[Sidenote: Preparations for the heliocentric doctrine.] Preparations had been silently making for a scientific revolution in various directions. The five memoirs of Cardinal Alliacus "On the Concordance of Astronomy with Theology," show the turn that thought was taking. His "Imago Mundi" was published in 1460, and is said to have been a favourite work with Columbus. In the very Cathedral of Florence, Toscanelli had constructed his celebrated gnomon, 1468, a sun-ray, auspicious omen! being admitted through a plate of brass in the lantern of the cupola. John Muller, better known as Regiomontanus, had published an abridgment of Ptolemy's "Almagest," 1520. Euclid had been printed with diagrams on copper as long before as 1482, and again in Venice twenty-three years subsequently. The Optics of Vitello had been published 1533. Fernel, physician to Henry II. of France, had even ventured so far, supported by Magellan's voyage, as to measure, 1527, the size of the earth, his method being to observe the height of the pole at Paris, then to proceed northward until its elevation was increased exactly one degree, and to ascertain the distance between the stations by the number of revolutions of his carriage wheel. He concluded that it is 24,480 Italian miles round the globe. The last attempt of the kind had been that of the Khalif Almaimon seven hundred years previously on the shore of the Red Sea, and with nearly the same result. The mathematical sciences were undergoing rapid advancement. Rhæticus had published his trigonometrical tables; Cardan, Tartaglia, Scipio Ferreo, and Stefel were greatly improving algebra. [Sidenote: Copernicus, the works of.] The first formal assertion of the heliocentric theory was made in a timid manner, strikingly illustrative of the expected opposition. It was by Copernicus, a Prussian, speaking of the revolutions of the heavenly bodies; the year was about 1536. In his preface, addressed to Pope Paul III., whether written by himself, or, as some have affirmed, for him by Andreas Osiander, he complains of the imperfections of the existing system, states that he has sought among ancient writers for a better way, and so had learned the heliocentric doctrine. "Then I too began to meditate on the motion of the earth, and, though it appeared an absurd opinion, yet since I knew that in previous times others had been allowed the privilege of feigning what circles they chose in order to explain the phenomena, I conceived that I might take the liberty of trying whether, on the supposition of the earth's motion, it was possible to find better explanations than the ancient ones of the revolutions of the celestial orbs."