By now he was convinced that the orbit must be an ellipse, because countless observed positions of Mars, which he knew almost by heart, irresistibly pointed to that curve; but he still did not realize that his equation, which he had found by chance-plus-intuition, was an ellipse. So he discarded that equation, and constructed an ellipse by a different geometrical method. And then, at long last, he realized that the two methods produced the same result.
