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Then the union of single and double emerges in one to two (1:2); the sesquialter union in two and three (2:3); and the sesquitertian in three and four (34).
Copernicus exclaimed, "Only in this way [the heliocentric arrangement] do we find a sure bond of harmony between the movement and magnitude of the orbital circles." (8) For Kepler, it was a life-long quest to convert this qualitative agreement into a quantitative expression: the ratio that exists between the periodic times of any two planets is precisely the ratio of the sesquialter power of the mean distances, i.e., [P.sub.1]/[P.sub.2] = [([a.sub.1]/[a.sub.2]).sup.3/2].
For example, the English phrase ONE AND ONE HALF is succinctly described by Polish POLTORA, German ANDERTHALB or Latin SESQUIALTER. (In fact the Polish even have the word POLOSMA for SEVEN AND ONE HALF!) Similarly, English THE DAY BEFORE YESTERDAY is more compactly expressed by German VORGESTERN or Spanish ANTEAYER, and English THE DAY AFTER TOMORROW, by German UBERMORGEN, Italian DOPODOMANI or Polish POJUTRZE.