Mr. T. S. Davies on Geometry and Geometers. 523 



" You can do nothing more agreeable to me than to point out any 

 mistakes you think I have made, for certainly nobody is readier to 

 commit them than me, as I know from long experience ; but what 

 you observe of the Corollary to Prop. 76 of the Data is no mistake 

 as you will easily perceive by reading the Demonstration of Prop. 76 

 with the annexed figure, only after the 

 words ' because the angle BAC is 

 given ' unto the words ' therefore, &c. 

 read in place of what is in print, and 

 the angles ADC, DCA are given be- 

 cause they are equal and their sum is 

 given. And which I should have told 

 you in the first place, after the words 

 'Isosceles triangle DBE' add, to the 

 base ED produced, therefore, by the 2d case of the Lemma, the 

 rectangle DE, CF is the space by which the square of BD, that is 

 of the difference of BA and AC is less than the square of BC. Also 

 at the end of the Demonstration, instead of what follows the words 

 ' and the rectangle DC, CE is the ' read Space by which the square 

 of the difference of the sides AB, AC is less than the square of BC. 



" I am, Dear Sir, much obliged to you for the warm expressions 

 of your kindness to me, my sentiments with regard to you are reci- 

 procal, and if my age allow me to travel so far as London, one of the 

 chief inducements for such a journey would be the pleasure of being- 

 some time with you. Let me hear from you as soon as your leisure 

 permits. I am, My Dear Friend, Yours very affectionately 



" Rob: Simson." 



matical Repository (vol. vi). The paper is, however, most remarkable for 

 some properties of the conic sections (the enunciations only of which are 

 given) that are commonly considered to be discoveries of more recent 

 times. Besides these, the propositions in the second edition of Simson's 

 Conic Sections (4to, 1750), which are marked (.r), are due, as Simson 

 states in his preface, to Dr. Stewart. It is the more important to notice 

 this, from the great philosophical historian, M. Chasles, having not re- 

 marked this circumstance, and hence having considered them to he Simson's 

 own ; whilst their importance in the gwmirie superieure renders it but an 

 act of common historical justice that Stewart's name should be attached 

 to them. Several of Simson's Porisms were the discovery, too, of Stewart 

 (and some of Trail), which were, with Simson's characteristic honesty, duly 

 acknowledged in the MS. on the Porisms. Stewart was a pupil of Sim- 

 son's; and there is t^ood reason to believe that he had also divined the 

 true character of this class of propositions at a very early period. In fact, 

 as I have shown in "An Analytical Discussion of Dr. Stewart's General 

 Theorems" (Edinburgh Transactions, vol. xvi.), a large portion of the 

 propositions which he published in 1746 (he being then a candidate for the 

 chair vacated by the death of Maclaurin) are, in the strictest sense of the 

 word, Porisms — even the formal enunciation being only disguised to the 

 extent of not interfering with Dr. Simson's restoration of Euclid's definition 

 of them. 



The remark quoted from Simson's letter is important, too, in respect to 

 its bearing upon another question — which, however, the length of this 

 note forbids my entering upon here, — as it would be impossible to do justice 

 to the subject within the prescribed space. 



2 M 2 



