Indeed they do not appear even to have had sufficient confidence in the real truth of the astronomical theories which they had adopted from the Greeks, always to correct and extend those where their observations showed that they required correction and extension. Sometimes they did this, but not generally enough. When Arzachel found by observation the Apogee of the Sun to be situated too far back, he ventured to correct Ptolemy's statement of its motion. But when Aboul-Wefa had really discovered the _Variation_ of the Moon's motion, he did not express it by means of an epicycle. If he had done so, he would have made it unnecessary for Tycho Brahe at a later period to make the same discovery. The moral of this incident is the same moral which we have perpetually to note as taught us at every step by the history of Science:--namely, the necessity of constant, careful and exact observation of Facts; and the advantage of devising a Theory, (even if it have to be afterwards rejected,) by which the Facts shall be bound together into a coherent whole. FOOTNOTES: [Footnote 45: _Hist. Ind. Sc._ b. iii. c. iv. sect. 8.] [Footnote 46: _Ibid._ b. ix. c. ii.] [Footnote 47: See _Hist. Ind. Sc._ b. iv. c. i.] CHAPTER IX. THE SCHOOLMEN OF THE MIDDLE AGES. In the _History of the Sciences_ I have devoted a Book to the state of Science in the middle ages, and have endeavoured to analyse the intellectual defects of that period. Among the characteristic features of the human mind during those times, I have noticed Indistinctness of Ideas, a Commentatorial Spirit, Mysticism, and Dogmatism. The account there given of this portion of the history of man belongs, in reality, rather to the History of Ideas than to the History of Progressive Science. For, as we have there remarked, theoretical Science was, during the period of which we speak, almost entirely stationary; and the investigation of the causes of such a state of things may be considered as a part of that review in which we are now engaged, of the vicissitudes of man's acquaintance with the methods of discovery. But when we offered to the world a history of science, to leave so large a chasm unexplained, would have made the series of events seem defective and broken; and the survey of the Middle Ages was therefore inserted. I would beg to refer to that portion of the former work the reader who wishes for information in addition to what is here given.