The Axioms of Projective GeometryUniversity Press, 1906 - 64 pagina's |
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A. N. WHITEHEAD AA'U anharmonic ratio Annal annexed figure axioms of order axis belongs to segm class of points coincide complementary segment complete quadrangle concurrent coplanar correlates Dedekind property deduced defined definition Desargues Descriptive Geometry distinct collinear points distinct points enlarged segment entities equivalent everywhere dense existence theorem F and G finite number follows further axioms g₁ Harm ABCD harmonic conjugates harmonic system harmonically projective correspondence hold homogeneous coordinates implies intersect Invola INVOLUTIONS least one point lies in segm LÜROTH-ZEUTHEN THEOREM Math Mathematics member of G non-collinear points nth set number of points numeration-system OEU OAU² OBU² OCU² OEU² OPU² Pappus Pascal's theorem perspective Pieri point-pairs Projective Geometry projective transformation propositions prosp proved quadrangular transformation rational respect S-order ABC S(ABCD satisfy Schur segm ABC set of points Staudt straight lines subclass three distinct collinear three points triangle Type
Populaire passages
Pagina 29 - A to A, B to B, C to C, and so on, without ever allowing one line to cross another or pass through another company's station.
Pagina 20 - Dedekind t. axiom, or as enunciating the Dedekind property, is as follows. XIX. If u is any segment of a line, there are two points A and B, such that, if P be any member of u distinct from A and B, segm (APB) is all of u with the possible exception of either or both of A and B which may also belong to u. Note that the axioms of order, viz. XVI, XVII, XVIII, and this axiom need only be enunciated for one line. Then by projection they can be proved for every line.
Pagina 25 - C, and A, B', C', and A', B, C', and A', B', C, are such that the three sides of the quadrangle EFGH through any set are concurrent in one of the angular points of the quadrilateral; while the four sets, A', B', C', aud A', B, C, and A, B' C, and A, B, C' are such that the three sides through any set form a triangle.
Pagina 6 - When two figures can be derived one from the other by a single projection, they are said to be 'in perspective