Examples of using Projective geometry in English and their translations into Tagalog
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During his imprisonment he studied projective geometry.
In 1880 Veronese described an n-dimensional projective geometry, showing that simplifications could be obtained in passing to higher dimensions.
He was one of the greatest contributors to projective geometry.
He made substantial contributions to projective geometry and wrote an important book on the topic.
He worked on conic sections andproduced important theorems in projective geometry.
This work contains fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity.
His work in geometry included a study of conics,quadrics and projective geometry.
We believe, moreover,that the abstract treatment is particularly desirable in projective geometry, because it is through the latter that the other geometric disciplines are most readily coordinated.
After graduating, he continued working for his doctorate at Trinity on projective geometry.
Appell's first paper in 1876 was based on projective geometry continuing work of Chasles.
One of the themes which were present in almost all his work throughout his career was projective geometry.
D'Ovidio also included in these lectures results of Veronese on projective geometry and of Weierstrass on bilinear and quadratic forms.
Veblen's interest in the foundations of geometry led to his work on the axiom systems of projective geometry.
It provides impressive evidence of the power of strictly classical projective geometry when applied to the right sort of problem.
One could certainly consider this work as laying the foundations for the theory of descriptive and projective geometry.
This impressive work extended apolarity theory as introduced by Reye to projective geometry in several dimensions using the theory of rational curves.
In Aperçu historique Chasles studied the method of reciprocal polars as an application of the principle of duality in projective geometry;
This was a very original approach to higher-dimensional projective geometry that Veronese developed.
In 1675 he published a more comprehensive work on conic sections Sectiones conicae which contained a description of Desargues' projective geometry.
Guarini was adept at most applications of advanced curvature and projective techniques,if not indulging outright in the projective geometry of Desargues as his modern admirers have alleged, confusing'projection' with' projective geometry'.
He introduced a configuration nowcalled a Möbius net, which was to play an important role in the development of projective geometry.
Since it is most natural to derive the geometrical disciplines associated with the names of Euclid,Descartes, Lobachevsky etc. from projective geometry than to derive projective geometry from one of them, it is natural to take the foundations of projective geometry as the foundations of all geometry. .
This treatise represented a major step forward in understanding the geometry of perspective andit was a major contribution towards the development of projective geometry.
Under their direction he laid the basis for the important work he was later to achieve in the fields of foundations of geometry, projective geometry, topology, differential invariants and spinors.
He wrote articles on such diverse topics as twisted cubics, developable surfaces, the theory of conics, the theory of plane curves, third- and fourth-degree surfaces,statics and projective geometry.
His time for research was now limited buthe still made important contributions undertaking research on infinitesimal geometry, projective geometry and the differential geometry of curves and surfaces.
White began teaching advanced courses in his area of research interest,in particular on algebraic geometry, projective geometry, and invariant theory.
He was promoted a number of times, to extraordinary professor in differential geometry, then extraordinary professor in projective geometry, then of analytic geometry. .
He examined problems in the areas of systems of lines, classification of space curves, enumerative geometry of plane conics,singular points of plane curves, projective geometry and differential equations, elliptic functions, and assorted questions in analysis.
This theorem gave, as a corollary,the complete structure of all finite projective geometries.