INVESTIGATION of PORISMS. 191 



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 neceffary 

 to take the afhftance 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 Newton himfelf, was to confider a fmall 

 part of the comets path as re&ilineai, 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, viz. 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 interfeclion with the given lines, 

 would determine, at leaft nearly, the diftances of the comet 

 from the earth, at the times of obfervation. . 



The geometrical problem here employed, of drawing a line 

 to be divided by four other lines given in pofition, into parts 

 having given ratios to one another, had been already refolved 

 by Dr Wallis and Sir Christopher 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- 

 vich, but not till after many trials, when, on its application 

 to the motion of comets, it had never led to any fatisfaclory 

 refult. I he errors it produced in fome inftances were fo confi- 

 derable, that Zanotti, feeking to determine by it the orbit of 

 the comet of 1739, found, that his conftruclion threw the co- 

 met on the fide of the fun oppofite to that on which he had 

 actually obferved it. This gave occafion to Boscovich, fome 

 years afterwards, to examine the different cafes of the problem, 



and 



