150 SIMSON. 



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 predeces- 

 sors. That great geometrician, 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 vaino-loriously, 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, inasmuch as there remained no account of 

 what those books contained, 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 

 demonstration of five propositions, " in order," he says, 

 " to show what a porisrn is, and to what purposes it is 

 subservient." These propositions are, indeed, porisms, 

 though their several enunciations are not given in the 

 true porismatic form. Thus, in the most remarkable 

 of them, the fifth, he gives the construction as part of the 

 enunciation. So far, however, a considerable step was 

 made ; but when he comes to show in what manner he 

 discovered the nature of his porisms, and how he de- 

 fines them, it is plain that he is entirely misled by the 

 erroneous definition justly censured in the passage of 

 Pappus already referred to. He tells us that his pro- 

 positions answer the definition ; he adds that it reveals 

 the whole nature of porisms ; he says that by no other 

 account but the one contained in the definition, could 



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

 metric! (aevi recentioris) nee vel de nomine cognoverunt, aut quod essct 

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



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

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

 (Epist. ib.) 



