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The poem rewritten as a prose paragraph might look something like this:
I have two joys, one which is faithful and like a rose, and one which is lost and like a thorn. I am rich because of the faithful joy, but just as sorrowful because of the lost joy. The rose, which is the faithful joy, is loved, and the thorn, which is the lost joy, is loving. They are inseparable and co-dependent. One can not exist without the other.
When the poem is translated into prose like this, it of course loses at least some of the rhythm the poet likely intended it to have. The first four lines of the poem, for example, have a regular syllabic meter, meaning that each line comprises a similar number of syllables. This lends a rhythm to the lines which perhaps reflects how the thorn and the rose exist harmoniously, and equally, one inseparable from the other. Although I have tried to make it clear in the prose translation that the rose and the thorn exist harmoniously, I have not been able to echo this sentiment in the rhythm of the language.
When you write your own prose translation of the poem, you might also want to consider the significance of the words immediately before and after the line breaks in the poem. The word "lost," for example, appears four times at the end of a line, and the brief pause which follows the word each time means that the word resonates throughout the poem.
In your prose translation, you might be able to place this word four times at the end of a sentence, but the pause created by a period is not quite the same as the pause created by a line break. The word "lost" in a prose translation might, therefore, not have quite the same impact, or resonance, as the same word in the original poem.