The Axioms of Descriptive GeometryUniversity Press, 1907 - 74 pagina's |
Overige edities - Alles bekijken
Veelvoorkomende woorden en zinsdelen
angle associated assumed axes axioms axis belong called centre CHAPTER cohere collinear common concurrent congruence group consider contains converse coordinates coplanar corresponding curve defined Definition Desargues Descriptive Geometry Descriptive Space determined distance distinct divided equations exist figure finite follows Geom Geometry given half-rays harmonic Hence hold Ideal Points identical imaginary immediately improper infinite plane infinitesimal rotation round infinitesimal transformation intersect latent plane lies lying metrical geometry motion neighbourhood one-one origin passes possesses Proj Projective Geometry projective line projective points Projective Space proper projective points proposition proved quadric reference relation relatum respect round the axis satisfied segment sheaf side spheres straight line surface tetrahedron theorem three planes tract triangle trihedrons vertex whole дф
Populaire passages
Pagina 9 - If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions.
Pagina 9 - If all points of a straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, there exists one and only one point which produces this division of all the points into two classes, this division of the straight line into two parts.
Pagina 30 - D, if it exist, is the harmonic conjugate of C with respect to A and B.
Pagina 8 - DBF. 2. Three distinct points not lying on the same line are the vertices of a triangle ABC, whose sides are the segments AB, BC, CA, and whose boundary consists of its vertices and the points of its sides. AXIOM VIII. If three distinct points A, B, and C do not lie on the same line, and D and E are two points in the orders BCD and CEA, then a point F exists in the order AFB and such that D, E, F lie on the same line.
Pagina 8 - ... \ABX\\ A is called the origin of the ray AB. III. If points C and D (C^D) are on the line AB, then A is on the line CD. IV. If A and B are two distinct points, there exists a point C such that A, B and C are in the order | ABC\ . V.
Pagina 8 - boundary' consists of its vertices and the points of its sides. VIII. If three distinct points A, B, C do not lie on the same line, and D and E are two points in the orders BCD and CEA, then a point F exists in the order AFB and such that D, E, F lie on the same line. Definition 5. A point 0 is 'in the interior of a triangle, if it lies on a segment, the end-points of which are points of different sides of a triangle. The set of such points 0 is ' the interior
Pagina 3 - A'B is the prolongation of the line beyond B, and B'A is its prolongation beyond A. VII. If A and B are distinct points, there exists at least one member of A'B. VIII. If A and D are distinct points, and C is a member of AD, and B of AC, then B is a member of AD. IX. If A and D are distinct points, and B and C are members of AD, then either B is a member of AC, or B is identical with C, or B is a member of CD. X. If A and B are distinct points, and C...
Pagina 9 - If A, B, C, and D are four points not lying in the same plane, they form a 'tetrahedron' A BCD, whose 'faces' are the interiors of the triangles ABC, BCD, CD A, DAB, whose 'vertices' are the four points A, B, C, and D, and whose 'edges' are the segments AB, BC, CD, DA, AC, BD. The points of faces, edges, and vertices constitute the ' surface
Pagina 3 - A and B. Definition. If A and B are points, the symbol A'B represents the class of points, such as C, with the property that B lies between A and C. Thus A'B is the prolongation of the line beyond B, and B' A is its prolongation beyond A.
Pagina 8 - B, and of all points X in one of the possible orders ABX, AXB, XAB. The points X in the order AXB constitute the 'segment