'54 



ROCHESTER ACADEMY OF SCIENCE. 



[Nov. 12, 



Examination of the symbol | e\'olves the rule for the extraction 



of square root in strokes : — Halve the angle of the stroke and lay off 

 alo7ig the bisector the mean proportional between the lerigth of the stroke 

 and unity for the length of the required stroke. 



In the case of roots of unity, this rule for square, cube, etc. , 

 roots becomes, halve, third, quatier, etc. , the angle of the stroke and 

 lay off along the trisector, etc., a tinit length. 



I give a few simple examples to illustrate the applicability of 

 strokes : 



OPERA- 



TION. 



OPERAND. RESULT. 



r 



STROKE 

 ANALYSIS. 



ALGEBRAIC 

 ANALYSIS. 



1/. 



2 



i/T . 



4/7- 



iVr 



• > K- 



I, + I, + 7, — / 



V-' ^\ 



/T 



l/^^l/^ 



v^^ <- 



The third column is arrived at by bearing in mind, e. g., that the 



angle of > is either o°, ±360°, ±720°, etc. A third of these 



gives 0°, ±120, etc.; a fourth, 0°, ±90°, ±180°, etc. 



The last column is arrived at by simple trigonometric or geomet- 

 ric calculation. 



Multiplication and division of strokes is performed with similar 

 facility, but I shall not go into these details here. The formal discus- 

 sion of the subject can be found in any book on the Theory of 

 Functions. 



