Add to ORKGSummary. A continuation of [5]. We introduce more configurational axioms i.e. orthogonalizations of “scherungssatzes ” (direct and indirect), “Scherungssatz ” with orthogonal axes, Pappus axiom with orthogonal axes; we also consider the affine Major Pappus Axiom and affine minor Desargues Axiom. We prove a number of implications which hold between the above axioms. MML Identifier:CONMETR. WWW:http://mizar.org/JFM/Vol2/conmetr.htm
ABSTRACT. An axiom system for n-dimensional affine geometry is presented; in the spirit of Hermann G...
The first method of introducing coordinates into a Desarguesian projective or affine plane was given...
Abstract. We consider a modal language for affine planes, with two sorts of formulas (for points and...
Summary. The classical sequence of implications which hold between Desargues and Pappus Axioms is pr...
Summary. We distinguish in the class of metric affine spaces some fundamental types of them. First w...
Summary. Investigations on affine shear theorems, major and minor, direct and indirect. We prove log...
A projectie confined configuration C in terms of a non-degenerate octagon gives rise to a configurat...
together with its indirect forms are introduced. Logical relationships between these formulas and be...
The union of geometry and algebra was initiated in an appendix to Discours de la methode, written by...
The author proves in a purely algebraic way that any flat geo-odular space is an affine space and vi...
AbstractIn the 1920s, Heyting attempted at axiomatizing constructive geometry. Recently, von Plato u...
Abstract. Motivated by the ubiquity of control-affine systems in optimal control theory, we investig...
AbstractUsing affine resolvable designs and complete sets of mutually orthogonal frequency squares a...
AbstractWe prove that in dimensions ⩾4 metric affine geometry over infinite fields is interpretable ...
AbstractWe give a constructive axiomatization of ordered geometry, based on an ordering with directe...
ABSTRACT. An axiom system for n-dimensional affine geometry is presented; in the spirit of Hermann G...
The first method of introducing coordinates into a Desarguesian projective or affine plane was given...
Abstract. We consider a modal language for affine planes, with two sorts of formulas (for points and...
Summary. The classical sequence of implications which hold between Desargues and Pappus Axioms is pr...
Summary. We distinguish in the class of metric affine spaces some fundamental types of them. First w...
Summary. Investigations on affine shear theorems, major and minor, direct and indirect. We prove log...
A projectie confined configuration C in terms of a non-degenerate octagon gives rise to a configurat...
together with its indirect forms are introduced. Logical relationships between these formulas and be...
The union of geometry and algebra was initiated in an appendix to Discours de la methode, written by...
The author proves in a purely algebraic way that any flat geo-odular space is an affine space and vi...
AbstractIn the 1920s, Heyting attempted at axiomatizing constructive geometry. Recently, von Plato u...
Abstract. Motivated by the ubiquity of control-affine systems in optimal control theory, we investig...
AbstractUsing affine resolvable designs and complete sets of mutually orthogonal frequency squares a...
AbstractWe prove that in dimensions ⩾4 metric affine geometry over infinite fields is interpretable ...
AbstractWe give a constructive axiomatization of ordered geometry, based on an ordering with directe...
ABSTRACT. An axiom system for n-dimensional affine geometry is presented; in the spirit of Hermann G...
The first method of introducing coordinates into a Desarguesian projective or affine plane was given...
Abstract. We consider a modal language for affine planes, with two sorts of formulas (for points and...