APPENDIX. 59 



this account has fuffered fo much from the injuries of time, 

 that the fenfe of one propofition only is complete. There was 

 no diagram to direct the Geometer in his refearches, nor any 

 general notion of the fubject, or of the form of the propofitions, 

 to ferve as a rule for his conjectures. The taflc, therefore, of re- 

 ftoring thefe ancient books, which DrSiMsoN now impofed on 

 himfelf, exceeded infinitely the ordinary labours of the Critic 

 or the Antiquary ; and it was only by uniting the learning and 

 diligence of thefe two characters, with the fkill of a profound 

 Geometer, that he was at laft fuccefsful in this difficult under- 

 taking. He had begun it as early as the year 1727, but feems 

 to have communicated the whole progrefs of his difcoveries to 

 Mr STEWART alone. 



WHILE the fecond invention of Porifms, to which more ge- 

 nius was perhaps required than to the firft difcovery of them, 

 employed Dr SIMSON, Mr STEWART purfued the fame fubject 

 in a different, and new direction. In doing fo, he was led to 

 the difcovery of thofe curious and interefting propofitions, which 

 were publifhed, under the title of General Theorems, in 1 746. 

 They were given without the demonftrations ; but did not fail 

 to place their Difcoverer at once among the Geometers of the 

 firft rank. They are, for the moft part, Porifms, though Mr 

 STEWART, careful not to anticipate the difcoveries of his friend, 

 gave them no other name than that of Theorems. They are 

 among the moft beautiful, as well as moft general propofitions 

 known in the whole compafs of Geometry, and are perhaps only 

 equalled by the remarkable Locus to the circle in the fecond book 

 of APOLLONIUS, or by the celebrated theorem of Mr COTES. 

 The firft demonftration of any considerable number of them, is 

 that which was lately communicated to this Society *, though I 

 believe there are few Mathematicians, into whofe hands they 

 have fallen, whofe fkill they have not often exercifed. The unity 

 which prevails among them is a proof, that a fingle, though ex- 



(H 2) tenfive 



* By the Reverend Dr SMALL. 



