Dr. R. Key's Propositions^ concerning 
Cor. 1. The law holds in unequal circles, when all nearer 
and further than ii have, respectively, their mean points nearer 
and further than that of ii: because the distance of the mean 
point from A is equal to the tangent. But the inequality may 
be such as to destroy this supposition. 
Cor. 2. If AO be less than AK, therefore less than the pa- 
rallel and equal line (OS in Fig. 4) which is the distance of 
the vanishing line from the eye*, and if the mean point of the 
nearest circle be beyond the picture ; then all the major axes 
are parallel to KI, all the minor directed to the centre of the 
picture. 
Cor. 3. When it is known which axis is parallel to KI, then, 
if one point of either be given, its direction is got by drawing 
a line to the centre of the picture, or else a line parallel to 
KI. 
Cor. 4. The extremities of the axes parallel to KI, are 
bounded by the following limits. Let PQ be the tangent-chord 
of A in the nearest circle, and GH the parallel diameter ; G and 
P being on one side of AK. If lines be drawn through G and 
P, parallel to AK, their representations are the boundaries of 
the extremities on that side of AK ; and the like on the other 
side. For PQ is the original of the axis: and the correspond- 
ing chord is greater, as the circle is more distant ; but always 
less than the diameter. 
Prop. IX. Prob. III. Fig. 10. To find the same, when the 
centres are in a line parallel to the central line. 
Let one rank of equal circles so placed be /, ii, /i 7 , &c.; let 
* This supposition may, when the objective plane is perpendicular to the picture, 
be expressed thus : If the height of the eye be less than the distance of the picture. 
Where bti^bt denotes perpendicular distance from any objective plane. 
