Cairnhouse, Ehrenfried Walter von

Cirnhaus received his initial education in his homeland, in the Luzhitsky Territory , where his family belonged to the local ancient nobility, once bearing the name Chernous ^[5] . By vocation and penchant for mathematical sciences, he came to Leiden in 1668 to study mathematics and physics. The outbreak of war between Holland and France carried him to the battlefield. He volunteered for the Dutch army, and at the end of the war he devoted himself to the study of science, traveled to England, where he met Henry Oldenburg , the learned secretary of the Royal Society of London .

Arriving in Paris in 1675, he, on the recommendation of Oldenburg, met Leibniz there , to whom he announced his first research on algebra. Later, in 1683, this study was published in the Acta eruditorum under the title: “Methodus auferendi omnes terminos intermedios ex data equatione,” that is, a method for removing all intermediate terms from a given algebraic equation. It is assumed that an nth degree algebraic equation with n + 1 terms is given. Using the auxiliary equation of the ( n-1 ) th degree, which contained another unknown quantity, a new equation was composed of these two equations, consisting of only two members: the n- th degree of the introduced unknown quantity and a constant term. In this way, purely algebraic, the author intended to solve an algebraic equation of any degree. The application of this method to equations of the 3rd and 4th degree turned out to be successful, but Leibniz already doubted that in this way one could solve the equation of the 5th degree (see the Abel – Ruffini theorem ).

In the essay entitled: “Medicus mentis seu tentamen genuina logicae, in qua disseritur de methodo detegendi incognitas veritates” (Amsterdam 1687 and Leipzig, 1695), devoted to logic and philosophy, the author considers the properties of curved lines with many tricks, indicates how to draw these curves using threads and determines the direction of the tangents to these lines. He also belongs to the study of the properties of incendiary ( catacaustic ) curves formed by parallel rays reflected from spherical concave mirrors and from mirrors whose meridional section is a cycloid. The Cirnhaus method in the theory of algebraic equations and his research on caustic curves were noted by the French Academy of Sciences, which accepted him among the foreign members.

After 1681, Cirnhaus lived for a long time in Saxony , where, with the support of the Elector, he founded three glass factories that made optical glasses of sizes never seen before. The largest concave mirror (made of copper) he built had 3 Leipzig elbows in diameter and 2 feet of focal length. By manufacturing and using extremely large focusing mirrors and lenses, innovative physical and chemical experiments have been carried out; for example, the Italian physicists Averani and Tarjioni in Florence first proved the combustibility of diamond in 1694 and 1695.

The cairnhouse was the inventor of European white porcelain , but after his death in 1708, Johann Böttger inherited the laurels.

In the essay Medicina mentis sive artis inveniendi praecepta generalia, published for the first time in 1687, Cirnhaus wants to give ars inveniendi - the art of scientific knowledge of real things, and not just the art of combining words. He sees the basis of all knowledge, along with Descartes, in the reliability of consciousness, justified by internal experience, but internal experience also confirms that some states are pleasant to us, while others are not, that we can understand something, and the other, finally, that we have perceptions and ideas about external objects. In these facts, Cirnhaus sees the basis of knowledge in general, the basis of morality, the basis of rational and empirical knowledge in particular. The task of science is to derive the quotient from the general; therefore, its method is deduction. Material of science - concepts. The work of science on concepts is expressed in three acts: since the material of science is the concept of the mind, and not the perception of the imagination, the first act consists in the correct definition, the second in the derivation of the axioms from the definitions, the third in the transition from the combination of definitions to theorems. Cirnhaus calls the system of knowledge obtained in this way physics or the science of the world. "By physics, I mean nothing more than the science of the world, which is proved a priori - by the exact mathematical method, and a posteriori - by the most obvious experiments that convince the imagination."

Chirnhaus did not give the theory of induction or experience, but he found out in more detail what he means by definition, axiom and theorem. "The definition is the first (basic) concept of a thing or the first that is understood in a thing." Three features Chirnhaus notes in the definition. First, the definitions are up to us; for example, we notice that movement cannot be represented without moving, moving - without extension; therefore, stretching is that first, before which motion cannot be understood. Secondly, the definition of a thing also includes its occurrence. He who has the correct definition of circle or laughter, in this definition also has the very thing. This idea is in full accordance with the spirit of rationalism of the XVII century, identifying causa and ratio, reason and foundation. Thirdly, the correct definition eliminates any doubt about the reliability of the thing being determined. The cairnhouse gives rather detailed instructions regarding the formation of definitions and moves from them to axioms. He calls axioms truths derived from definitions; as a result, the question of whether a certain position is one of the axioms depends solely on the definitions by which we arrive at the correct concepts. If we have formed a number of correct definitions, then for the development of knowledge we must combine them with each other; in this way theorems arise. What was previously taken as an independent element (natura) may turn out to be an element dependent - and vice versa, it may happen that a new element, or a new opportunity, or a new truth arises from such a connection. Truths obtained in this way, Cirnhaus calls theorems. From the above it is clear that “Medicina mentis” is one of those works that mean to establish in more detail the logic and methodology of rationalist philosophy.

• Chirngauz // Brockhaus and Efron Encyclopedic Dictionary : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.
• Bogolyubov A.N. Chirnhaus (Chirnhausen) Ehrenfried Walter von // Mathematics. The mechanics. Biographical reference . - Kiev: Naukova Dumka, 1983 .-- 639 p.
• Shawl, Michelle . A historical review of the origin and development of geometric methods . T. 1, ch. 3, n. 16-21. M., 1883.