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



tioned : whether the present completion of it, or that given in 

 the note upon /. 24- be satisfactory or not, will give rise to 

 different opinions. It will be necessary to prove what Dr. 

 Simson assumes in the opening of the above reply, that DFE 

 is less than a right angle ; and as to that in the note in Euclid, 

 there is an assumption not at all warranted by anything prior 

 to i. 24< : — except, indeed, the warranty of his own precedent 

 in /. 13. 



Simpson administers a very proper and dignified rebuke to 

 the Doctor in the same note, but which is not noticed either 

 in this MS. or in print. 



" Professor Simson (at p. 359 of his Euclid, 4toedit. 1756) 

 has been a little severe upon me, on this head, for attempting 

 to supply, what I thought a small defect in Euclid. ' Who is 

 so dull (says he) tho' only beginning to learn the Elements, as 

 not to perceive that the circle described from the centre F &c.' 

 It is not without a real concern that I here see this able Geo- 

 meter drop his own character so far as to express himself in 

 a manner so very ungeometrical . If the thing is indeed so 

 easy to be perceived, it must be so either as an object of the 

 senses, that is, in plain terms, by inspection; or else it must 

 be in consequence of geometrical reasonings antecedent to the 

 thing itself. Now I am clear that he would not be thought 

 to mean the former ; and as to the latter nothing had been 

 given from which the evidence of the inference could be so 

 clearly seen : For though, &c." 



It may be added, that a particular object induced me a 

 little time ago to note the assumptions that are tacitly made in 

 the first book of Euclid. Whoever does the same will not be 

 a little sui'prised at their number. 



There is no doubt that Simson removed a great number of 

 small blemishes from Euclid's Elements; but, it is equally 

 certain, that he has still left a great many more than he has 

 removed. He found some of them too firmly rooted into the 

 system to be able to eradicate them without venturing upon 

 far greater changes than he has done — and he showed no 

 *' lack of courage " in that way, either. The present is one of 

 them; for the proof ought to form part of the text; whereas 

 it is treated in a note as a thing " easy to see." The same 

 assumption in a still more objectionable connexion occurs in 

 the construction of?. 13. For there it is assumed that the 

 circle whose centre is C, and which passes through a point D 

 oji the other side of the line AB, will cut that line in two points, 

 F and G; as otherwise the construction following could not 

 be performed. It is also to be presumed that the circle can 

 only cut the line in those two points ; as if it cut in more than 



