318 
Mr. Robertson's Demonstration 
G-j-t/F __ G a F 
4 ^ ~ r, ci £v 
aF -{- bE (iFx^ — i t b E-fi 
a-iV ~ * ' « 4 v £ £ V 
b E -f cD __ JEx»-2 cDx 3 
. (3<i'v —••••••• g £V 4 
cD -f rfC _ cD xv— 3 d C x 4 
y yw y^v £y v 
d C -f g B _ d Cxv — 4 t <B x.J 
$0 v ~~ Tyv tgv 
eB +/ A _ <«Bxv— s l /A x 6 
£az/ e / 3 » + ' 777 ‘ 
•££±£ - /Ax^l6 
^ “ -JZT+ 
And consequently 2 _+fZ + iLt.1? + »*■ jf* + + 
d C-f e B , e B -f / A . / A+ g- G ■ a F ■ b-E ■ c D . dC ■ e B . 
$13 V ~T t a. v * ‘ (3 e "T*y5'^y'£g*" 
19. This being proved from the relations between the two 
contiguous perpendicular lines, and these relations being the 
same between any two perpendicular lines whatever (for they 
are as regular and certain as the laws of continuation in the 
multiplicand and multiplier with which we set out in the 13th 
n -f~ 1 — m t 
article) it follows that if pz " x -~ — express the whole of any 
perpendicular line, the next perpendicular line to the right 
n + i— m + i t 
will be l ~ m rz + •* — 1 And therefore the 
g xm+ 1 r m + I 
series x r + n -xx T 
+ 
