the Elliptic Representation of a Circle. 395 
beyond F (from B), two such lines may be assumed, at 
different distances from BE ; the one nearer to BE being for 
the remotest circles. As to mean points between F and H, 
yet not within the circle LOR with the centre A ; find the 
minor axes, each separately, for as many, of the nearest to H, 
as requisite. If any remaining circles on that side of AF, as 
a &c, should seem better referred to some law observed ; 
then, with the centre W equidistant from O and the M of 
describe a circle MOI cutting the directing line in I beyond 
A. If any mean point be within this circle, the directing point 
of the minor axis is beyond I. And, if any other objective 
circle have its mean point U in the circumference MOI, or if 
U in MOI can be found as the mean point of a circle purposely 
added or supposed (of the given magnitude, and having itscentre 
in BE), then any mean points between that M and U will have 
the directing points of the minor axes beyond I. If how much 
beyond be inquired ; the points P and G may be found, as 
(fig. 19) when the mean points were in a right line: and G 
will be a limit beyond which, at least, the directing points 
cannot go. And U will perhaps frequently be found with 
sufficient accuracy, if taken as the intersection of the right 
line MF with MOI. If the mean point come to U, the direct- 
ing point returns to I ; and if the mean point move from U to 
F, the directing point moves from I to A. Triangles con- 
structed as * before, and transferred to the picture, will give 
lines which may be taken as parallel to the axes; though 
with some abatement from strict accuracy. But such is a law% 
or laws, which may be considered as observed, when the 
centres are in a right line. 
• As LOA, GOA, &c; in prop. IX, X. 
