Ji REV. T. P. KIEKMAN ON MKEMftJTC AIDS 



pin is ^n abbreviation of jjlua iniiwuS, + — ^ H ••..•• 



rqnn is plus -and minus alternately, -reversed j 

 or -|- — -j ^ read backwards froln the la^ttenn. 



Examples are 

 2* Cos ^6 = Cos 5^ + 5 €os 3^ + 10 Cos S 

 2» Cos ^'d =: Cos bd 4- 6 Cos 4^ -f l5 Cos 2^ + 10 

 2* Sin '6 =. Sin 5^—6 Sin 3^ -f 10 Sin 6 

 2* Sin ^d =— Cos 6^+6 Cos 4^ — 15 Cos 2^ -f 10 

 t8.) I shall now proceed to Select a few mnemonics, from the 

 multitude which I have been accustomed to employ, so as to 

 exhibit instances of various mnemonical devices, and shall pay 

 no regard to the order of the mathematical topics to which they 

 belong. None of these devices have been invented for one 

 emergency only, being all of them repeatedly applicable in the 

 concise expression of formulae. 



(a.) per ab is (a' — b^)K per ba is (b^ — a^)*^ 

 (6.) poth ab is (a^ -j- J^)*. 



(a2 — b^^ is the ^perpendicular in the right angle triangle 

 whose base is b, and whose hypothenuse is a : and (a* -|- 6^* is 

 hjpo^Aenuse to the sides a and b about the right angle. 

 Thus, to remember the equation to the conchoid, say,'-*- 



(xy a dissyUabie,) , 



In conch, a pole ord, and^od, 

 xy is moi per^ Sum yci. 

 In the concJtoi^i a being the oreKnate of thfe pole, and jfi^ 

 modaluB, 



xyz=±if' —y)*. 0/ + a). 

 Again, 



Witch x^p is two a per &I)ax. 

 In the witch, xi/ =z 2a (a^ — (a — - a:)-)* =r 2a (.2ax — a:*)* 

 Dax being a — x, per a Dax is (a? — (a — xY)* i D means 

 Diff. here. 



(c.) If TO rz ax and n zz by, (aV — W^f ZZL (m? — ^^)* is 

 a perpendicular of the same kind : call this perprod {ax by), or 

 smoother, peprod (ax by), or shorter still, pep. (ax by): i. e-, the 



