Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

GENERATION AND CLASSIFICATION OF LINES 77

Draw the focal radii F-P and Ft-P, and bisect their external
angle by the line P-O. The line P-O is the required tangent.
209. Problem 142. To draw arectilinear tangent to a parabola at a
point assumed on the curve.
Construction. In Fig. 83 let A-C A F
represent the axis of the parabola,
let A-B represent the directrix,
let D represent the vertex, and Fic. 82
let P represent the point assumed on the curve.
Draw P-L perpendicular to A-C. Lay off D-0 equal to D-L.
B The straight line O-P through O
p.^^ ~ and P is the required tangent.
210. Problem 143. Todrawarectilinear tangent to a hyperbola at a
A DF i C point assumed on the curve.
\ L Construction. In Fig. 84 let A-B
T\.~ ~represent the axis of the hyperFI\. Lobola, let F and F' represent the
foci, let A and B represent the
FIG. 83 vertices of the two branches of
the curve, and let P represent the point assumed on the left-hand
branch of the curve.
Draw the focal radii P-F and /
P-F' and bisect the angle F-P- P
F' by the line P-O. The line
P-0 is the required tangent. /
211. Normals to Curves. A cAl B F'
straight line is normal to a
curve at a given point when it
is perpendicular to the recti-
linear tangent to the curve at / K \ p
that point.
A normal to a curve of single FIG. 84
curvature, like the rectilinear tangent, lies in the plane of the curve.
212. Rectification of Curves. A curve is said to be rectified
when its length in linear units is determined.