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



in the mean time I join with you in thinking that he will not he 

 able to do any thing to the purpose on Euclid's Porisms *. . . . 



" I have taken Emerson's 3 books rather to help Mr. Foulis Sale 

 of those you sent him than for any other reason ; I believe your opi- 

 nion of them is much the Same with my own ; what think of you of 

 his saying at the foot of page v. of his Geometry ' For it is an Axiom 

 in Logick, that that Supposition must needs be true which destroys the 

 contrary Supposition-^ ' for what if the contrary supposition be true ? 



* * * * 



" I desire you to let me know in what respect you think that Dr. 

 Stewart has deviated Something from the Antients, for he gives the 

 Analysis as well as the Composition of the Theorems, for 1 do not 

 observe that he gives any of his Propositions as Problems, and so has 

 no occasion to make use of Euclid's Data. When I get your next, 

 I shall more fully let you know my opinion of his great merit;.. 



* I am warned by my own paging in the MS. to abstain from making 

 some remarks here whicli 1 fully intended to give as a note on the Porisms. 

 It may be as well this should be deferred ; for though the general principle 

 of the porismatic system has been, beyond all doubt, established by Dr. Sim- 

 son, there remain difficulties sufficiently formidable about this class of in- 

 quiries to inspire caution in speaking dogmatically on the subject. When- 

 ever I may offer an opinion on either the principle or the details of the 

 porism, I shall at least have had the advantage of the criticism and discus- 

 sion of the most eminent geometers (in strictness of language) in Europe, 

 both as opposed to, and as coinciding with, my own views. The seventh 

 book of Pappus is not entirely unravelled yet. 



\ The only instance I find in all these letters of " marking for italics." 

 Even here it is not underscored but overscored — an instance, 1 think, not 

 often found. 



\ This has reference, without doubt, to Stewart's Propositiones Geome- 

 tricce, published in 17b'3 ; a work which contains a most remarkable series of 

 properties of circles and triangles, which are often referred to a later date, 

 and many of which are even now but little known to geometers. A great 

 number of these properties, slightly varied in their enunciations, hold good, 

 too, in the conic sections ; and 1 cannot point out a more useful exercise 

 for the young geometer than to attempt the extensions here suggested. 

 Very many years ago I myself found this exercise most beneficial ; and I 

 venture to predict, that whoever follows the same steps will find himself in 

 a position to follow with little difficulty, one of the most important sections 

 of the geometrie superieure of the modern French School. 



It is singular enough that whilst Dr. Stewart's writings are of a kind cal- 

 culated to render them peculiarly attractive to the non-academic school of 

 English geometers, they remain to this day less generally known than the 

 writings of any geometer of these kingdoms. Even his " physical tracts," 

 and the supplementary one on the " sun's distance," though admitted to 

 be of little physical value, are yet as replete with specimens of geometrical 

 skill, as even the Principia itself. Besides his separate works, however, 

 there are some stray pieces of Dr. Stewart. One is a discussion and ex- 

 tension of Pappus, iv. 4, which was printed in the " Essays Physical and 

 Literary, read heforethe Philosophical Society of Edinburgh," — the parent 

 of the present Royal Society of Edinburgh (Ed. 3 vols. 8vo, 1754-71). 

 These essays are rarely to be met with now; and at my suggestion, 

 a good many years ago, this paper was reprinted in Leybourn's Mathe- 



