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EEV. T. P. KIEKMAN ON MNEMONIC AIDS 



The angles are to be distinguished from their opposite sides, 

 a, b, c, not only to the eye by the letters A, B, C, but to the 

 ear by the sounds Aug, Bang, Gang. Read now, or rather 

 chaunt, the above mnemonic slowly, and very often, with as 

 strong an emphasis as possible on the accented syllables ; and 

 you will thus teach it to your ear, your tongue, and your Itps^ 

 which have all their own powers of memory. The meaning of 

 the abbreviations si. and co. is obvious: they are put for sin. 

 and COS., for smoothness merely. The proposition 



cot A. sin C -|- cos b. cos C zz cot a. sin b, 



is difficult to remember, chiefly because, when you attempt to 

 pronounce it unambiguously, it is long and inharmonious. Con- 

 tract it and smooth it as above, giving it a little sing-song 

 cadence, and the ear and other organs cheerfully undertake the 

 task of remembering its twelve monosyllables, which never can 

 fail to suggest the expanded formula with accuracy j a task 

 which, in some men who have more talent for language than 

 for science, these organs will continue faithfully to discharge, 

 after the reasoning faculty has forgotten the proof and much of 

 the application of the theorem. But I do not see, although 

 some persons may have sagacity enough to perceive this, that a 

 student is the less likely to be able to prove a proposition be- 

 cause he can easily recall the enunciation : this may suggest, but 

 can hardly conceal, the argument. 



The mnemonical rule quoted above is a hint offered to the 

 judgment ; that which I have proposed is a short lesson to be 

 taught by rote to the unreasoning sensuous organs. What these 

 have once engraved on their tablets becomes a ready instrument 

 of rapid thought ; the judgment reads the formula without effijrt, 

 and performs at leisure its proper function of interpreting and 

 applying it. 



(2.) The 12th and 13th propositions of the second book of 

 Euclid's Elements are as follows : — 



" In an obtuse-angled triangle, the square of the side (6) subtending 

 the obtuse angle, exceeds the sum of the squares of the sides (a and «) 

 which contain that angle, by double the rectangle under either of these 



