And so, since the equations disagreed with the truth, I began once more to accuse these perfectly correct distances, and the planet's reciprocation, of the crime for which my false method was to be blamed. What need is there for many words? The very truth, and the nature of things, though repudiated and ordered into exile, sneaked in again through the back door, to be received by me under an unwonted guise. (p.575)

Chapter 58

Jumping ahead to a figure from chapter 60, you have a diagram of the change from the puff-cheeked orbit to the correct orbit. The puff-cheeked orbit locates the planet at Z, where Z is on the line NK, and length NZ is equal to length KT. The correct location of the planet, M, is the same length KT away from N, but now the length is rotated over to the perpendicular line KL. Placing the planet at point M causes the planet to move in an ellipse. The three equal lengths, KT, NZ, NM are blue.