117

x= c(sec.<p-l), x' = c'(sec.p-l)

•\ ——— each = sec. * - 1.

C C ^

y = cm log. tang. (45°-j-£) and y' =cm.log.tang.(45°-f-|-p) - = 4- each =m

log. tang.(45°+i? ! )

r z:z'

Hence

c: c

► from which

t : t 1x: x'

y-y’

the proposition is manifest.

14. From art. 9. Case V. we have

j _ y __ ysec.tp __

m.cos.<plog.tang-.(45°+i <f) mlog.tang.(45°+ £ 41 )

and if in this last expression we make yconstant and <p — 0, we have

t= £ii = dro = o = infinity, and, stillmaking y constant, if <p be taken in-definitely near to 90°, 45°-j-^?s will alsobe indefinitely near to 90°: and, in thatcase, sec.if5 and tang. (45°-{-£?) must,by Trigonometry, both be indefinitelygreat, and be to each other in a ratio inde-finitely near to that of equality. Hence

i 8