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= CE S ; or CE is a mean proportional be-tween FI and ji . In the same manner itmay be shown that CE is a mean propor-tional between GK and gk ; and betweenHL and hi.

Again put OM=EF = ?/, and FG or GH-ny\ then PN=EG = EF + FG=?/+n# =iand QB = EH=EF+2FG =y+2ny =— 1 + 2 n)y. Whence by art. 8. OM —y—cm

log. ^=cm log.^p, and by multiplying each

side of this equation by 1-j-w, we have i +n)y

pj

—cm log.^gX(l-}-n), which by the nature oflogarithms — cm log. (^) . But i +n)y=

PN =cm log.§§, consequently cm log.^=

cm log.(^|) 1+re i or b y dividing each side

, , i GK, , FI\l+»

by cm, we have log. 1 °gd"cE'- / 5 or

since numbers which have equal logarithms,in the same system, are themselves equal,GK ( FI \(l+w) C'XT / r 1T|'' ( FI \1+M r

ce =( ce> 01 GK=CE (ce) • In

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