SIMSON. 499 



It is remarkable enough that before Halley's at- 

 tempts 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 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 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 restora- 

 tion was quite impossible, inasmuch as there remained 

 no account of what those books contained, except- 

 ing 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. Never- 

 theless Fermat gave a demonstration of five propo- 

 sitions, " 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 

 enumerations 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 enuncia- 



* " Intentata ac velut disperata Porismatum Euclidaea doctrina. 

 Geometric! (aevi recentioris) nee vel de nomine eognovemnt, aut 

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



f " Nobis in tenebris dudum csecutientibus, tandem se (Natura 

 Porismatum) clara ad videndum obtulit, et pura per noctem luce 

 refulsit." (Epist. ib.) 



2K 2 



