MENSURATION. 



XXIX 



(3 = 36o7«, 



s = 2 r tan ^ ft = 2 J? sin ^ (3, 



/> = ;i s = 2 u r tan ^ /3 = 2 u J? sin i^ (3. 



See table under c, below. 



c. In ellipse. 



a = semi-axis major, 



d = semi-axis minor, 



e =: eccentricity = (i — b'ja'^y-, 



7^= perimeter of ellipse, 



;/ = {a - b)l{a -}- I?) 



+ N/x-^ 





8 



64 



Distance from centre to focus ■= a e, 



Distance from focus to extremity of major axis =^ a (1 — e), 



Distance from focus to extremity of minor axis = a. 



P= TT Or+ /.) (i + i ;/2 + ^ n' + ,}_ ,fJ^.. .) 



= TT (rt- -f- b) q, say, where q stands for the series in //. The values of q cor- 

 responding to a few values of n are : — 



-^1 



a 



2. Areas. 



a. Area of plane triangle. 

 (See table on p. xix.) 



b. Area of Trapezoid. 



upper base of trapezoid, 

 lower base of trapezoid, 

 altitude of trapezoid, or perpendicular distance between bases. 



Area :=.\ibx-\- A,) a. 



