以 + [noun] + [verb phrase]
[verb phrase] + 以 + [verb phrase]
以 has two jobs in written Chinese. Before a noun it means "with" or "by means of", naming the means, manner or basis of an action. Between two verb phrases it means "in order to".
The 以 phrase goes before the verb. It often frames a longer noun: 以…的速度 "at a speed of", 以…的方式 "by way of", 以…的身份 "as", in the capacity of.
以…出名 or 以…闻名 says what someone or something is known for.
The second verb phrase is the purpose of the first, and both share a subject. 以 comes after the first verb phrase, so this use never opens a sentence. To put the purpose first, use 为了.
以…为… "take X as Y", 以便, 以免, 以来 and 以上 / 以下 each have their own entry.