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Briefly:
Descartes said:
..
Philosophy (since it extends to everything accessible to human knowledge) alone distinguishes us from savages and barbarians, and every people is the more civil and educated the better they philosophize in it; therefore, there is no greater good for the state than to have true philosophers.
...First of all, I would like to find out what philosophy is... the word "philosophy" means the occupation of wisdom, and that by wisdom is meant not only prudence in business, but also a perfect knowledge of everything that a person can know; this same knowledge, which guides life itself, serves to preserve health, as well as discoveries in all sciences.
..
There is no vice that is so harmful to the well being of people as envy, because those who are infected with it not only grieve themselves, but also darken the joy of others.
...The majority of votes is not an irrefutable evidence in favor of truths that are not easy to discover, for the reason that such truths will be encountered by an individual rather than a whole nation.
...In order to improve the mind, you need to think more than memorize.
...The goal of scientific knowledge should be to direct the mind in such a way that it makes solid and true judgments about all the objects encountered.
..Reading good books is a conversation with the best people of the past times, and moreover, such a conversation when they tell us only their best thoughts.
...In most disputes, one can notice one mistake: while the truth lies between the two views being defended, each of the latter departs from it the further the more fervently it argues.
...Cowardice is very harmful because it keeps the will from useful actions.
...The mind is an incendiary glass, which, igniting, itself remains cold.
See also:
Rene Descartes.
ABOUT THE RAINBOW: >>>
The rainbow is such a wonderful miracle of nature, and its causes, hitherto so little known, have been so persistently thought about by inquisitive minds at all times, that it is difficult for me to find a question on which I could better show how, with the help of the method I used, it is possible to come to knowledge that those whose writings we have did not possess.
First, when I took into account that a rainbow can appear not only in the sky, but also in the air near us every time there are drops of water illuminated by the sun, as can sometimes be seen from experience in fountains, it was easy for me to conclude that it depends on how the rays of light act on these drops, and from them reach our eyes.
Knowing that these drops are spherical, and seeing that the rainbow always appears in the same way with both large and small drops, I set myself the goal of creating a very large drop in order to be able to better examine it.
Read on:>>> About the rainbow
Rene DESCARTES (1596-1650).
© Vladimir Kalanov "Knowledge is Power".
The great French mathematician, physicist and philosopher Rene Descartes was born on March 21, 1596 in the small town of La Gaie in the province of Touraine.
Descartes ' life was relatively short and was accompanied by many dramatic events.
And these events began immediately after the birth of little Rene.
His mother, having delivered from the burden, died a few days later.
The boy remained alive, but signs of poor health appeared for a long time in the form of a dry, short cough and a pale complexion.
Rene Descartes came from a poor noble family.
Rene spent his childhood in Touraine, famous for its gardens, fertility and mild climate.
At the age of 16, Descartes graduated from the Jesuit school in Anjou.
And what is it?
The effect of studying at school turned out to be unpredictable: a young man with an exceptionally inquisitive mind and a passion for knowledge had an aversion to science, to mastering knowledge.
Rene abandoned books and scientific studies and spent all his time practicing horse riding and fencing.
He was then in his seventeenth year.
But his thought did not sleep.
His creative mind quickly processed all sorts of impressions into generalizations and laws.
And as a result of his fencing amusements, a “Treatise on Fencing " appeared.
In the spring of 1613, Rene went to Paris: it was time for the young nobleman to take care of acquiring a secular gloss and useful connections for future everyday success.
In Paris, Rene met, no, not with a beautiful Parisian woman, but with the scientist Franciscan monk Mersenne and the mathematician Midorge.
The learned monk Mersenne was the author of a very ambiguous commentary on the book of Genesis (for atheists, we will explain that this is part of the Bible), when reading which pious Catholics shook their heads.
Descartes for some time gets into the company of "golden youth", leads a distracted life, is fond of a card game.
But in vain Descartes ' secular friends thought that Rene would always remain in their company.
After a year and a half of scattered life, an unexpected change occurs in Rene's behavior.
Secretly from his friends and Parisian relatives, Rene moves to a secluded house in the faubourg Saint – Germain, locks himself here with his servants and plunges into the study of mathematics mainly geometry and the analysis of the ancients.
Descartes spent about two years in this voluntary imprisonment.
When he turned twenty one, he decided to leave France to see the light.
The years of wandering began.
Descartes wrote that he wanted to read “in the great book of the world, to see courts and armies, to come into contact with people of different mores and positions, to collect different experiences, to test himself in meetings that fate will present, and to reflect everywhere on the objects encountered.”
Descartes began " reading the great book of the world” with the fact that in 1617 he put on the uniform of a volunteer of the Dutch army and now lives in the town of Breda.
He refuses the army salary in order to be free from all official duties, does not even go to parades.
The conditions of service, frankly speaking, are fantastic, from the point of view of every ordinary soldier.
Descartes sits at home and studies mathematics.
The habit of a reclusive life, acquired in the Parisian Faubourg Saint Germain, has borne fruit: as a result, Descartes becomes one of the greatest mathematicians of his era.
An entry in his diary has been preserved: "On November 10, 1619, I began to understand the grounds for a wonderful discovery.”
Researchers of Descartes ' work have no doubt that the wonderful discovery that Descartes is talking about here was the discovery of the foundations of analytical geometry.
The essence of analytic geometry consists in the application of algebra to geometry and vice versa geometry to algebra.
