4CV EEV. T. P. KIEJKMA» OH MNEMONIC AIDS 



(ff.) d^ is <?*stancq of/ocua from fangent, and r:z b. (/*:/)* at 

 b of root of qxiotQ of fops. v. (8,/) toeq is squaWs. 

 root of gnote. 

 ^'^) h is the mean proportional of the two difta. 



CA) oonga is tbe 8emi"diameter aeo»;ugateto a point (aj|y,> 

 a' — ba by diet j «' = (#0*. (A.) 



(./.) rAo is g, the radius of Qurvsture ; ^ 6a ~ a'' ; cwbed a*. 



(m.) g 6a zz (a^ — «'^)^i a cwbed ^perpendicular, (8, a.) 



(».) jpoc is distance of (arjr) or/? from centre, n R : ^ 



; This last property (compare e) \b expressed by Ijeslie in his 

 " Geometrioai Analysis," in the following luminous and encou- 

 raging language j Prop. yii. p. 206 :— 



*' If the transverse axis of an ellipse or hyperbola, be divided 

 into segments equal to lines dr^Tsvo fyom the foci to 8.ny point in 

 tbe curve, the square of its distance from the centre will be 

 equivalent to the sum or difference of the squares of the semi- 

 conjugate axis, and the distance of intermediaite section from the 

 centre." 



Alas for the student who is doomed tp pick yp his notions of 

 advanced geometry from such authors as Leslie ! 



It is understood, of course, in all that precedes .in this article, 

 tlaat 6* is, of either sign, positive for the ellipse ^nd negative for 

 the hyperbola. 



(11.) Many persons find it difficult tp remerpbej: the principal 

 theorems in combinations. I found it so, for on?, until I ta,ught 

 them to my ear and tongue in the fashion following— 



If *p ele'ms. are 'm, a'sj ei, b's ; ^ c's ; 



The pe'rms in' p are 'p fagp (a) 



by 'm fags, e fags, i fags. 



The comb, repe's of n in ^p's 



are p-n-dps by p faga. (6) 



Com. non-repe's of ^n in 'p's 



fire *p-n-backs by 'p fags. ^^c) 



Jfou repe. vars. of 'n i» p's ^re 'p-n-ba<sks j id) 



The repe. vars. of *n in 'p's, arg *n tp p*. (e) 



