Prose
The word "prose" first appears in English in the 14th century. It is derived from the Old French "prose", which in turn originates in the Latin expression "prosa oratio" (literally, straightforward or direct speech).
Sine
Etymologically, the word "sine" derives from the Sanskrit word for chord, "jiva"*("jya" being its more popular synonym). This was transliterated in Arabic as "jiba" جيب, which however is meaningless in that language and abbreviated "jb" جب . Since Arabic is written without short vowels, "jb" was interpreted as the word "jaib" جيب, which means "bosom". When the Arabic texts were translated in the 12th century into Latin by Gerard of Cremona, he used the Latin equivalent for "bosom", "sinus" (which means "bosom" or "bay" or "fold"). Gerard was probably not the first scholar to use this translation; Robert of Chester appears to have preceded him and there is evidence of even earlier usage. The English form "sine" was introduced in the 1590s.