

from a point 
from a line 
Pascal: 9 points  7 lines A Point Conic The conic is described by a set of points 
Brianchon: 9 lines  7 points A Line ConicThe conic is described by a set of lines 


from a point 
from a line 
P: If triangle ABC is Perspective with triangle A'B'C' with center of perpective O then the Ppoints of intersection of AB, A'B'; AC,A'C'; BC,B'C' all lie on the same Pline.
P':If triangle abc
is Perspective with triangle a'b'c' with axis of
perpective o then the Plines joining
of a, a'; b,b'; c,c' all pass through on
the same P point.
Notice: P' is also the converse of P!
Curves and Surfaces:What is possible? what is not?
What is the difference between Euclidean Geometry, Projective Geometry, and "Topology"
Euclid: congruence, similar... measurements, scale Questions: Is a triangle congruent/similar to another triangle?
Is an ellipse congruent /similar to a parabola?
Is a triangle congruent/similar to a square?
Projective: perspectivity, projectivity, lines, points of intersection and contact (tangency).
Questions: Is a triangle projectively related to another triangle?
Is an ellipse projectively related to a parabola?
Is a triangle projectively related to a square?
Topology: "Bounded", "closed", "open", "connected"
Questions: Is a triangle topologically related to another triangle?
Is an ellipse topologically related to a parabola?
Is a triangle topologically related to a square?
Topology: Counting on a line. Counting on a curve.
Counting in the plane. Counting on a surface.
V+R = E + 2