SIMSON. 489 



the investigation as satisfied himself. Before 1715, 

 three years after he began his course of teaching, he 

 was deeply engaged in this inquiry ; but he only re- 

 garded it as one branch of the great and dark subject 

 which Halley had recommended to his care. After he 

 had completely examined, corrected, and published, 

 with most important additions, the Conies of Apollo- 

 nius, which happily remain entire, but which, as we 

 have seen, had been most inelegantly and indeed alge- 

 braically given by De la Hire, L'Hopital, and others, to 

 restore the lost books was his great desire, and formed 

 the grand achievement which he set before his eyes. 



We have already shown how scanty the light was 

 by which his steps in this path must be guided. The 

 introduction to the seventh book of Pappus contained 

 the whole that had reached our times to let us know 

 the contents of the lost works. Some of the sum- 

 maries which that valuable discourse contains are suffi- 

 ciently explicit, as those of the Loci Plani and the 

 Determinate Section. Accordingly, former geometri- 

 cians had succeeded in restoring the Loci Plani, or 

 those propositions which treat of loci to the circle 

 and rectilinear figures. They had, indeed, proceeded 

 in a very unsatisfactory manner ; Schooten, a Dutch 

 mathematician of great industry and no taste, had 

 given purely algebraic solutions and demonstrations. 

 Fermat, one of the greatest mathematicians of the 

 seventeenth century, had proceeded more according to 

 the geometrical rules of the ancients ; but he had kept 

 to general solutions, and neither he nor Schooten had 

 given the different cases, according as the data in each 

 proposition were varied, so that their works were nearly 



