Mathematics and to Natural Htjlorji, 295 



thematical truths are difcovercd. Number and figure, points 

 and lines in all their polliblc combination?, magnitudes or 

 quantities, are the fubjcfts of mathematical inveftigation. 

 Of thefe, we brins not into the world, by reminilcence from 

 a former (late, or bv innate infpiration, any original know- 

 ledge prior to experience by the ienfes. So fimple, liowever, 

 and primarv arc their ideas, that thev mav be confidered as 

 nearly coeval with the tlrli: opening of the mind to percep- 

 tion. The line, the point indeed, which we perceive by 

 fenfe, poflefs not each that perfeftion in its kind which ma- 

 thematical fciencc afcribes to it. Yet from fenfe are our 

 primary notions of the mathematical line and point never- 

 thelcfs derived. Wc obtain the notions of animal and vege- 

 table forms and colours more perfe&ly beautiful than any 

 which are aclually to be feen, folely by abftrafting and again 

 combining in idea the beauties which are in nature diftri- 

 buted among different animals and vegetables. We form in 

 imagination the charafter of a truly wife and good man by 

 a fimilar abltraclion and combination of qualities, which in 

 real life arc never to be feen together. We exalt our minds 

 to conceive the exiflence of the all perfc6l Ruler of the uni- 

 verfe, alfo by the abftraftion of the beft qualities which we 

 difcover in liis creatures, and by combining them in our 

 thoughts in the higheil perfedlion in which we are able to 

 imagine their coexillence. And it is juft in the fame manner 

 that, bv abftraftion from the point and line, which can be 

 materially rcprefented to our eyes, we attain to the concep- 

 tion of a mathematical point without length, breadth, or 

 thicknefs; and of a mathematical line, which of thefe qua- 

 lities has none attributed to it but length. 



Thus far, then, the fundamental notions in mathematical 

 fciencc arc gained precifely in the fame manner in which we 

 arrive at the knowledge of generic, fpecific, or claihfic cha- 

 rafters in natural hidory; by obferving individuals in ma- 

 teria! nature, and by abflradling thofe qualities which are 

 connnon to numbers; leaving out thofe which ferve but to 

 particularize individuals, and making the qualities abffraded 

 and combined anew, to our mindSj the common reprefenta- 

 tives of all. 



Numbers are generated from points; all other definite 

 magnitudes from lines ; and a line itielf is alfo produced from 

 a point. But wc have no reafon to believe, that, if material 

 nature did not fuggeft to our conception the repetitions of 

 unity, by prelenting more individual objedls than one to our 

 notice, we (liould ever have formed the idea of two. Nor is 

 it certain that wc fliould have l)een able, in imagination, to 



T 4 diltinguilh 



