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



business ; and when he did, it was only to go to Oxford where 

 he had relatives — a brother, Sir Charles Nourse, and a sister, 

 the wife of Dr. Hornsby, the Radcliffe astronomer. One of 

 the letters seems to imply that he was a short and somewhat 

 corpulent man, who always fancied himself to be " wasting 

 away." He was always alive to his business, and the number 

 of works of which he was the publisher was unprecedented in 

 his day; his undertakings appear to have been generally 

 successful, and his dealings scrupulously honourable. He 

 does not appear from any allusions in these letters to have 

 been married : and he amassed considerable property, which 

 was bequeathed to his brother and sister. 



The mathematical character of Nourse is best shown by a 

 specimen of his geometry. I therefore annex two : one a de- 

 monstration of the converse of Euc. v. 25, which he required 

 as lemma for some emendations of a proposition on the conic 

 sections in the works of Mylne and Simson ; and the other a 

 remarkably simple and elegant problem in Angelisdeinf. Pa- 

 rebolis. These are given precisely as I find them in the MS., 

 taking in the textual corrections made by himself. 

 " Lemma (Euclid v. 25 convers). 

 " Si quatuor magnitudines fuerint proportionales, et prima cum 



quarta major fuerit secunda cum 

 tertia ; erunt prima et quarta maxima 

 et minima quatuor proportionalium. 

 " Sint enim proportionales AF. 

 BH. C & D. Et quoniam prima cum 

 quarta major est secunda cum tertia. 

 non erit igitur prima AF tertia C. 

 sequalis, sed vel major vel minor ea. 

 Sit primo maj or . fiat que ipsi C . sequalis 

 AE. et ipsi D sequalis BG. et quo- 

 niam tota AF. est ad totam BH. ut 

 ablata AE. ad ablatam BG ergo re- 

 liqua EF est ad reliquam GH. ut 

 tota ad totam. Jam ipsi D. eequalis 

 fiat AM. et ipsi C. sequalis BN. et 

 erit MF. sequalis primse cum quarta. 

 et NH eequalis secundse cum tertia. 

 Estitaque MF (ex hypothesi) major 

 quam NH. Sed ME sequalis est 

 NG. etenim ipsarum utraque equalis 

 est C & D simul. Ergo, si ab in- 

 sequalibus MF & NH. quarum MF 

 major est, auferentur sequales ME 

 M &NG.residuse erunt etiam inequales, 



nempe EF major erit quam GH. 

 Sed supra ostensum est EF. esse ut 

 GH ut AF. ad BH. Ergo AF major 



