We should have been very ungrateful had we not given him the required assurances, agreeing that we would merely state the fact that we had found the canoe on the bank of the river, and that as, from the time it had been there, its owners were not likely to return, we had appropriated it. (In the Wilds of Florida by W.H.G. Kingston）
動画の後半部分でリスニング用音声が流れます。
英文を前から読んでいくために、語句のかたまりを作ります。こんな具合に課題文をスラッシュ（斜め線）で区切ります（スラッシュリーディング）。語句のかたまりを意識すると、リスニングで英語の意味をつかむのが楽になります。
We should have been very ungrateful／（if 省略の仮定法過去完了の前）had we not given him the required assurances,／（動詞のing形の前）agreeing that we would merely state the fact／（接続詞の前）that we had found the canoe on the bank of the river,／（接続詞の前）and that as, from the time it had been there, its owners were not likely to return,／（主語が文頭にないときの主語の前）we had appropriated it.
語句のかたまりを前から訳していきます。
We should have been very ungrateful
私たちは、ひどく恩知らずになっていただろう
had we not given him the required assurances,
私たちが求められた確約を彼に与えなかったとしたら
agreeing that we would merely state the fact
そこで私たちは、事実を述べるだけにするということに同意した
that we had found the canoe on the bank of the river,
私たちが川岸でそのカヌーを見つけたという
and that as, from the time it had been there, its owners were not likely to return,
そしてカヌーがそこに放置されていた期間から、持ち主が戻ってくる可能性が低かったので
we had appropriated it.
私たちはそれを自分たちのものにした（という）
We should have been very ungrateful had we not given him the required assurances, agreeing that we would merely state the fact that we had found the canoe on the bank of the river, and that as, from the time it had been there, its owners were not likely to return, we had appropriated it.
had we not given him the required assurances→ 仮定法過去完了です。if が省略されているので、had が前に来ています（倒置）。
agreeing that〜 → 分詞構文です。前の主節を受けて「そして」「そこで」といった言葉でつなげます。
求められた確約を彼に与えなかったとしたら、私たちは、ひどく恩知らずになっていただろう。そこで私たちは、そのカヌーを川岸で見つけたという事実と、カヌーがそこに放置されていた期間から、持ち主が戻ってくる可能性が低かったので、自分たちのものにしたという事実を述べるだけにするということに同意した。
今回の課題文は、agreeing 以下の構造が複雑になっているので解説します。
We should have been very ungrateful had we not given him the required assurances, agreeing that we would merely state the fact that we had found the canoe on the bank of the river, and that as, from the time it had been there, its owners were not likely to return, we had appropriated it.
agreeing that we would merely state the fact→ 事実を述べることに同意した、というのが大意です。
that we had found the canoe on the bank of the river,→ この that は「同格のthat」で、that以下は前にある the fact の内容です。
and that→ この that も上と同様で、that以下は前にある the fact の内容です。
as, from the time it had been there, its owners were not likely to return, we had appropriated it.→ from the time it had been there が挟み込まれた後、as its owners were not likely to return という理由で we had appropriated it したわけです。
