§ 56. =The East.= The formation of an astronomical school at the court of the Caliphs: revival of astrology: translations from the Greek by _Honein ben Ishak_, _Ishak ben Honein_, _Tabit ben Korra_, and others 76 §§ 57-8. The Bagdad observatory. Measurement of the earth. Corrections of the astronomical data of the Greeks: _trepidation_ 78 § 59. _Albategnius_: discovery of the motion of the sun’s apogee 79 § 60. _Abul Wafa_: supposed discovery of the _variation_ of the moon. _Ibn Yunos_: the _Hakemite Tables_ 79 § 61. Development of astronomy in the Mahometan dominions in Morocco and Spain: _Arzachel_: the _Toletan Tables_ 80 § 62. _Nassir Eddin_ and his school: _Ilkhanic Tables_: more accurate value of precession 81 § 63. Tartar astronomy: _Ulugh Begh_: his star catalogue 82 § 64. Estimate of oriental astronomy of this period: Arabic numerals: survivals of Arabic names of stars and astronomical terms: _nadir_ 82 § 65. =The West.= General stagnation after the fall of the Roman Empire: _Bede_. Revival of learning at the court of Charlemagne: _Alcuin_ 83 § 66. Influence of Mahometan learning: _Gerbert_: translations from the Arabic: _Plato of Tivoli_, _Athelard of Bath_, _Gherardo of Cremona_. _Alfonso X._ and his school: the _Alfonsine Tables_ and the _Libros del Saber_ 84 § 67. The schoolmen of the thirteenth century, _Albertus Magnus_, _Cecco d’Ascoli_, _Roger Bacon_. _Sacrobosco’s Sphaera Mundi_ 85 § 68. _Purbach_ and _Regiomontanus_: influence of the original Greek authors: the Nürnberg school: _Walther_: employment of printing: conflict between the views of Aristotle and of Ptolemy: the celestial spheres of the Middle Ages: the _firmament_ and the _primum mobile_ 86 § 69. _Lionardo da Vinci_: _earthshine_. _Fracastor_ and _Apian_: observations of comets. _Nonius._ _Fernel’s_ measurement of the earth 90 CHAPTER IV. COPPERNICUS (FROM 1473 A.D. TO 1543 A.D.), §§ 70-92 92-124 § 70. The Revival of Learning 92 §§ 71-4. Life of _Coppernicus_: growth of his ideas: publication of the _Commentariolus_: _Rheticus_ and the _Prima Narratio_: publication of the _De Revolutionibus_ 93 § 75. The central idea in the work of Coppernicus: relation to earlier writers 99