To determine the point of inter of two right lines whose equations are known.
To pass a plane, 1o through three given points; 2o through a given point and parallel to a given plane; 3o through a point and through a given right line.
Knowing the equations of two planes, to find the projections of their inter.
To find the inter of a right line and of a plane, their equations being known.
Knowing the co-ordinates of two points, to find their distance.
From a given point to let fall a perpendicular on a plane; to find the foot and the length of that perpendicular (rectangular co-ordinates).
Through a given point to pass a plane perpendicular to a given right line (rectangular co-ordinates).
Through a given point, to pass a perpendicular to a given right line; to determine the foot and the length of that perpendicular (rectangular co-ordinates).
Knowing the equations of a right line, to determine the angles which that line makes with the axes of the co-ordinates (rectangular co-ordinates).
To find the angle of two right lines whose equations are known (rectangular co-ordinates).