Any curve can be expressed by an equation with two variables, and vice versa any equation with two variables can be expressed by a curve.
This discovery was of great importance not only for mathematics, in the history of which it formed an epoch, but also in general for all natural sciences dealing with exact quantities and methods of calculating them.
The wanderings in Europe continued.
Together with the army, Descartes visited first Prague, then Hungary and Brussels.
In 1623, Rene appears in Paris, then travels around Europe again.
In 1625, Descartes returned to France, but soon left it again and went to Holland to get away from numerous Parisian acquaintances and study science in solitude.
In Holland, Descartes liked the very structure of the life of an active people, as well as the religious tolerance of society.
For the first time in Holland, Descartes continues to work on the treatise “On the Deity", which he started in Paris, but soon abandons this work and goes on to study natural sciences.
In 1629, a rare natural phenomenon was observed in Rome: five false suns (pargeliev) appeared around the Sun.
This natural phenomenon arouses Descartes ' interest in optics and in the study of the rainbow, since the scientist is quite correctly looking for the cause of pargeliae in the phenomena of refraction and reflection of light.
In addition to optics, he is engaged at this time in astronomy and medicine, more precisely, anatomy.
Descartes studies anatomy not only from atlases and books, but also anatomizes animals himself.
He wants to apply his mathematical method to these sciences and expects brilliant results from this.
In the middle of 1633, Descartes informed Mersenne that he had almost finished the treatise " On the World”, but postponed it until the autumn to finalize it later.
Having begun to finalize his treatise, Descartes decided to first familiarize himself with Galileo's” Dialogues on the Systems of the World".
However, the work of Galileo requested from friends in Leiden and Amsterdam could not be obtained.
Descartes received the news that struck him that in July of the same year (1633), the “Dialogues” of Galileo were burned by the Inquisition, and their elderly author, despite the intercession of influential people, was first sentenced to imprisonment in an inquisition prison, and then arrested in a village house, where he was ordered to read penitential psalms once a week for three years.
Descartes was seriously frightened and even wanted to burn his manuscripts out of fear.
What can you do, and great thinkers are sometimes subject to fear…
In 1634, Descartes drew up a sketch of his study " On man and the formation of the embryo”.
It is interesting that Descartes at this time had the opportunity to make direct "observations" on the issue that interested him, since in 1635 his daughter Francine was born.
Information about the life of this child is extremely scarce, except for the point about which in other cases it is customary to keep silent even in the most detailed biographies.
On a blank page of one book, Descartes left an entry: "Conceived on October 15, 1634”" But nothing is known about the child's mother, the connection was obviously fleeting.
It is unlikely that romantic impulses were inherent in Descartes ' nature, and therefore his biographer Mageffi suggests, not without reason, that Francine's birth was the fruit of the scientist's curiosity.
Nevertheless, Descartes was warmly attached to his little daughter.
For him, the death of Francine, which occurred in 1640 from scarlet fever, was a heavy blow.
What is the future fate of Descartes 'treatise" On the World"?
In June 1637, Descartes published a book called " Reasoning about the Method”, in which the author included the harmless sections “On Light” (dioptrics), “On meteors” and the newly written “Geometry” from the “World”.
This was a major event in the history of science: elements of a new worldview appeared, the path along which the development of human thought will go further was once again outlined.
Descartes, of course, understood the great importance and generality of the method of analysis he discovered, but he was in no hurry to share this method with other scientists.
He deliberately wrote geometry in a confusing way, in order, as he said, “to deprive envious people of the opportunity to say that they have known all this for a long time.”
For example, when describing solutions to the most difficult problems, Descartes released an analysis, leaving only the construction.
We see now that great thinkers are not always generous...
The sections of Dioptric and Meteors were written much more popularly and accessible for reading.
In” Geometry " (1637), Descartes first introduced the concepts of a variable and a function.
Descartes ' variable appeared in a double form: as a segment of variable length and constant direction – the current coordinate of a point describing a curve with its movement, and as a continuous numeric variable running through a set of numbers expressing this segment.
The double image of the variable caused the interpenetration of geometry and algebra.
Descartes interpreted a real number as the ratio of any segment to a single one, although only I. Newton formulated such a definition.
Negative numbers received a real interpretation from Descartes in the form of negative ordinates.
Descartes improved the notation system by introducing the later generally accepted signs for variables (x, y, z) and coefficients (a, b, c, ...), as well as the notation of degrees.
Descartes ' writing of formulas is almost no different from the modern one.
Descartes initiated a number of studies of the properties of equations, formulated the sign rule for determining the number of positive and negative roots (Descartes ' rule), raised the question of the boundaries of real roots.
In analytical geometry, the main achievement of Descartes is the method of coordinates created by him.
In Geometry, Descartes outlined a method for constructing normals and tangents to plane curves (in connection with the study of lenses) and applied it, in particular, to some fourth order curves (the so called Descartes ovals).
Having laid the foundations of analytical geometry, Descartes himself did not make much progress in this area – negative abscissas were not considered, the issues of analytical geometry of three dimensional space were not touched upon.
Nevertheless, his " Geometry” had a huge impact on the development of mathematics.
>>>Read more: Rene Descartes (part 2).
* Rene Descartes [1 2] Rene Descartes.
About the rainbow [1 2] •
>>> Read in German:
Rene Descartes.
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