SOUTH AFRICAN 



QUARTERLY JOURNAL. 

 SEcorrs ssxiZES. 



Wo. 4. SEPTEMBER, 1835. Part 3. 



Remarks on tJic Logic ^f Elementary Gcoinetnj. — By the 

 Rev. J. Adamson, d.d. 



[Read at the Institution, June 3, 1835.] 



Geometry being that science which investigates the relations 

 of extension, and parts of extension, in all modes according 

 to which extension can be conceived, we have to consider, — 



1. What kind of subjects ought to be included in a system 

 of Geometry. 



In regard to this it is clear that the subjects ought to be as 

 strictly geometrical as the subjects of a system of Chemistry 

 are chemical, and the absurdity of incumbering the system 

 with any thing extraneous is as great in the one case as in the 

 other. There are numerical relations of magnitudes, or rela- 

 tions of magnitudes expressible by functions of numbers, the 

 investigation of which would evidently be out of place in a 

 system of chemistry, though it be necessary to consider and 

 apply the results of these investigations. If for instance it were 

 necessary to state, in regard to substances which are the ob- 

 jects of chemical analysis, that half the sum of two quantities 

 added to half their difference would afford the larger of the 

 two, the demonstration of this relation would not be thought 

 necessary in the construction of a system of chemical know- 

 ledge. It might be done as being required by the state of 

 general knowledge among those for whom the system was 

 prepared, but the argument would be felt and announced to 

 be extraneous, and its occurrence to be an interruption of 

 the logical course of that proceeding in which it is proposed to 

 demonstrate only the effects and relations of chemical affinities. 

 The same ought to be the case in regard to the relations of 

 extension. The demonstration of any truth which is extra- 

 neous to the relations of extension, or does not arise from these 

 relations alone, ought in strict logic to be excluded from our 

 procedure. No theorem therefore, of which the hypothesis 

 ^nd conclusion present a relation which is true of magnitude 



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