io6 ESSAYS AND OBSERVATIONS 



eent to the curve at C, meet BD 

 in E ; join AD, AE, BC, and let 

 AE meet the curve in F : the tri- 

 angle ABC will be greater than the 

 fe6tor ACF, but lefs than the fe- 

 aor ACD. 



Join CD. Becaufe AC, BE, are parallel, 

 the triangles, ABC, AEC, will be equal: 

 but the triangle AEC is greater than the 

 fedor ACF ; therefore the triangle ABC 

 is greater than the fedtor ACF. Again, be- 

 caufe AC, BD, are parallel, the triangles, 

 ABC, ADC, are equal : but the triangle 

 ADC is lefs than the fedlor ACD ; therefore 

 the triangle ABC is lefs than the fedtor ACD. 



PROP. II. R'g. 2. 



Let there be a curve AEB, wholly 

 concave towards the flreight line 

 AB, and let C, D, be two points in 

 the line AB ; draw DE to any point 



E 



