. Ferrari even challenged Tartaglia to a public debate, which he shamefully lost. But from then on, the formula for solving the cubic equation was already associated with “Great Art” and over time the name “Cardano’s formula” was assigned to it.
The last years of Cardano's life were not easy. One of his sons poisoned his wife out of jealousy and was executed. The second became a gambler and robbed his own father. In 1570, Cardano himself was imprisoned - he was persecuted by the Inquisition. Seven months later he was released on bail without the right to publish his works or teach. He moved to Rome and began practicing medicine. However, in 1575 he took up his pen again and began writing the book “About My Life.” In it, he reflected on his appointment, summed up his achievements and defeats, and recalled unusual cases what happened to him. This book has become a valuable source of information not only about his fate, but also about those times...
Dmitry Stefanovich
Celebrity card | |
Cardano Gerolamo | |
Was born | 24 September 1501 |
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Died | 21 September 1576 |
Activity | Italian physician, mathematician, philosopher, engineer and astrologer |
Achievements | Made a huge contribution to the development various industries medicine, in particular, showed the importance of the general healthy state of the body in the treatment of various diseases, described typhoid fever, studied syphilis, gonorrhea and other diseases |
Biography
Gerolamo Cardano was born in the Italian city of Pavia in Lombardy. He was the natural child of lawyer Facio Cardano. Gerolamo claimed in his autobiography that his mother tried to have an abortion. The boy had a difficult childhood; he was sick very often.
In 1520, Cardano entered the Faculty of Medicine at the University of Pavia, against the wishes of his father, who wanted his son to study law. Due to the closure of the university, Gerolamo completed his studies at the University of Padua (in 1526). Due to his confrontational and eccentric nature, as well as the fact of his illegal birth, the young physician had difficulty finding work, but he managed to gain a good reputation as a doctor. Cardano taught in Padua and Pavia. In 1535 he received the title of professor of mathematics, and in 1539 he was admitted to the Milan College of Medicine.
From 1562 he taught medicine in Bologna, but did not stop studying other sciences. In addition, Cardano compiled astrological horoscopes and almanacs. For compiling and publishing the horoscope of Jesus Christ in 1570, the scientist was accused of heresy and imprisoned for several months. He was forced to go to Rome to ask Pope Pius V for absolution. According to legend, Cardano, a dedicated astrologer, predicted the date of his death, so he committed suicide.
Contribution to medicine
Cardano was a pioneer in the field of allergy treatment. When the Archbishop of St. Andrews John Hamilton from Scotland, who had suffered from asthma for more than 10 years, approached him, the doctor observed the patient for more than a month and prescribed him treatment - a diet, water procedures and a change in the entire household environment. The bishop's feather bed was replaced with a silk mattress, and the leather pillow was replaced with linen, stuffed with finely chopped straw. Hamilton quickly felt relieved. Most likely, the cause of the disease was chicken feathers and down.
The famous physician cured the head of the Augustinian order in Milan named Francesco Gaddi from scrofulous infection (tuberculoid leprosy). Cardano concluded that the main cause of the disease was neglect of all bodily needs. The doctor prescribed the patient regular exercise, good sleep, frequent bathing, wearing underwear over his naked body (instead of burlap) and a diet of fish and wine. After some time, Gaddi fully recovered his health. Cardano successfully applied similar methods to other patients suffering from tuberculosis.
Cardano was the first to describe typhoid fever. The doctor determined that this disease is transmitted through fleas and lice. In the field of surgery, he developed a quick way to operate on a hernia. The physician also studied syphilis and gonorrhea, determined the sequence of menstruation, discovered methods of treating gout, established the difference between measles and petechial fever, and developed a method for teaching the blind and deaf-mutes. In addition, he dealt with problems of psychiatry, paying special attention to epilepsy.
Other achievements
Although Cardano practiced medicine almost his entire life, he made contributions to many other fields of science. Eg, scientist first in Europe he used algebraic negative roots of equations and wrote a work on the theory of probability in gambling. In the field of mechanics, Cardano described many different mechanisms, incl. own inventions - combination lock, cardan shaft, etc. He proposed a simple grid for encoding messages.
