118 ESSAYS Anp OBSERVATIONS. 
and draw CF, parallel to DE, meeting 
the curve in F ;,let EG, a tangent to 
the curve at E, meet CF in G, and join 
DF, DG,; and let DG meet the curve 
in H;-let the point D be between the 
points A,C: The fector AGE will be 
greater than the fector ADH, but lefs 
than the fector ADF; and the fector 
BCE will be greater than the fector 
BDF, but lefs than the fector BDH. 
Because the triangle DEC is greater 
than the fector EDH, let the fector. ADE 
be.added to both; and the fpace ACE 
will be greater than the fetor ADH: And, 
becaufe the triangle DEC is lefs than the 
feftor EDF, let the fector ADE be added 
to both; and the fector ACE will be lefs 
than the fector ADF. see Ae 
AGAIN, becaufe the fector ACE toge- 
ther with the fector BCE, is equal to the 
fef&tor ADF together with the fector BDF, 
and the fe@or ACE is lefs than the fector 
ADF; therefore the fector BCE is greater 
than the fector BDF: And, becanfe‘the 
fector ACE together with the fector BCE, 
; is 
Pp a ee ag 
