In any triangle, (the sum of) two sides taken together in any (possible way) is greater than the remaining (side). For let $ABC$ be a triangle. I say that in triangle $ABC$ (the sum of) two sides taken together in any (possible way) is greater than the remaining (side). (So), (the sum of) $BA$ and $AC$ (is greater) than $BC$, (the sum of) $AB$ and $BC$ than $AC$, and (the sum of) $BC$ and $CA$ than $AB$.   <prf>  Thus, (the sum of) $BA$ and $AC$ is greater than $BC$. Similarly, we can show that (the sum of) $AB$ and $BC$ is also greater than $CA$, and (the sum of) $BC$ and $CA$ than $AB$.Thus, in any triangle, (the sum of) two sides taken together in any (possible way) is greater than the remaining (side).