ANCIENT ANALYSIS. POEISMS. 75 



most extraordinary, and indeed inexcusable ignorance of the 

 subject is to be seen in some who, long after Simson's paper 

 had been published, were still in the dark ; and though that 

 paper did not fully explain the matter, it yet ought to have 

 prevented sxich errors as these fell into. Thus Castillon, in 

 1761, showed that he conceived porisms to be merely the 

 constructions of Euclid's Data. If this were so, there might 

 have been some truth in his boast of having solved all the 

 Porisms of Euclid ; and he might have been able to perform 

 his promise of soon publishing a restoration of those lost 

 books. 



It is remarkable enough that before Halley's attempts and 

 their failure, candidly acknowledged by himself, Fermat had 

 made a far nearer approach to a solution of the difficulty 

 than any other of Simson's predecessors. That great geo- 

 metrician, after fully admitting the difficulty of the subject, 

 and asserting * that, in modern times, porisms were known 

 hardly even by name, announces somewhat too confidently, 

 if not somewhat vaingloriously, that the light had at length 

 dawned upon him,f and that he should soon give a full 

 restoration of the whole three lost books of Euclid. Now the 

 light had but broke in by a small chink, as a mere faint 

 glimmering, and this restoration was quite impossible, inas- 

 much as there remained no account of what those books con- 

 tained, excepting a very small portion obscurely mentioned in 

 the preface of Pappus, and the lemmas given in the course of 

 the Seventh book, and given as subservient to the resolution 

 of porismatic questions. Nevertheless, Fermat gave a demon- 

 stration of five propositions, " in order," he says, " to show 

 what a porism is, and to what purposes it is subservient." 

 These propositions are, indeed, porisms, though their several 



* " Intentata ac velut disperata Porismatum Euclidsca doctrina. Geo- 

 metrici (aevi recentioris) ncc vel de nomine cognoverunt, aut quod esset 

 solunimodo sunt suspicati." (Var. Opera, p. 166.) 



t "Nobis in tenebris dudum csecutientibus tandem se (Natura Poris- 

 matum) clara ad videndum obtulit, et pura per noctem luce refulsit." 

 (Epist. ib.) 



