The Ptolemaic system is, therefore, essentially a geocentric system.  It left the earth in her position of superiority, and hence gave no cause of umbrage to religious opinions, Christian or Mohammedan.  The immense reputation of its author, the signal ability of his great work on the mechanism of the heavens, sustained it for almost fourteen hundred years—­that is, from the second to the sixteenth century.

In Christendom, the greater part of this long period was consumed in disputes respecting the nature of God, and in struggles for ecclesiastical power.  The authority of the Fathers, and the prevailing belief that the Scriptures contain the sum, of all knowledge, discouraged any investigation of Nature.  If by chance a passing interest was taken in some astronomical question, it was at once settled by a reference to such authorities as the writings of Augustine or Lactantius, not by an appeal to the phenomena of the heavens.  So great was the preference given to sacred over profane learning that Christianity had been in existence fifteen hundred years, and had not produced a single astronomer.

The Mohammedan nations did much better.  Their cultivation of science dates from the capture of Alexandria, A.D. 638.  This was only six years after the death of the Prophet.  In less than two centuries they had not only become acquainted with, but correctly appreciated, the Greek scientific writers.  As we have already mentioned, by his treaty with Michael iii., the khalif Al-Mamun had obtained a copy of the “Syntaxis” of Ptolemy.  He had it forthwith translated into Arabic.  It became at once the great authority of Saracen astronomy.  From this basis the Saracens had advanced to the solution of some of the most important scientific problems.  They had ascertained the dimensions of the earth; they had registered or catalogued all the stars visible in their heavens, giving to those of the larger magnitudes the names they still bear on our maps and globes; they determined the true length of the year, discovered astronomical refraction, invented the pendulum-clock, improved the photometry of the stars, ascertained the curvilinear path of a ray of light through the air, explained the phenomena of the horizontal sun and moon, and why we see those bodies before they have risen and after they have set; measured the height of the atmosphere, determining it to be fifty-eight miles; given the true theory of the twilight, and of the twinkling of the stars.  They had built the first observatory in Europe.  So accurate were they in their observations, that the ablest modern mathematicians have made use of their results.  Thus Laplace, in his “Systeme du Monde,” adduces the observations of Al-Batagni as affording incontestable proof of the diminution of the eccentricity of the earth’s orbit.  He uses those of Ibn-Junis in his discussion of the obliquity of the ecliptic, and also in the case of the problems of the greater inequalities of Jupiter and Saturn.