[I]t does not follow that because heaven moves in a circle that the ea — Saving the appearances

"When Newton wrote his Mathematical Principles of Natural Philosophy and System of the World, he distinguished the phenomena to be saved from the reality he postulated. He distinguished the "absolute magnitudes" that appear in his axioms from their "sensible measures" which are determined experimentally. He discussed carefully the ways in which, "the true motions of particular bodies [may be determined] from the apparent," via the assertion that "the apparent motions... are the differences of true motions."

"In the 1590s... Kepler adopted the ideas of Copernicus. In the heliocentric model... the simultaneous motion of the earth around the sun and about its own axis explained the observed motion of the planets and stars. Kepler set out to prove that this... hypothesis... an attempt to "save the appearances", did... correspond with reality. In doing so, however, he noticed that the circular orbits... proposed by Copernicus were not in keeping with his... observations. ...Kepler wanted... to glorify God, who... was responsible for the harmonious arrangement of the universe... This aim is... in the... first lines of the preface to The Secret of the Cosmos: "It is my intention... to show... that the most great and good Creator, in the creation of this moving universe and the arrangement of the heavens, looked to these five regular solids... so celebrated from the time of Pythagoras and Plato... and that he fitted to the nature of those solids the number of the heavens, their proportions and the law of their motions."

"The statement of Diogenes, that Herakleides attended the Pythagorean schools is of... importance... as it is... likely... their influence (which is also perceptible in his ideas about atoms, which he calls masses...), tended to convince him of the truth of the... simple explanation of the daily motion of the stars proposed by Hiketas and Ekphantus. ... He first alludes to Herakleides when discussing the chapter in which Aristotle considers the motion of the starry vault. Aristotle... remarks that, taking for granted that the earth is at rest, the starry sphere... and the planets might either both be at rest, or both be in motion, or one be at rest and the other in motion. And these cases he considers (says Simplicius) "on account of there being some, among whom were Herakleides of Pontus and Aristarchus, who believed they could save the phenomena (account for the observed facts) by making the heavens and the stars be immovable, but making the earth move round the poles of the equator... from the west, each day one revolution as near as possible; but as near as possible is added on account of the [daily] motion of the sun of one part (degree); so that, if then the earth does not move, which presently he (Aristotle) is going to show, the hypothesis of both being at rest cannot possibly save the phenomena.""

"[I]n Plutarchs book On the face in the disc of the Moon...[o]ne of the persons in the dialogue, being called to account for turning the world upside down, says that he is quite content so long as he is not accused of impiety, "like as Kleanthes held that Aristarchus of Samos ought to be accused of impiety for moving the hearth of the world.., as the man in order to save the phenomena supposed... that the heavens stand still and the earth moves in an oblique circle at the same time as it turns round its axis.""

"[T]he principal reason why the heliocentric idea fell perfectly flat, was the rapid rise of practical astronomy, which had commenced from the time when the Alexandrian Museum became a centre of learning in the Hellenistic world. Aristarchus had no other phenomena to "save" except the stationary points and retrograde motions of the planets as well as their change of brilliancy; he may even have neglected the inequality of the suns apparent motion originally discovered by Euktemon and recognized by Kalippus. But when similar and much more marked inequalities began to be perceived in the motions of the other planets, the hopelessness of trying to account for them by the beautifully simple idea of Aristarchus must have given the deathblow to his system, which thereby even among mathematicians lost its only claim to acceptance, that of being able to "save the phenomena." Most likely, as we have already said, these new inequalities had already more or less dimly commenced to make themselves felt in the days of Apollonius... and in that case we can understand why he did not feel disposed to simplify the system of movable excentrics by gathering the reins of all the unruly planetary steeds into one mighty hand, that of ."

"The first book contains the general description of the universe and the foundations by which he undertakes to save the appearances and the observations of all ages. He adds as much of the doctrine of sines and plane and spherical triangles as he deemed necessary to the work."