3 «s Dr. R. Hey's Propositions concerning 
by perspective,^#, or gv, or vt\ and, upon the line so found, 
make a triangle gvt similar to OKB, having the angle g equal 
to O, and v to K. Then are gv and vt two semi-axes. For R 
and B are the directing points of GV and GT. 
Cor. 2. Fig. 5, 6 , When E is not in the central line of the 
plane, neither GH nor ST is perpendicular to LR ; therefore 
neither axis tends to the centre of the vanishing line of the 
plane. 
Cor. 3. Fig. 5, 6. Wheresoever O is in the, arc LMR, the 
same chords GH and ST are the originals of the axes. 
Cor. 4. Fig. 6. The major axis has its directing point on 
that side, of the central line AO, on which E is placed. For, 
draw ML, MB, MR. Then, if O were at M, gv would be * 
equal to vt, and the angle vtg to tgv. Therefore LMB is •f 
equal to BMR. But, if O be in the arc between L and M, the 
angle LOB stands on a greater arc in the circle LMR than 
LMB does, and BOR on a less than BMR; whence LOB, 
therefore OBK, is greater than BOK, OK than KB, and gv 
than vt. 
Prop. VII. Fig. 7. If the object be a sphere in any oblique J 
position ; the major axis, of the representing ellipse, is directed 
to the centre of the picture. 
Dem. To a given sphere conceive any tangents drawn from 
O the eye. The points of contact are in the circumference of 
a circle, whose representation (as to the outline) is that of the 
* .Cor. 3 to prop. V. 
f Or, without perspective, these angles arc equal; by Cor. 5 to introd. prop. X: 
where they are (fig. 10) IMR, RMK. 
X By oblique position is here meant any except that in which a right line, from the 
eye to the centre of the sphere, passes through the centre of the picture. 