Famous doctors of all times | ||
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Austrian | Adler Alfred Auenbrugger Leopold Breuer Joseph Van Swieten Gaen Antonius Selye Hans Freud Sigmund | |
Antique | Abu Ali ibn Sina (Avicenna) Asclepius Galen Herophilus Hippocrates | |
British | Brown John Harvey William Jenner Edward Lister Joseph Sydenham Thomas | |
Italian | Cardano Gerolamo Lombroso Cesare | |
German | Billroth Christian Virchow Rudolf Wundt Wilhelm Hahnemann Samuel Helmholtz Hermann Griesinger Wilhelm Gräfenberg Ernst Koch Robert Kraepelin Emil Pettenkofer Max Ehrlich Paul Esmarch Johann | |
Russian | Amosov N.M. Bakulev A.N. Bekhterev V.M. Botkin S.P. Burdenko N.N. Danilevsky V.Ya. Zakharyin G.A. Kandinsky V.Kh. Korsakov S.S. Mechnikov I.I. Mudrov M.Ya. Pavlov I.P. Pirogov N.I. Semashko N.A. Serbsky V.P. Sechenov I.M. Sklifosovsky N.V. Fedorov S.N. Filatov V.P. | |
French |
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| Yuri Polunov
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| Girolamo Cardano
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This exceptional genius caused all future generations to doubt him. We must believe that the greatest intelligence is very closely connected with the greatest extravagance, or its character will remain an insoluble mystery.
G. E. Lessing (1729–1781)
His life is one of the most unusual we know. Falling from one extreme to another, from contradiction to contradiction, he combined sublime wisdom and incredible absurdity.
G. Morley (1822–1894)
He's very scientist philosopher and a doctor of our time, but at the same time he looks more like a delirious patient than a normal person.
F. Sankhets (1552–1632)
He is filled with so many rash ideas that he is practically unable to think critically about even one hundredth of them.
I. Kepler (1571–1630)
No one is wiser than him when he is right, and no one is crazier when he is wrong.
G. Boerhaave (1668–1738)
We should not say that his great mind is mixed with madness, but on the contrary, that his madness is mixed with great mind.
G. Naudet (1600–1653)
Cardano... is likened to a rude and insane writer of fables, although he is a thousand times more learned.
D. Bruno (1548–1600)
In his voluminous volumes, he did not convey to posterity anything on this issue that would be worthy of a philosopher, but only some information taken and copied from other authors or unsuccessfully invented.
W. Gilbert (1564–1603)
Genius, but not character.
M. Kantor (1829–1920)
I undertake to find the thoughts of any authors from Cardano.
S. L. Montesquieu (1689–1755)
Cardano sees science everywhere in connection with his personality, with his way of life. Therefore, from his works a naturalness and liveliness comes to us, which attracts us, excites us, refreshes us and forces us to act. This is not a doctor in a long robe who teaches us from the pulpit, but a person who walks nearby, makes comments, is surprised, and is sometimes filled with pain and joy, and this all fascinates us.
W. Goethe (1749–1835)
He was not equal in anything! Sometimes he would walk so quickly as if he were running from an enemy; sometimes he acts importantly, as if he were carrying the sacred utensils of Juno!.. Either he speaks lofty speeches about kings and tetrarchs, then he suddenly says: “That’s enough for me, if only I had a table, even a tripod, a simple salt shaker for salt, a rough toga for the cold!”
Horace.
"Satires"
Sixteenth century - Cinquecento - the last century of the Renaissance, this heroic and sublime era when, according to the historian, “man trembled like a taut string set in motion by a bow: he showed exceptional energy, brilliant ingenuity, breathtaking imagination and reached heights with unheard-of speed pure heroism." The returned culture of classical antiquity, the high moral values of pre-Christian civilization, the great artistic creations of antiquity, revealed to man, removed the scales from his eyes, broke the chains of the giant, and he turned into a creator and creator, humanist, philosopher, scientist, poet, artist, with incomprehensible generosity and with reckless faith in his own strength, creating a pantheon of his own glory.
The Cinquecento is the century of Leonardo da Vinci, Titian, Ludovico Ariosto, Torquato Tasso, Michelangelo Buonarotti, Nicolaus Copernicus, Erasmus of Rotterdam, Tycho Brahe, Martin Luther, Ferdinand Magellan, Andreas Vesalius, François Vieta, Giordano Bruno and many, many others.
