SIMSON. 159 



of gravity : for the system is in equilibrium by the 

 proposition. Another is famous in the history of the 

 mixed mathematics. Sir Isaac Newton, by a train of 

 most profound and ingenious investigation, reduced 

 the problem of finding a comet's place from three ob- 

 servations (a problem of such difficulty, that he says 

 of it, " hocce problema longe difficilimum omnimodo 

 aggressus,"*) to the drawing a straight line through 

 four lines given by position, and which shall be cut by 

 them in three segments having given ratios to each 

 other. Now his solution of this problem, the corollary 

 to the twenty-seventh lemma of the first book, has a 

 porismatic case, that is, a case in which any line that 

 can be drawn through the given lines will be cut by 

 them in the same proportions, like the lines drawn 

 through three harmonicals in the porism already given 

 of the harmonical curve. To this Newton had not 

 adverted, nor to the unfortunate circumstance that the 

 case of comets is actually the case in which the pro- 

 blem thus becomes capable of an infinite number of 

 solutions. The error was only discovered after 1739, 

 when it was found that the comet of that year was 

 thrown on the wrong side of the sun by the Newtonian 

 method. This enormous discrepancy of the theory 

 with observation, led to a full consideration of the sub- 

 ject, and to a discovery of the porismatic case. 



When the studies of a philosopher, and especially 

 of a mathematician, have been described, his dis- 

 coveries recorded, and his writings considered, his 

 history has been written. His private life is generally 

 unvaried, filled with speculative inquiry, amused by 

 scientific reading, variegated only by philosophic con- 

 versation, unless when its repose is broken by contro- 

 versy, an incident scarcely possible in the story of 

 mathematicians. Dr. Simson loved to amuse his 

 leisure hours, and unbend his mind in the relaxation 



* Pi-incipia, lib. iii., prop. xli. 



