igo On the ORIGIN and 
31. ANOTHER fpecies of impoffibility may frequently arife 
_ from the porifmatic cafe of a problem, which will very much 
affect the application of geometry to aftronomy, or any of the 
{ciences of experiment, or obfervation. For when a problem is 
to be refolved by help of data furnifhed by experiment or ob-. 
fervation, the firft thing to be confidered is, whether the data fo 
obtained, be fufficient for determining the thing fought; and 
in this a very erroneous judgment may be formed, if we reft 
fatisfied with a general view of the fubje@t: For though the 
problem may in general be refolved from the data that we are 
provided with, yet thefe data may be fo related to one another 
in the cafe before us, that the problem will become indeter- 
minate, and inftead of one folution, will admit of an infinite 
number. 
Suppose, for inftance, that it were required to determine 
the pofition of a point F, (fig. 4.) from knowing that it was fi- 
tuated in the circumference of a given circle ABC, and alfo 
from knowing the ratio of its diftances from two-given points 
E and D; it is certain, that in general thefe data would be fuf- 
ficient for determining the fituation of F: But neverthelefs, 
if E and D fhould be fo fituated, that they were in the fame 
ftraight line with the centre of the given circle; and if the 
rectangle under their diftances from that centre, were alfo e- 
qual to the fquare of the radius of the circle, then, as was 
fhewn above, (§12.) the pofition of F could not be deter- 
mined. 
Tuis particular inftance may not indeed occur in any of the 
practical applications of geometry ; but there is one of the fame 
kind which has aétually occurred in aftronomy: And as the 
hiftory of it is not a little fingular, affording befides an 
excellent illuftration of the nature of Porifms, I hope to be ex- 
cufed for entering into the following detail concerning it. 
32. Sir Isaac NewrTon having demonftrated, that the tra-. 
jectory of a comet is a parabola, reduced the actual determina- 
tion 