This is the age when the Earth was overthrown from its pedestal and transferred from the center of the Universe to the orbit in which it revolved around the great and motionless Sun. This dealt a crushing blow to religious anthropocentrism, for if the Earth is an ordinary planet, then man is not the crown of divine creation. And even earlier, the Augustinian monk Martin Luther nailed a sheet with his famous theological theses to the door of the church in Wittenberg, thereby marking the beginning of the end of religious monopoly catholic church. The Church Reformation tore away entire countries and peoples from papal power. Faced with the threat of a further decline in the authority of the Roman Church, its leaders took a number of energetic measures, and in the second half of the century the religious liberalism of the Renaissance was replaced by the brutal orthodoxy characteristic of Spanish Catholicism.
Dark night, descending on Europe, captured first of all the birthplace of the Renaissance, where, as Machiavelli put it, the power of the pope was not strong enough to unite the country, but strong enough to prevent such a unification. State fragmented, consisting of numerous small monarchies and urban republics, Italy became easy prey for two powerful powers - France and Spain. The rivalry between them led to the fact that the French were eventually driven out of the country and most of it came under the heel of the Spanish Habsburgs: according to the peace treaty of 1559, Spain received Lombardy, the southern part of the country and Sicily. Thus, in Italy of the 16th century, religious oppression was combined with the oppression of foreign domination, and this double pressure, strengthened by the general economic decline in the country, at the beginning of the next century moved the birthplace of the Renaissance to the background of the theater of European history.
During this difficult time, the great Italian mathematician, doctor, philosopher, astrologer, inventor and writer Girolamo Cardano lived in Italy. Its long and fast paced life was full of ups and downs: he either became an ascetic, or indulged in all sorts of excesses;
he knew the dungeons of the Inquisition and the palaces of nobles; he had to experience hunger, poverty, humiliation, insults, but also acquire the reputation of the best doctor in Europe, whose advice was sought by popes and sovereigns, taste the glory of a great mathematician, a famous writer, and the author of many dozens of books. Almost the same age as his age, he learned and accepted all its prejudices and misconceptions: his brilliant algebraic discoveries coexisted with medieval ideas about the world, descriptions of ingenious mechanisms were interspersed with reports of miracles, various prophecies and monsters. A fearless philosopher who denied the immortality of the soul, he was in awe of any foreboding and firmly believed in amulets, recognized “ prophetic dreams", other omens, the mystical power of numbers.
For us, of course, what is important is not the delusions of Cardano, so characteristic of his time, but the remarkable mathematical discoveries and bold philosophical constructions. History will forever preserve his name among the names of those who, in the words of A. I. Herzen, “prepared the propylaea of the new science”: “At their head (not in time, but in power) was Giordano Bruno, then Vanini, Cardan, Campanella, Telesius, Paracelsus and others. Main character of these great figures consists in a living, true feeling of crampedness, dissatisfaction in the vicious circle of contemporary science, in an all-consuming desire for truth, in some kind of gift of foresight of it.”
Hundreds of articles are devoted to the life and work of Girolamo Cardano; about two dozen biographies of the scientist have been published in different time in Italy, England, France, Germany, USA. There are relatively few publications about him in Russian, and there is no detailed biography. The book offered to the reader is an attempt to fill this gap. When working on it, we used, first of all, Cardano’s autobiographical book “About My Life,” as well as publications by domestic and foreign authors.
The first version of the book “Girolamo Cardano” was published thirty years ago and received favorable reviews from readers. Over the past years, a lot of interesting data has appeared about the outstanding Italian scientist - and thus was born A new book, which the reader holds in his hands. Unfortunately, Rafail Samoilovich Guter (1918–1978), a charming man of encyclopedic knowledge, my teacher, friend and co-author, will not see her.
Yu. L. Polunov
On a September day in 1501, a young widow named Clara Miceri hurriedly passed through the city gates of Milan on the road that led to Pavia. Leaving the city, she was fleeing not only from the plague, which claimed many lives, but also from the wrath of Fazio Cardano: this man opposed the birth of his child, whom Clara carried under her heart...
