the Elliptic Representation of a Circle, 375 
five plane, are those in which that plane is cut by the picture 
and directing plane respectively : and the centres of those two 
lines are the points in which they are cut by perpendiculars 
from the eye. 
Def. 4. The intersecting point and directmg pointy of an ob- 
jective line or of its representation, are those two points in 
which the objective line cuts the intersecting and directing 
lines respectively. 
Def. 5. The director is a right line from the eye to the di- 
recting point. 
Def. 6. The central line, in an objective plane, is a right line 
cutting the directing line perpendicularly in its centre. 
Def. 7. The centroid, of an objective circle, is the point re- 
presented by the centre of the representing ellipse. 
Def. 8. Conjugate chords are chords represented by conjugate 
diameters of the ellipse. 
For brevity, the representation of any point A or line AB 
in any figure, is called a or ab; although the a or ab should 
not appear in the figure : small letters every where denoting 
points in the picture, whether exhibited in the figures or not. 
Each figure, after the first, represents a single plane: which, 
except in fig. 4 and 7, is the objective plane. 
Prop. I. Fig. 1. The perspective representation of an entire 
circle, is an ellipse-* 
Dem. Let the circle ABC be an object, viewed by art eye 
placed at O. Let FD be the plane of the picture, MR the 
directing plane, DE the intersecting line of the objective plane, 
and LR its directing line. Conceive an indefinite line, passing 
* In these propositions, ellipse includes the case in which the representation is a 
circle ; except the contrary be expressed or implied : a circle being an ellipse with 
equal axes. 
3C3 
