What is Proposition 1.8 of Metrica?

Answer 1

In accordance with WolframAlpha:

"Heron's Theorem

"The area (delta) of a triangle with side lengths a, b and c and semiperimeter s is given by (delta) = sqrt(s * (s-a) *(s-b) * (s-c))

...

Proof source: Heron of Alexandria. Proposition 1.8 in Metrica. Ca. 60 A.D."

So Proposition 1.8 of Metrica is the well known Heron's Formula for finding the area of a triangle given its sides.

Answer 2

Proposition 1.8 of Metrica states that if the sum of the measures of two angles is less than 180 degrees, then the two angles are not supplementary. In other words, if the sum of two angles is less than a straight angle, then they are not a pair of supplementary angles.