Re-statement without demonstration of the properties of this surface, found by analysis, principally as to what regards the axis, the vertices, the principal planes, and the generation by conic s.
Hyperboloid of raccordement to a ruled surface along a generatrix; all their centers are in the same plane. Transformation of a hyperboloid of raccordement.
Surface of the biais passé. Construction of a hyperboloid of raccordement; its transformation into a paraboloid.
Construction of the tangent plane at a given point.
Lessons 26–28. Curvature of Surfaces. Lines of Curvature.
Re-statement without proof of the formula of Euler given in the course of analysis.
There exists an infinity of surfaces of the second degree, which at one of their vertices osculate any surface whatever at a given point.
In the tangent plane, at a point of a surface, there exists a conic , whose diameters are proportional to the square roots of the radii of curvature of the normal s to which they are tangents. This curve is called the indicatrix. It is defined in form and position, but not in magnitude. The normal s tangential to the axes of the indicatrix are called the principal s.
The indicatrix an ellipse; convex surfaces; umbilici; line of spherical curvatures.