Mathematics and to Natural H'lJIory, 299 



certain primary objefts, whether founds, words written in 

 alphabet, or diftinft exiftences in nature. In the higher 

 parts oF algebra, and indeed throughout ail mathematics, 

 are nianv abbreviations nearly fimilar to that in which arith- 

 metic fubititutes nuiitiplicaiion for addition. But has not 

 every branch of knowledge, in like manner, its abbrevia- 

 tions, by means of which its reafonings are brought con- 

 tinually nearer to the quicknefs and certamty of intuition ? 



If. All that i'cicnce does is, not to create new exiftences, 

 to brino; into the knowledcre of man fomethino- that was never 

 before known to mind, but merely to oblerve individuals, 

 and to form, bv abftraftion, general notions by which human 

 th')Ught mav become capable of a much greater number of 

 individual conceptions than it could by other means poflibly 

 comprehend. In -fiiort, all human fcience is thus reduced to 

 arrangement convenient to memory, and ferving merely, as 

 it were, to enlarge the range of the mind's eye. Now, ma- 

 thematics is not a folitary exception : all its difcoveries are 

 merely difcoveries of exiftence and arrangement. A mathe- 

 matical point is the genus general'ijfnnum of the fcience. 

 Points repeated with relation merely to numerical quantity; 

 and, on the other hand, points repeated fo as to form ex- 

 tenfion ; are tiie two great genera included imniediatelv under 

 that genus generaliffimum. If we purfue lineally extended 

 quantity into fubdivifions continually lower, we fliall find 

 next the three fpecies of lineal extenfion by Itraight lines, by 

 curves, and by angrles. Under the fpecies of ftraight lines are 

 all the fubordinate fpecies of merely longitudinal extenfion, 

 with their mutual relations and difiercnces. The fpecies of 

 curves has under it all the inferior fpecies of magnitudes or 

 figures, which can be formed and bounded by curved lines 

 alone, without the intervention of angles or itraight lines. 

 The fpecies of angles comprehends, as fubordinate, all the 

 difterent forts of linsile angles which can be formed bv the 

 meeting of two flraight lines. Subordinate to the angle and 

 the ftraight line, jointly, are all thofe figures complete on all 

 fides, which are formed by the combination of ihaight lines 

 and angles only. There is a fifth clafs of fubordinate fpecies 

 referable to the angle, the (Iraight line, and the cur<'e, jointly, 

 which includes all the fubordinate fpecies of figures, all thofe 

 modes of extenfion, in which angles, ftraight Hues, and curves 

 arc combined. It were ealy to purfue thefe (ubdivilions con- 

 tinually lower, even to every conceivable diverfity, in the 

 monies of extenfion. It might be fhown that number is 

 liiercly arrangement into genera and fpecies, iv,c. with the 



fame 



