Knowing the equation of a plane, to find the angles which it makes with the co-ordinate planes (rectangular co-ordinates).
To determine the angle of two planes (rectangular co-ordinates).
To find the angle of a right line and of a plane (rectangular co-ordinates).
Surfaces of the second degree.
They are divided into two classes; one class having a centre, the other not having any. Co-ordinates of the centre.
Of diametric planes.
Simplification of the general equation of the second degree by the transformation of co-ordinates.
The simplest equations of the ellipsoid, of the hyperboloid of one sheet and of two sheets, of the elliptical and the hyperbolic paraboloid, of cones and of cylinders of the second order.
Nature of the plane s of surfaces of the second order.—Plane s of the cone, and of the right cylinder with circular base.—Anti-parallel of the oblique cone with circular base.
Cone asymptote to an hyperboloid.