To set up a straight line at right angles to a given plane from a given point in it.
Let the plane of reference be the given plane, and A
the point in it; thus it is required to set up from the point A
a straight line at right angles to the plane of reference.
Let any elevated point B
be conceived, from B
be drawn perpendicular to the plane of reference, [XI. 11
] and through the point A
be drawn parallel to BC
. [I. 31
Then, since AD
are two parallel straight lines, while one of them, BC
, is at right angles to the plane of reference, therefore the remaining one, AD
, is also at right angles to the plane of reference. [XI. 8
has been set up at right angles to the given plane from the point A