# Leibniz’s patrons and admirers were gradually dying, the circle of correspondence was narrowing.

At first Gottfried understood little, but by reading the captions under the pictures, comparing them with the content of the illustrations and reading them page after page several times, he eventually learned Latin and later could not only read and speak fluently but also write in that language poems.

After Latin, Leibniz quickly learned Greek. At the age of 14, he often performed in the evenings at the gymnasium where he studied, with his own poems written in Latin or Greek. At the age of 15, he became a student at the University of Leipzig, but moved to Jena to study mathematics better. At the age of 17, Leibniz received a bachelor’s degree, and a year later – a master’s degree in philosophy. At the age of 20, Leibniz was already a doctor of law.

He could have taken a professorship at the first-best university, but he still felt unprepared for the job.

As a child, Gottfried in the parent library read the works of the ancient Greek philosopher Aristotle. At university, he was fascinated by the philosophy of Descartes, and after graduation began to seriously study the philosophical views of the so-called Rosicrucians. Convinced that their teachings were far from real science, Leibniz returned to a deeper study of Descartes’ scientific legacy and became convinced that he was insufficiently introduced with analytical geometry.

The young man persistently bridges the gaps in the knowledge of this new mathematical science, studies the works of other scientists in physics and mathematics. During his self-study in 1667 he met an influential diplomat and made a very good impression on him. On the recommendation of a new acquaintance, Leibniz became a lawyer in Mainz at the duke’s court and has since become a diplomat, while at the same time persistently engaged in research.

As a diplomat, the young scientist led a progressive movement of the advanced circles of bourgeois society in their struggle for the unification of Germany. He passionately defended and promoted the idea of such an association, demanding the spread of education for peasants, artisans and workers.

Having embarked on the path of diplomatic activity, Leibniz visited the capitals of European states – Paris, London, the administrative centers of small and large principalities and duchies in Italy, the Netherlands, Austria. He communicated with many of his contemporaries – prominent scientists, socio-political and statesmen, constantly corresponded with them on various issues of philosophy, science and culture and public life. The scientist compiled a special file for the people he corresponded with, and at the end of his life there were 1,054 cards in this file, which is still kept in the library of Hanover.

In 1672 Leibniz was elected a member of the Paris Academy of Sciences, and a year later – a member of the Royal Society of Scientists in London. He took an active part in founding the Berlin Academy of Sciences and was its first president. Russian Tsar Peter I, being in 1711-1716 pp. abroad, several times consulted with a scientist about the organization of the Russian Academy of Sciences in St. Petersburg.

Leibniz’s scientific activity is multifaceted. He was interested in a variety of fields of knowledge used in the development of relevant areas of social practice. He, for example, dreamed of creating a means of mathematical symbolism of a single language common to all sciences. This, in his opinion, would facilitate the communication of scientists of different nationalities and would accelerate the development of science itself.

Leibniz refuted Descartes’ misconception that animals feel nothing, that only man can feel. The scientist derived the formula of a heavy chain line, which contributed to the improvement of construction techniques of bridges, viaducts and arches; he improved Pascal’s calculator, put forward the idea of using in machines a cylinder with a piston to drive the wheels on the basis of the conversion of rectilinear motion into rotational. Later that idea was implemented in steam engines.

In the modern sense, mathematical logic is a new science. It arose in the middle of the XIX century. But the first ideas of this science, if we do not take into account the logical studies of Aristotle, belonged to Leibniz, as well as attempts to build a logical calculus.

But the most significant successes, both with Newton and independently of him, Leibniz achieved in developing the foundations of differential and integral calculus. In his mathematical works, the scientist set out the relevant rules without proof, immediately showing their practical application. Sometimes it is very difficult to separate what Newton did from what Leibniz created in the development of mathematics as a science.

As a result, controversy arose over the priority in developing the foundations of infinitesimal analysis (see I. Newton). But these disputes are not of fundamental importance in the historical development of science. Both scientists independently reached the same conclusions in the problem, solving it in their own way.

Leibniz’s memoir, which presented the rules of differentiation and integration, was written in 1677, and published only in 1684 under the title "A new method of maxima and minima, as well as tangents, for which neither fractional nor irrational quantities are an obstacle, and a special method of calculus"… Two years later (1686) the second work of the scientist was published "About hidden geometry"… In it, the rules of integration of many elementary functions are stated, in particular those by means of which formulas of calculation of areas, surfaces and volumes-bodies of rotation and the bodies limited by curved surfaces in general were deduced quickly and easily.

