172

Again, since y : z

c : t and z =

Ct

we have y : —--— : : c : t .’. y = - / * ■vA—c*

Also, since A — ‘ { ir . f, we have x \ y w

y c J

\/f -c* : c

Or by substituting the value of y, x :

: -c* : c

Or af: c % t~ x t : : s/1* - c l : : c \/ f — c*

Or x : :x c : 1 x —

t *

Now, as x , y, and z, all begin together,and when any one of them = 0, t = c bytaking the correct fluents of the values of x ry, and z, we have

#=c.hyp.log.£- c.hyp,log.c. = c.hyp.log.|— cm log. y — c x circular arc whose

secant is ~ or whose secant — t and ra-dius == c, and z —c. hyp. log. l +^f ~z£ —

cm log.

t + \/ t 7 - — c zc

Again from the nascent triangle F/r, wehave Ff:fr: : rad. : cos. Z.CFE, or z : y : :1 : cos.?.