_Sect._ 1. Researches which verified the Theory. 157 _Sect._ 2. Researches which did not verify the Theory. 159 _Sect._ 3. Methods of Observation of the Greek Astronomers. 161 _Sect._ 4. Period from Hipparchus to Ptolemy. 166 _Sect._ 5. Measures of the Earth. 169 _Sect._ 6. Ptolemy's Discovery of Evection. 170 _Sect._ 7. Conclusion of the History of Greek Astronomy. 175 _Sect._ 8. Arabian Astronomy. 176 BOOK IV. HISTORY OF PHYSICAL SCIENCE IN THE MIDDLE AGES. Introduction. 185 CHAPTER I.--ON THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES. 1. Collections of Opinions. 187 2. Indistinctness of Ideas in Mechanics. 188 3. " " shown in Architecture. 191 4. " " in Astronomy. 192 5. " " shown by Skeptics. 192 6. Neglect of Physical Reasoning in Christendom. 195 7. Question of Antipodes. 195 8. Intellectual Condition of the Religious Orders. 197 9. Popular Opinions. 199 CHAPTER II.--THE COMMENTATORIAL SPIRIT OF THE MIDDLE AGES. 201 1. Natural Bias to Authority. 202 2. Character of Commentators. 204 3. Greek Commentators of Aristotle. 205 {16} 4. Greek Commentators of Plato and Others. 207 5. Arabian Commentators of Aristotle. 208 CHAPTER III.--OF THE MYSTICISM OF THE MIDDLE AGES. 211 1. Neoplatonic Theosophy. 212 2. Mystical Arithmetic. 216 3. Astrology. 218 4. Alchemy. 224 5. Magic. 225 CHAPTER IV.--OF THE DOGMATISM OF THE STATIONARY PERIOD. 1. Origin of the Scholastic Philosophy. 228 2. Scholastic Dogmas. 230 3. Scholastic Physics. 235 4. Authority of Aristotle among the Schoolmen. 236 5. Subjects omitted. Civil Law. Medicine. 238 CHAPTER V.--PROGRESS OF THE ARTS IN THE MIDDLE AGES.