S7^ R* Hey*s Propositions concerning 
Cor. 3. If therefore one chord througrh the centroid V were 
the diameter, consequenlly ^ perpendicular to LR and passing 
through M; the conjugate chord would be parallel to LR, 
therefore bisected in V. 
Prop. IV. If any right-lined figure, having an even number 
of sides, be inscribed in a circle, or described about one, and if 
its diagonals, joining opposite angles, pass through the cen- 
troid ; the opposite sides of the representation are parallel 
respectively. 
Dem. If the circle be parallel to the picture, the centroid 
is the centre, and all the respectively opposite sides, of the in- 
scribed or circumscribed figure, are parallel ; therefore also 
their representations. Let the centroid be another point. The 
opposite sides “f will meet, if at all, in the indefinite base to the 
centroid taken as a vertex, that is, in J the directing line of the 
objective plane. If any two opposite sides will not meet, they 
are § parallel to the directing line. Therefore, in all cases, 
the representations are parallel, g. E. D. 
Cor. This is applicable, mutatis mutandis, to non-inscribed 
figures.il 
Prop. V. Fig. 3. If the centre of an objective circle be in 
the central line of its plane ; one axis of the representing ellipse 
is parallel to the intersecting line, the other perpendicular. 
Dem, Let V be the centroid, A the centre of the directing 
line LR, and AO, in the central line, equal to the distance of 
A from the eye ; BF the diameter through V, and PQ the 
chord bisected in V. Then, since FA cuts the intersecting line 
• Cor. I, 2. to introd. prop. I. f Introd. prop. X, and cor. 6, 8, 9. 
t Prop. II. § lb, with cor. i, 6, 8, 9, of introd. prop. X. 
II Introd. prop, XII, and cor. 1 and 8. 
