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NOTE TO THE LIFE OF SIMSON. 



The remarkable circumstance of the case of the comet's 

 motion, for which Sir I. Newton's solution was intended, 

 proving to be the porismatic case of the construction, has 

 been mentioned in the text. It has been sometimes con- 

 sidered as singular, that this did not occur to himself, the 

 more especially as he evidently had observed two cases in 

 which the problem became indeterminate namely, when 

 the lines were parallel, and when they all met in one point, 

 for he excepts those cases in express terms (Prin. lib. 1. 

 Lem. xxvii.) It may be observed, that such oversights 

 could very rarely happen to the ancient geometers, because 

 they most carefully examined each variation in the data, 

 and so gave to their solutions such a fulness as exhausted 

 the subject. 



The commentators on the Principia (Le Seur and Jac- 

 quier) make no mention of the omission. The circum- 

 stance of the Porismatic case was not discovered till ten 

 yea'rs after their publication, when F. Boscovich found it 

 out, in 1749. But it is very extraordinary that Montucla 

 appears to have been unaware of the matter, although the 

 first edition of his work did not appear till 1758. Nor is 

 the least reference made to it in the second edition, which 

 was published the year he died (1799.) There are other 

 omissions in both editions, and also in the continuation. 

 He appears well to have understood the ancient method, 

 and to have read and examined some of the most celebrated 

 works upon it. He had given due praise to Simson in his 

 first edition; and to Lord Stanhope, who sent him the 

 ' Opera Reliqua ;' and we find in the second edition a full 

 note upon the subject, II. 277. In the continuation 

 III. 11, and seq., we have further indications of the atten- 

 tion which he had bestowed upon the ancient geometry ; 



