ON NAPIER S RULES. 



333 



tion circle CF in C. Let CF cut the equator FD in F. And, 

 lastly, let FD cut the meridian DB in D. Then all these inter- 

 sections take place orthogonally in the points B, E, C, F, D; 



Fig. 3- 



the other intersections taking place obliquely in the points Z, P, 

 S, 0, Q. And by this means five right-angled triangles will be 

 formed, namely, PBS, SFO, OEQ, QDZ and ZCP, of which 

 though the parts are different the circular parts are the same. 



"The same uniformity of circular parts for quadrantal triangles 

 may be made to appear by joining in the preceding figure PQ, 

 QS, SZ, ZO, OP] by which means five quadrantal triangles will 

 be formed having different parts with the same circular parts. 



" The rules for the solution of the circular parts may be proved 

 in each case separately, but besides this proof the general truth 

 of the rules may be seen from what precedes. For the homo- 

 logous constitution of the circular parts argues the similarity of 

 the relations connecting them; so that any proposition which 

 can be enunciated concerning the relation of any middle part to 

 the adjacents or opposites may be at once concluded to be true of 

 every other part regarded as the middle part." 



Thus it appears that Napier himself did not regard his rules 

 as a mere memoria technica, but saw them in their mutual 

 relation, and in fact conceived them in the very best manner 

 possible. Hence, it is very strange that we should find such 

 statements as the following : 



