OF PROJECTIONS

Excerpts

OF PROJECTIONS
The point where the perpendicular from a given point on a given plane or a given line meets the plane or line is called the projection (or more precisely the orthogonal projection) of the point on the plane or line.
OF PROJECTIONS
It is convenient to take one direction of the line of projection (say from left to right) as the $+$ direction and the opposite as the $-$ direction;
OF PROJECTIONS
If $BAC$ be acute, $\cos BAC$ is $+$, and $A'B'$ is $+$ and is measured from $A'$ in the $+$ direction; but if $BAC$ be obtuse, $\cos BAC$ is $-$, and $A'B'$ is $-$ and is measured from $A'$ in the $-$ direction.
OF PROJECTIONS
The projection of a broken line is the algebraic sum of the projections of the parts of which it is made up.
OF PROJECTIONS
both in the case where all these projections are $+$ and also where, as in the figure, $B'C'$ is $-$.

OF PROJECTIONS
A'B'= AB \cos BAC
The projection A'B' of a line AB on the line of projection equals the length of AB times the cosine of the angle BAC between the two lines, taken with the sign of the projection.
OF PROJECTIONS
A'D' = A'B' + B'C' + C'D'
The projection A'D' of the broken line ABCD on the line of projection equals the algebraic sum of the projections of its three parts AB, BC and CD.

No exercises in this chapter.