Fazio was then fifty-six years old. A doctor of law and medicine at the same time, “well versed in mathematics,” he was famous in Milan for his learning, temper and far from good-natured humor. Maybe that’s why they tried to poison him twice, but he only paid with the loss of all his teeth. The hunched and tongue-tied Fazio “had a ruddy face... and his eyes were whitish and capable of seeing well in the dark.” As a member of the city bar, he wore red cloth and always covered his head with a black cap, since “some parts of his skull were removed due to the wound he received.” Fazio had a carefree attitude towards money and easily gave loans; among his acquaintances he was known as a fan of telling all sorts of things mysterious stories, but had few friends. Among them he singled out Senator Angelo Selvatico, his former student, and the mechanic Galeazzo del Rosso, who made wonderful swords and armor of unprecedented strength. Fazio Cardano believed in spirits and demons and revered above all else the great Hellenic geometer Euclid. He earned his daily bread as a lawyer and also as a teacher civil law and mathematics; was close to the circle of Milanese scientists and engineers, which included the mathematician Luca Pacioli, the architect Donato Bramante, members of the engineering college Pietro Monti, Giacomo Andrea Ferrari and Leonardo da Vinci. The great Leonardo repeatedly consulted Messer Fazio on questions of geometry.
One day, a certain Milanese publisher set out to publish something useful for the scientists of his city. He turned to Fazio for advice and help, and he willingly prepared for publication a manuscript on geometric optics “Perspectiva Communis”, written by the Archbishop of Canterbury John Peckham (12401292). Fazio Cardano not only corrected the archbishop's numerous mistakes, but also provided the treatise with additions and commentaries. The book, published in 1480, had big success and was then republished in Leipzig, Venice, Nuremberg and Paris.
This is how, when we first meet him, a man appears before us, whose wrath the widow Clara Mikery feared.
Girolamo Cardano wrote about his birth: “I was born, or rather taken out of my mother’s womb, with curly black hair and no signs of life; I was brought back to my senses only by a bath of warm wine.” This happened in Pavia, in the house of Isidore dei Resti, a wealthy citizen and acquaintance of Fazio, at about seven o'clock in the evening on September 24, 1501. Girolamo later noted: “The position of the planets foreshadowed that I would certainly be born a freak, which almost did not happen ... [I] would have some cunning and lack of freedom of spirit, and at the same time a tendency to rash and thoughtless decisions.”
Horoscope of Girolamo Cardano, compiled by him
Born in Pavia, Girolamo, however, always considered himself a Milanese. Members of the Cardano family lived in this city and its surroundings for many centuries: back in 1189, Milone Cardano was the prefect of Milan, and a century and a half later, Francesco Cardano led the militia of Duke Matteo Visconti. Some even argued that the Cardano family was a branch of the noble Castiglione family, which produced Pope Celestine IV, whose pontificate (high priesthood) lasted only five months. True, Girolamo himself did not particularly insist on this version, although on the title pages of his first books he called himself “Girolamo Castiglione Cardano, Milanese.” He loved Milan and was proud of it.
Lombardy is northern Italy, the most fertile region of the country. In its center, at the crossroads of routes connecting the peninsula with France, Germany and Switzerland, is the rich and powerful Milan. For one hundred and seventy years (1277–1447) the city was ruled by the talented and energetic Visconti family of plutocrats. For three years there was a republic in Milan, then power was seized by the son-in-law of the last Visconti, condottiere Francesco Sforza, who appropriated the title of Duke of Milan. Sforza is the ideal warrior of the Renaissance: athletic, handsome, brave. No one could surpass him in hand-to-hand combat, horse riding, or fencing. He shared the difficulties of camp life with his soldiers and was famous as an excellent military leader and diplomat.
Milan. Large Hospital (Ospedale Maggiore)
According to most historians, the reign of the first Sforza was as successful as his campaigns. He organized public works, strengthened the irrigation system of Lombardy, and under his patronage the architect and sculptor Antonio Filarete built the Ospedale Maggiore - Big hospital. He encouraged the sciences, arts and crafts; invited famous humanists to Milan, prompted Vincenzo Foppa to open a later famous art school in the city; under him, the fame of Milanese gunsmiths thundered throughout Europe. By order of the Duke, the architect Aristotle Fioravanti, the future builder of the Assumption Cathedral in the Moscow Kremlin, began to build Castello Sforzzesco - Milan Castle, whose high and thick walls, reinforced with frequent buttresses, stretched for six and a half miles.
