What is the outline of the logical structure of Parmenides's poem "On Nature"?

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Written Analysis of Parmenides' Poem On Nature.

The conclusion of Parmenides’s argument is that we live in a world of “seeming” that covers up the world of “being.” The principle structure of reality is the One. Even though our senses tell us that we live in a world pluralities, what underlies all of reality is a simple oneness.
Unfortunately, we have only a fragment of Parmenides work sometimes titled “On Nature.” For the explication of the extant text, I will use G.S. Kirk’s translation, The Pre-Socratic Philosophers. Kirk places Parmenides’ birth at around 515-510 B.C., and we are not sure whether or not Socrates may have met him before he died. The difficulty in deciphering is argument is first, some of the phrases in the “proem” are obscure, and second, scholars are not certain about the meaning of some lines (p. 265)....