It is known that the theorems of Desargues and Steiner are the main theorems of projective geometry. In all sources, the proofs of these theorems are given by axiomatic methods. Since the axiomatic method consists of theory, it will not be easy for everyone to understand it. The article presents analytical proofs of the theorems of Desargues and Steiner in projective coordinates. When introducing the projective coordinate system, a set of three vertices was used. A single point is taken as the center of the projection. When proving Desargues' theorem, he effectively used the equation of a projective line on a projective plane, as well as homogeneous coordinates. The equations of second-order curves on the projective plane are derived as the common points of two central families of straight lines.
| Mualliflar | E.Q. Qurbonov |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashr sanasi | 2025-03-29 |
| Jild | 1 |
| Son | 1 |
| Betlar | 52-57 |
| Til | en |
| DOI | 10.59251/2181-1296.2025.v1.149.2.3292 |
DOI: 10.59251/2181-1296.2025.v1.149.2.3292 · Maqolaning asl sahifasi
In this work, interactions of glyoxal in ethyl alcohol, water and dimethylsulfoxide (DMSO) complexes and their spectral manifestations were studied using ab-initio calculations. The molecular forces, bond structure and…
This paper investigates the self-similar analysis of a system of equations given by a diffusion process. The study focuses on a coupled system of nonlinear parabolic partial differential equations (PDEs) that describe…
The structural, electronic, and bonding properties of hydrogen-bonded complexes between formamide and urea in different stoichiometric ratios (1:1, 1:2, and 2:1) have been investigated using Density Functional Theory…
In this paper, the characteristic vibrational modes of aniline were analyzed using polarized Raman and two dimensional Raman correlation spectroscopy methods. Polarized Raman spectra revealed the presence of anomalous…
By periodate oxidation of inulin, samples of polyaldehydinulin with varying degrees of oxidation have been obtained. The obtained polyaldehydinulines were used for the chemical modification of the low molecular weight…
To study the chemical and mineralogical composition of the selected clays, montmorillonite clays from the Navbahor deposit (Navoi region) were studied in order to determine the degree of this sorbentity. The work used…
In this work, the synthesis of iron ( Fe(II)), cobalt (Co(II)) and zinc (Zn(II)) ion complexes with flavonoids quercetin and rutin was studied and their stability constants at different pH values were estimated. The…
7H-Pyrrolo[2,3-d]pyrimidines or 7-deazapurines are analogs of purines, which are part of DNA and RNA found in the human body, and therefore exhibit a high level of biological activity. There are also several approved…
The effect of a mixed solvent of water - isopropanol was studied on the relative volume of polyvinyl alcohol gel in solutions of various electrolytes of different concentrations. Kinetic curves of the change in the…
In this paper, we developed a method for synthesizing low-porosity silica gel modified with nanomagnetic material Fe3O4, and studied its textural and sorption characteristics. The resulting material was characterized by…
Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi — barcha maqolalar