in Mathematical Reasoning. 353 
erroneous. Boscovich inquired into the reason of this singular 
result, and having first assured himself of the accuracy of the 
solutions, he discovered that in a particular relation between the 
given lines the problem became indeterminate, and admitted of 
an infinite number of solutions, and that the case of a Comet 
approached extremely near to this, and consequently that any 
very small error in observations must produce an extremely large 
one in the result. 
As an instance of the curious and elegant properties to which 
such an examination of the relations of the data contained in the 
final equation sometimes leads, I shall propose the following 
problem. 
A circle whose radius is r being given, and 
also three points in one of its diameters, at 
what angle must three parallel chords be 
drawn through these points so that the sum of 
the squares of two of them shall be equal to 
a gwen multiple n of the square of the re- 
maining one ? 
Let the distance of the three points in the diameter from the 
centre be 
v0, Vy and U3, 
and calling the angle which is sought 6, we have 
CP = —vcosé+ /r* — v (sin 6)', 
and 
CQ = +vcos 0 + /r — v* (sin 6), 
hence 
PQ=2,/r—v (sin OF, 
and similarly for the other two chords 
P,Q, =2 aire — v,” (sin 8), 
and P,Q; = 2 r= co (sm 0)*. 
