INVESTIGATION of PORISMS. IQ 
tion of the orbit of any particular comet, to the folution of a 
geometrical problem, depending on the properties of the para- 
bola, but of fuch confiderable difficulty, that it is neceflary 
to take the afliftance of a more elementary problem, in order 
to find, at leaft nearly, the diftance of the comet from the earth, 
at the times when it was obferved. The expedient for this pur- 
pofe, fuggefted by Newron himfelf, was to confider a fmall 
part of the comet’s path as rectilineal, and defcribed with an 
uniform motion, fo that four obfervations of the comet being 
made at moderate intervals of time from one another, four 
ftraight lines would be determined, vz. the four lines joining the 
places of the earth and the comet, at the times of obfervation, 
acrofs which if a ftraight line were drawn, fo as to be cut by 
them into three parts, in the fame ratios with the intervals of 
time above mentioned ; the line fo drawn would nearly reprefent 
the comet’s path, and by its interfeCtion with the given lines, 
would determine, at leaft nearly, the diftances of the comet. 
from the earth, at the times of obfervation. 
‘ Tue geometrical problem here employed, of drawing a line 
to be divided by four other lines given in pofition, mto parts 
having given ratios to one another, had been already refolved 
“by Dr Wa tis and Sir Curistopuer Wren, and to their 
folutions Sir Isaac NewTon added three others of his own,in 
different parts of his works. Yet none of all thefe geometers 
obferved that peculiarity in the problem which rendered it in- 
applicable to aftronomy. This was firft done by M. Bosco- 
vic, but not till after many trials, when, on its application 
to the motion of comets, it had never led to any fatisfaCtory 
refult. he errors it produced in fome inftances were fo confi- 
derable, that Zanorrri, feeking to determine by it the orbit of 
the comet of 1739, found, that his conftrudiion threw the co- 
met on the fide of the fun oppofite to that on which he had — 
actually obferved it. This gave occafion to Boscovicu, fome 
years afterwards, to examine the different cafes of the problem, 
and. 
