^ EEV. T. P. KIKKMAN ON MNEMONIC AIDS 



lor ia the constant c divided iy the hypothenusQ to the Jics or 

 coe^ient*, a and b, of the variables. 



In (i), plor is the shortest distance P from the origin, of the 

 jp/ane Ax -|- By -}- C;? zn: H, referred to right axes. 



diff means diaffonskl, sometimes diaff or dta. Dig bac is 



dig Jics is (A^ -f" ^' 4" C^)*> diagonal of the right solid whose 

 sides are A, B, and C. Then we have if) thus explained, 



p , H 



— (A^ + B^ -f C^)4 

 (9.) Useful formulae are the following on lines and planes re- 

 ferred to right axes. 



plan's vagiU, if lor's con in h \ (a) 



plap is vapltf, if plor's con in 6. (b) 



(a.) plin is the distance of a point p from a /me 

 ^. ay -f- Jo; -|- c rz: ; 



gil means ^^tven line ; gil « is the f ^«» or zero just written j 

 vagil** is the value of that expression, when a:,yi of the point p 

 are put for xy, or ayi -|" ^^i ~f" ^' This is the length pliriy if 

 the cowstant c in that a *«*' is the length lor^ (8, K). 

 (b.) plap is the distance of a point p from a plane 

 Ax + B^ + C2 -f- H =z 0. 

 vapla is the value of this jo/a, or plane's ^^e", at jd (XiPiZt) : and 

 this value, Axj -|- Byi -|~ QiZ^ -j- H, is the length plap. provided 

 that the constant H in that a or zero be the length plor, (8,i,). 



Generally, let the co-ordinate axes contain an angle V : 

 Plin by sine V^ is vagil « at '/> by *bas (fics V). 

 (c) Plin and vagil u as above. 



(c.) bos jies Vis the base of the triangle, whose sides are the 

 JicSy or coe^cientj of the variables x and y, and contained angle 

 V. That is, 



Plin (axx -f- bxi + «) (c) 



SmTV — (a* — 2a^ Cos.V + 5')* 

 and this is true whatever c may be, whether lor or not. 



If my space were not limited, I could easily give mnemonics, 

 equally brief and simple, for all the formulae required about the 



