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The tangencies barely graze, or Oppenheimer chooses to share little of them.

“All I could see were these unresolved tangency breaks.”

Let t be the point of tangency; draw s u and t u, cutting the cycloidal path a r in x and y.

A circle is a happy thing to be— Think how the joyful perpendicular Erected at the kiss of tangency Must meet my central point, my avatar!

It is not certain, for instance, whether Euclid meant that the circles could not cut at some other point than that of tangency.