Differential and integral calculus as laws of action on variables proved to be very useful not only for mathematics. but also for solving many practical problems in physics, mechanics, geodesy, etc.

The famous Dutch scientist, a contemporary of Leibniz, physicist and mechanic Christian Huygens, said, for example, that with astonishment and admiration-notices the generality and extraordinary productivity of new methods of mathematical research and computation in the first-best field of knowledge. He foretold their infinite development and progress, and life confirmed these predictions. Without integral and differential calculus, mathematics as a science would not be able to achieve its modern development.

Opening new ways in the development of mathematics as a science, Leibniz also improved the mathematical apparatus: he introduced many symbols, terms, signs of action. This made it possible to get rid of writing words of various operations on constants and variables. Leibniz, for example, proposed that the action of multiplication be denoted by one dot and division by two, using parentheses, square brackets, and curly braces in formulas and various transformations.

The concept of dependent and independent variable was introduced into mathematics by Descartes, and terms "function" (which corresponds to the concept of the dependent variable) and "argument" (corresponding to the concept of independent variable) introduced by Leibniz, as well as the term "coordinates"… He also introduced the signs of derivative, differential, integral and some other mathematical symbols.

Leibniz’s work was of great importance for the development of world science. K. Marx highly valued the scientific heritage of the scientist, and F. Engels said that the mind of this talented man, gifted with creative imagination and the desire for knowledge, seemed to radiate the most ingenious ideas around him.

At the end of the XVII century. Leibniz’s fame resounded throughout Europe. There was no scientist, diplomat, king, prince or duke who would not consider it an honor if not to correspond, then at least once to see and talk to a prominent person.

For the last 40 years of his life, Leibniz held the position of political adviser to the Duke of Hanover. In old age, an acute disease of the joints of the hands and feet chained the scientist to a chair. At the beginning of the XVIII century. the importance of Hanover as a major political and administrative center began to decline. Leibniz’s patrons and admirers were gradually dying, the circle of correspondence was narrowing.

The circumstances of the death of this famous man are mysterious. On November 14, 1716, the scientist felt worse than usual. His old acquaintance, a Jesuit, came to see the patient. He also brought home-made medicine, a tincture of a potion. Leibniz drank it, but immediately began to feel even worse. While searching and bringing a doctor, the scientist died. It happened an hour after he drank "medicine"…

The coffin of a man who was once the pride of European science was followed by only one person – the secretary of the scientist. And mankind remembers the name of an outstanding scientist. In November 1966, the world scientific community, by decision of the World Peace Council, widely celebrated the 250th anniversary of the death of Leibniz – a scientist, humanist and ardent fighter for social progress.

09/14/2011

## Local historian Pavlo Chubynsky. Abstract

### Pavlo Chubynsky is known in the scientific world as an ethnographer-folklorist and the author of the anthem "Ukraine has not perished"… And as a geographer-local historian – little known

His activities are closely connected with the Russian Geographical Society, which at that time played a significant role in the scientific and cultural life of Russia. From an early age, Paul became fascinated with the era of geographical discoveries, dreaming of long journeys.

He entered St. Petersburg University, Faculty of Law, where he met Georgy Semenov Tien-Shansky, who in buy best compare and contrast essay cheap turn introduced Chubinsky to such prominent geographers as Nikolai Przhevalsky and Nikolai Miklouho-Maclay. It was Miklouho-Maclay who persuaded Chubinsky to join the Russian Geographical Society, and it was under the influence of this eminent geographer, a researcher who had already visited the Canary Islands and Madagascar at the time, that Chubinsky became seriously interested in economics.

He dreams of an expedition to the north of Russia and also fruitfully collects information about the ethnography and geography of Ukraine. For the fact that Chubinsky joined the revolutionary – literary organization he was sent to the Arkhangelsk region where he works as a secretary in the local court.

But he does not lose touch with his friends and homeland. In addition, he collects valuable ethnographic materials abroad. Two years later, at Przewalski’s request, he was released from exile and returned to normal work.

In his works he raises the issue of the use of natural resources. He came up with the idea of plowing virgin lands in northern Russia to increase sown areas, because at that time the tsar was faced with the question of providing bread to the state, which was catastrophically lacking.