1842.] 



Remarks on Capt. Shortrede's Note. 



783 



tary property which must be clearly seized: for which purpose we 

 may put it thus : Let the angle and the angular-space be in any ratio' 

 say a : b. Then d dividendo the angle is to the difference between it 

 and the angular space, a finite rectilineal figure, as a : a-b. But the 

 angle is infinitely greater than the finite rectilineal figure : hence a is 

 infinitely greater than a — b, whence the latter is zero, or a=b, and the 

 angle = the angular space. 



The matter lies in a simple compass : if the angle be not an infinite 

 surface, what is it ? If it be, it must be discussed according to its 

 nature. There can be no arbitrary limitations to the province of 

 geometry : if you will adhere to them, you must try to do without 

 angles, for they are interlopers. The Greek confined himself to the 

 geometry of the line and the circle, and did wonders therewith ; but the 

 trisection of the angle and the duplication of the cube required him to 

 extend his armory. The Italian (Mascheroni) yet more chivalrous, 

 used only the circle : but his was a tilt-yard exercise. The only oath 

 administered to the candidate for mathematical knighthood is, that he 

 shall seek always for Truth in the realms of Space and Number, and that 

 he will do his devoirs with every lawful weapon of sound logic. The 

 attempt to assign forced and arbitrary limits to things which do not 

 admit of them, has always been productive of mischievous consequences 

 in retarding our onward progress in physics as in legislation, in poetry 

 as in mathematics. 



Errata in the Essay on Angular Geometry. 



ige 231, line 16 



from bottom, 



for Bossat read Bossut 



„ n „ 3 ... 







,, cerelations 

 „ Thomson 



, correlations 



„ 233 „ 1,14 



„ 



top 



, Thompson 



„ 235 ., 9 



,, 



bottom 



„ 2nn + A 



„ 2n 7T + A 



„ 236 „ 6 



,, 



top 



,, devote 



, denote 



„ 237 „ 17 



„ 



bottom 



,, angle 



, angles 



„ „ u 13 



„ 



„ 



„ Each of 



, each side of 



„ 238 ,, 15 



,, 



,, 



„DED 



, DEB 



„ n ,, 9 



„ 



H 



, , straight cuts , 



, straight line cuts 



>, » „ 2 



a 



>» 



„ Fig. 12. 



, Fig. 11 



,, 239 „ 3 



„ 



top 



„ c 



, A 



,» ii i, 4 



„ 



„ 



„ Fig. 13 



, Fig. 12 



M >, » 6 



„ 



This line 



should run thus 



Let A C meeting A B, not meet 



E D, consequently, 



Sac 









