We have seen how to determine the points of intersection of a straight line with a Conic defined by five points. We will then see the dual problem.
This problem consists of determining the possible two straight tangent from a point to a Conic defined by five tangent.
The theoretical models of projective geometry can be proposing problems that are not of direct application. We will have that “dress up” therefore exercises to infer in the student further analysis and a transverse treatment of knowledge: Can I apply what they learn to solve this problem?.
After analyzing in detail the operations with overlapping series of second order, Let's see an example of application which does not consist in obtaining new tangents or points of contact of a conical.
Involutionary transformations are applications bijective of great interest to be applied in geometric constructions, since they simplify them considerably.
We will see how defined an involution in second-order series, with base a conical, Comparing the new model of transformation with overlapping series of second order previously studied.
You do projective concepts that we have developed to studying overlapping of second order, whose base is a conical, They allow to solve problems of determination of points of contact in the tangents of a Conic defined by five tangent or five restrictions through the combination of tangent and their respective tangent points. We will see the implementation of Brianchon point in this type of problems
To study the tangential Conic, and in particular the proyectividades between beams of second order superimposed on a same curve, We can rely on the dual study of the accomplished with overlapping series of second order.
The projective concepts that we have developed to study the overlapping series of second order, whose base is a conical, They allow to solve problems of determination of tangent points of a Conic defined by five points or five restrictions through the combination of points and tangents with their respective points of tangency.
When the base of a series is a conical series is second order.
As in the case of series of the first order when the overlapping series were defining, we can establish proyectividades between two sets of second order with the same base (in this case a conical).
