PROCEEDINGS OF PROVINCIAL SOCIETIES. 305 



dednctions from them, " ope et interventu mathematicae ;" — a philo- 

 sophy of amusement and recreation, rather than of instruction and 

 discipline. He must take the former word, therefore, in its most 

 general sense, and the latter one in its most dignified ; and then he 

 should not only obtain what he considered the most eligible result, 

 but should also fix exactly the same meaning upon the desideratum 

 of the Surgeons as upon that of the Apothecaries, viz., that the 

 former mean by their term 



Mathematics, 



Pure Mathematics Mixed Mathematics, or 



The math. prin. of Nat. Phil. ; 

 and that the latter mean hy their terms 



Mathematics Natural Philosophy 



Pure Mathematics The math. prin. of Nat. Phil. 



As to the designation of these lectures, he should feel inclined to 

 adopt the term " Mathematics," used by the Royal College of Sur- 

 geons, Edinburgh ; since it is the most simple, and there is no ety- 

 mological reason why that word should be limited to comprehend 

 abstract science only ; since it is used in the universities of this land 

 and on the continent, also to comprehend physical science ; and, 

 lastly, because such an interpretation exactly coincides with the de- 

 finition given by Lord Bacon : — '^ Mathematica aut pur a est aut 

 mioda. Ad puram referuntur scientise, quae circa quantitatem occu- 

 patae sunt, a materia, et axiomatibus physicis penitus abstractam.* * * 

 Mixta habet pro subjecto axiomata et portiones physicas : quantita- 

 tem autem considerat, quotenus est ad ea elucidanda et demonstran- 

 da et actuanda auxiliaris." As then the term mathematics, in 

 this sense, includes two departments — Pure Mathematics and Mixed 

 Mathematics — and as the time during which students are required 

 to attend the lectures at this institution comprehends two summers ; 

 it appeared that he should be following the most natural process, if 

 h« allotted to the students of the first year, and to those of the se- 

 cond year, these two departments respectively. He should there- 

 fore divide the whole of his pupils into two classes ; one of them, 

 containing pupils in their first year, to be lectured in " Pure Mathe- 

 matics ;" the other, consisting of pupils in their second year, who, 

 having attended in their former year the former course, would be 

 then qualified to be lectured in " Mixed Mathematics." 



The lecture was concluded by some observations on the advan- 

 tages of such a course as he had projected, in the way of m.ental and 

 moral discipline ; in confirmation of which, were brought forward 

 the two following quotations ; the former from Lord Bacon, the lat- 

 ter from Bishop Berkley : — ^' Si cuipiam ingenium tale sit, quale 

 est avium, ut facile abripiatur, nee per moram (qualem oportet) in- 

 tentum esse sustineat, remedium huic rei preebebunt mathematica, 



VOL. IV. — NO. XVI. Y 