Milan. Castello Sforzzesco
After the death of Francesco in 1466, power passed to his son Galeazzo Maria, a drunkard, libertine and murderer, who in 1476 was stabbed to death by three young men in the Milan church of St. Stephen. The heir of the second Sforza was at that time only seven years old, and his uncle Lodovico, the fourth son of Francesco, nicknamed Moro because he had black hair and dark eyes, began to rule in his place. Lodovico was one of the most educated people in Italy at that time, a cunning diplomat, and patron of the arts and sciences. Under him the power of Milan reached highest level, but Moreau himself became a victim of his own political intrigues, which contributed to the start of the so-called “Italian Wars”, and died in 1508 as a prisoner in France. In the years 1494–1535, Milan became the scene of hostilities between the French and the Spanish. The Dukes of Sforza went over to one side or the other and, in the end, lost the city, which was annexed to the possessions of Charles V. From now on, the fate of the Milanese was controlled by the viceroys - rulers appointed by the Spanish emperor.
But Milan is not only power and wealth, it is also beauty. This city has always been famous for its architecture: at the end of the 15th century, Pietro Antonio Solari and Giovanni Antonio Amadeo decorated its buildings with captivating marble and terracotta reliefs; in the second half of the 16th century, the brilliant Bramante worked here. The great Frenchman Henri Bayle, better known by his literary name Stendhal, wrote “about naturalness in behavior, kindness and the greatest art of being happy, which is so widespread here.” In love with this city, he wished in his own epitaph to call himself “Arrigo Baylem, Milanese.”
It was believed that a baby who survived a difficult birth was destined to live a long life. In addition, all Cardanos and Mikeri were distinguished by their longevity. But Girolamo seemed unwilling to follow this custom. He was less than a month old when his first nurse died of the plague, and the baby himself developed five abscesses on his face, which then turned into pockmarks. While they were looking for a new nurse, the boy was taken in by his mother, who continued to live in the house of dei Resti. Thirty-four-year-old Clara, daughter of the mathematician Giacomo Miceri, “was quick-tempered, had a good memory and talent, was short, rather obese, and was distinguished by piety,” which, as we see, did not prevent her from having an illegitimate child. When Girolamo was just a little More than a month, Clara's children from her marriage to a certain Antonio Alberio - two sons and a daughter - died of the plague in Milan.
A new nurse was found in Moirago, a place located seven miles from Milan. To protect the boy from the “Black Death,” he was bathed in vinegar and, still wet after the bath, taken away from the city. But in Moirago he began to lose weight quickly, his tummy swelled and became hard as a drum. The boy was handed over to the next nurse. There he took root and spent several years - the child was weaned only in the third year of life. When Girolamo was four years old, his mother took him to Milan. Here she settled with her son and sister Margherita in a house on Peschanaya Street, which was rented for them by the elderly Fazio, who, however, did not want to marry Clara and live with them. Girolamo more than once heard his mother’s complaints about her bitter fate. And he himself, noto, illegitimate, met with a rod much more often in childhood than with affection. He was often flogged for no reason - both by his mother, for whom he was a burden and a disgrace, and by his father, who, although he did not live with the family, considered it his duty to take part in the punishment of his son, and by his aunt, who, as Cardano later wrote, “It seemed that she was completely deprived of a gall bladder,” for she poured out all her bile on the unfortunate child. After the beating, Girolamo usually fell ill, and the first years of his conscious life remained in his memory as a time of fear and pain.
When the boy was seven years old, his parents abandoned corporal punishment. Perhaps they made this decision on the advice of Dr. Lazzaro Sancino, to whose house on Main Street Fazio moved his family. In Sancino's house, the boy finally found some semblance of a family home, since Fazio decided to settle under the same roof with Clara, although without marrying her.
