48 Mr Venn, On geometrical diagrams for the [Dec. 6, 



of reasoning. A historic sketch of their origin will be found in 

 Hamilton's Discussions, Ed. in. p. 666. 



As regards then the employment of what I term analytical 

 diagrams, viz. those meant to distinguish between subject and 

 predicate, and also between the different kinds of proposition, — ■ 

 there can be little doubt that their practical employment dates 

 from Euler. That is to say, he first familiarized logicians to their 

 use, and the particular kind of circular diagram which he em- 

 ployed has consequently very commonly been named after him. 

 But their actual origin is very much earlier than this. The 

 earliest instance that I have seen is in the Be Censura Veri of 

 Ludovicus Vives*, where the mutual relations of the three terms 

 in Barbara, as given by the two premises, are represented very 

 much as on the Eulerian plan. He speaks of representing them 

 by means of containing triangles, but the actual figures drawn 

 are those of the letter V, as thus, 



This is the only diagram to be found, I believe, in the work. 



Priority in this direction has also been claimed by Hamilton 

 for Alsted, who, as he maintains, had in his Systema logicum 

 anticipated the linear kind of diagram proposed by Lambert 

 and which will presently be explained. I cannot however perceive 

 that Alsted had the slightest idea of representing what Euler 

 and the others aimed at representing. All that he says (speaking 

 of the first figure), is that the middle term is 'below' the major 

 term and ' above ' the minor, and he just draws three lines of 

 equal length, one under the other, to illustrate what he means. 

 " Etenim omne medium, quod est inter duo extrema secundum 

 altitudinem, id est, inter extremum superius et inferius, illud 

 inquam medium debet habere aliquod extremum supra se, et 

 aliquod infra se. Atqui medius terminus in prima figura est 

 talis : habet enim terminum supra se, nempe praedicatum con- 

 clusions in majore propositione positum, et habet terminum infra 



* His ■words are: "Si aliqua pars a capit totum b, et aliqua pars b capit 

 totum c, c totum ca2)ietur ab a : ut, si tres trianguli pingantur, quorum unus B 

 sit maximus, et capiet alteram A, tertius sit minimus intra A, qui sit C, ita 

 dicimus, si omne b est a, et omne c est b, omne c est a : adhibeatur regula quaru 

 diximus esse canonem artium et vita? totius." De Censard Veri, Lib. n. (My 

 attention was directed to this by F. A. Lange's Loghche Studien, p. 10.) I do not 

 understand how the capital and small letters here agree with each other. 



