7th Paragraph

Translation

For the Athenians who died in this war, Simonides, an outstanding poet [one of the best known and appreciated of Greek poets] wrote the following epigram:
If to die well is the greatest part of courage/virtue/excellence, [then] fortune bestowed this upon us above all others. For hurrying eagerly to bring freedom to Greece [we fell and] are now lying here enjoying everlasting praise. [their eagerness to make sure all of Greece enjoys freedom is just as enduring as the praise generations will sing, that's why, despite the fact that they rushed into battle first, before being laid to rest

σπεύδοντες (present participle) is used instead of σπεύσαντες (aorist participle)
because it means "we were being keen, striving eagerly to save Greece, rather than just "we hurried".