One of the oldest buildings in Milan is the Basilica of St. Lawrence
However, life with his father did not turn out to be a good thing for the boy, although he was no longer whipped - even when he seemed to fully deserve it. The old man needed a famulus, a servant who would accompany him everywhere, carrying a bag with papers, books and everything else that a lawyer needed when visiting his clients. This concern was placed on the fragile shoulders of seven-year-old Girolamo. All day long he followed his father around the city, dragging a heavy bag with weak hands and listening to the sarcastic remarks that the sharp-tongued Milanese made towards Fazio and Clara. The daily “intense and almost continuous movement” tired the boy very much. He suffered deeply from the fact that neither his mother nor his aunt ever expressed sympathy for him, did not feel sorry for him, or stood up for him before Fazio. At night, fatigue and daytime grievances often turned into fantastic dreams, from which the boy woke up excited, with his heart pounding.
But despite the indifferent, if not cruel, attitude of Girolamo’s parents, he subsequently never spoke disrespectfully of them. He only noted: “...they were little constant in their love for their son. My father seemed kinder to me and loved me more tenderly than my mother.” But all of Fazio’s love was manifested in the fact that he sometimes allowed his son to soak in bed in the morning. Remembering his joyless childhood in old age, Cardano spoke of these morning minutes as the happiest. Lying in bed, he indulged in dreams, one vision was replaced by another, “castles, houses, animals, horsemen, plants, trees appeared, musical instruments, theaters, people dressed in a variety of clothes and different types, mainly trumpeters, as if they were playing trumpets, but without making any sound; then I saw warriors, crowds of people, fields... meadows, forests and many other things... I indulged in this contemplation with great enthusiasm.”
Girolamo was often ill for a long time. One day - this happened in the eighth year of his life - he became so ill that his family accepted: the boy was not longing for this world. But, after being ill for seven or eight months, he, despite the silent verdict of those around him, recovered (Fazio was convinced that this could not have happened without the intervention of St. Jerome, whom he asked for help, having become convinced of the powerlessness of the doctors). Cardano remembered this day because then “the French, having defeated the Venetian troops on the banks of the Adda, organized a celebration to mark the victory.” From the window of his room, a thin red-haired boy, very pale and very serious, looked at the armor of French soldiers marching through the streets of Milan sparkling under the rays of the May sun, heard the neighing of horses and military music.
The French came to Italy for the third time. In August 1494, King Charles VIII crossed the Alps with a huge army and artillery for that time and crossed the country from north to south, plundering and destroying everything in his path. Thus began the Italian wars, which lasted sixty-five years. Italy, which did not then have centralized power, was an unstable conglomerate of small states: the Republic of Venice (the main cities are Venice, Padua, Verona, Brescia), the Duchy of Milan (Milan, Pavia, Cremona), the Papal States (Rome, Ravenna, Bologna), The Florentine Republic, the Kingdom of Naples and others. Such political fragmentation country was a decisive circumstance that determined the course of the Italian wars.
The French were eventually driven out of the country, not by the Italians, but by the Spaniards, led by the Holy Roman Emperor Charles V. In 1527, his huge army of Spanish soldiers and German mercenaries, having devastated most of Italy, captured and sacked Rome. And although fighting continued for about thirty years, the Spaniards became masters of the situation in the country.
The illness temporarily freed Girolamo from the role of a servant, but, barely getting stronger, he again had to carry his father’s heavy bag. True, Fazio became a little more lenient towards his son. Talking with him while walking around Milan, he could not help but notice the boy’s intelligence, his thirst for knowledge and the ease with which he learned everything new. And the old man began to look at the boy with different eyes: now he saw in him an emerging personality, and not just some creature with two legs, suitable only for meekly dragging his belongings behind him. Fazio taught his son to read and write, then introduced him to the beginnings of arithmetic and astrology, and when the boy was twelve years old, he forced him to study the first six books of Euclid. He now talked a lot with his son, telling him all sorts of stories, mainly about various miracles. Girolamo liked these stories extraordinarily and left an indelible mark on his soul, although, of course, such upbringing and education “on the go” rather disturbed Girolamo’s imagination than gave him a solid foundation of knowledge. Somehow he replenished them, reading greedily fathers books, not understanding everything about them, of course.
Having changed several houses, Fazio settled with his family with his relative Alessandro Cardano and took two nephews into his service. Girolamo felt better - now he accompanied his father along with one of his cousins.