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The purpose of the research lies in generalizing, improving and supplementing an iron-cementite diagram. The aim was to study historical aspects of the diagram. The method of solving the problem was to find the lost and forgotten historical facts. An improved phase diagram of iron-cementite conditions is given in the paper. The novelty of this diagram lies in combining phase transformations, structural components and glow colors at different temperatures and concentrations of the components that allows obtaining the maximum amount of information by using the diagram. A historical aspect of the diagram was also studied, the origin of names of phases and structural components was considered as well. The diagram of iron-carbon has a great practical value and gives the basis for studying the processes of treating iron and steel with heat. It is used for determining the types of heat treatment, temperature ranges of transformations, etc. In addition, the diagram can be used for predicting the microstructure at any preset temperature., Представлена усовершенствованная диаграмма состояния железо-цементит. Новшество данной диаграммы заключается в комбинировании фазовых превращений, структурных составляющих и цветов свечения при разных температурах и концентрациях компонентов, что позволяет получать максимальный объем информации при использовании данной диаграммы. Также в статье изучен исторический аспект диаграммы, описано происхождение названий фаз и структурных составляющих., Представлена вдосконалена діаграма стану залізо-цементит. Нововведення даної діаграми полягає в комбінуванні фазових перетворень, структурних складових і кольорів світіння при різних температурах і концентраціях компонентів, що дозволяє отримувати максимальний обсяг інформації при використанні даної діаграми. Також у статті вивчено історичний аспект діаграми, описано походження назв фаз і структурних складових.

The purpose of the research lies in generalizing, improving and supplementing an iron-cementite diagram. The aim was to study historical aspects of the diagram. The method of solving the problem was to find the lost and forgotten historical facts. An improved phase diagram of iron-cementite conditions is given in the paper. The novelty of this diagram lies in combining phase transformations, structural components and glow colors at different temperatures and concentrations of the components that allows obtaining the maximum amount of information by using the diagram. A historical aspect of the diagram was also studied, the origin of names of phases and structural components was considered as well. The diagram of iron-carbon has a great practical value and gives the basis for studying the processes of treating iron and steel with heat. It is used for determining the types of heat treatment, temperature ranges of transformations, etc. In addition, the diagram can be used for predicting the microstructure at any preset temperature.

Mathematics, in its operations with variable quantities, enters the field of dialectics; and it is significant that it was a dialectical philosopher, Descartes, who introduced this advance. The relation between the mathematics of variable and the mathematics of constant quantities is in general the same as the relation of dialectical to metaphysical thought. Engels, Anti-Duhring, Part I Philosophy, Chapter 12, Dialectics, Quantity and Quality . . . The primary subject matter of mathematics is still the variation of quantity in time and space, but that also this primacy is partly of the nature of a "first approximation", is reflected in the increasing importance of structures (not only of quantities) in the mathematics of the last 100 years. For example, a first approximation to a theory of a material situation involving three apples might be simply the number (constant quantity) 3. The idea of an abstract set of three elements is a somewhat more accurate theory. If one of the apples happens to be distinguished, for example, by being green, we may consider the simple structure of an abstract set with a distinguished element, a theoretical refinement which the quantity three does not really admit; the unique non-trivial automorphism of this structure is a theoretical operation which again the quantity itself does not admit. This simple example indicates that at least in some cases the idea of a structure (representing a quality) is a refinement of the idea of a quantity. The abstraction from structure/quality to quantity (obvious in the above simple example) is present and is significant also among variable structures and variable quantities. . . . Platonic idealism, while mistaken on the relation between consciousness and matter, contains an aspect of truth when applied within the realm of ideas. For example, the doctrine of algebraic theories begins with the affirmation that there exists as a definite mathematical object the "perfect idea of a group" of which the idea of any particular group is "merely an imperfect representation". Indeed, it is a simple further step to form as a mathematical object the "idea of an algebraic theory" of which any particular algebraic theory is a representation, as was carried out as a part of Benabou’s 1966 dissertation. Of course, even here Platonic idealism is wrong on the order of development, since the ideas of several particular groups were concentrated from practice well before the idea of a group in general was concentrated from the practice of mathematicians around 1800., F. William Lawvere (1972) Perugia Notes: Theory of Categories over a Base Topos, Universita di Perugia, Perugia.