by reason, that all science requires mathematics. And the arguments which are used to establish this doctrine, show a most just appreciation of the office of mathematics in science. They are such as follows:-That other sciences use examples taken from mathematics as the most evident :-That mathematical knowledge is, as it were, innate to us, on which point he refers to the well-known dialogue of Plato, as quoted by Cicero:-That this science, being the easiest, offers the best introduction to the more difficult:-That in mathematics, things as known to us are identical with things as known to nature:-That we can here entirely avoid doubt and error, and obtain certainty and truth:-That mathematics is prior to other sciences in nature, because it takes cognizance of quantity, which is apprehended by intuition (intuitu intellectus). Moreover,' he adds," 'there have been found famous men, as Robert, bishop of Lincoln, and Brother Adam Marshman (de Marisco), and many others, who by the power of mathematics have been able to explain the causes of things; as may be seen in the writings of these men, for instance, concerning the Rainbow and Comets, and the generation of heat, and climates, and the celestial bodies.' "But undoubtedly the most remarkable portion of the Opus Majus is the Sixth and last Part, which is entitled 'De Scientia experimentali.' It is indeed an extraordinary circumstance to find a writer of the thirteenth century, not only recognizing experiment as one source of knowledge, but urging its claims as something far more important than men had yet been aware of, exemplifying its value by striking and just examples, and speaking of its authority with a dignity of diction which sounds like a foremurmur of the Baconian sentences uttered nearly four hundred years later. Yet this is the character of what we here find. Experimental science, the sole mistress of speculative sciences, has three great Prerogatives among other parts of knowledge: First she tests by experiment the noblest conclusions of all other sciences: Next she discovers respecting the notions which other sciences deal with, magnificent truths to which these sciences of themselves can by no means attain: her Third dignity is, that she by her own power and without respect of other sciences, investigates the secrets of nature.' 17 Op. Maj. p. 64. 18 "Veritates magnificas in terminis aliarum scientiarum in quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum domina speculativarum, potest dare."Op. Maj. p. 465. "The examples which Bacon gives of these 'Prerogatives' are very curious, exhibiting, among some error and credulity, sound and clear views. His leading example of the First Prerogative is the Rainbow, of which the cause, as given by Aristotle, is tested by reference to experiment with a skill which is, even to us now, truly admirable. The examples of the Second Prerogative are three :-first, the art of making an artificial sphere which shall move with the heavens by natural influences, which Bacon trusts may be done, though astronomy herself cannot do it-'et tunc,' he says, 'thesaurum unius regis valeret hoc instrumentum ;'-secondly, the art of prolonging life, which experiment may teach, though medicine has no means of securing it except by regimen ;19-thirdly, the art of making gold finer than fine gold, which goes beyond the power of alchemy. The Third Prerogative of experimental science, arts independent of the received sciences, is exemplified in many curious examples, many of them whimsical traditions. Thus it is said that the character of a people may be altered by altering the air. Alexander, it seems, applied to Aristotle to know whether he should exterminate certain nations which he had discovered, as being irreclaimably barbarous; to which the philosopher replied, ‘If you can alter their air, permit them to live; if not, put them to death.' In this part, we find the suggestion that the fire-works made by children, of saltpetre, might lead to the invention of a formidable military weapon. "It could not be expected that Roger Bacon, at a time when experimental science hardly existed, could give any precepts for the discovery of truth by experiment. But nothing can be a better example of the method of such investigation, than his inquiry concerning the cause of the Rainbow. Neither Aristotle, nor Avicenna, nor Seneca, he says, have given us any clear knowledge of this matter, but experimental science can do so. Let the experimenter (experimentator) consider the cases in which he finds the same colors, as the hexagonal crystals from Ireland and India; by looking into these he will see colors like those of the rainbow. Many think that this arises from some 19 One of the ingredients of a preparation here mentioned, is the flesh of a dragon, which, it appears, is used as food by the Ethiopians. The mode of preparing this food cannot fail to amuse the reader. "Where there are good flying dragons, by the art which they possess, they draw them out of their dens, and have bridles and saddles in readiness, and they ride upon them, and make them bound about in the air in a violent manner, that the hardness and toughness of the flesh may be reduced, as boars are hunted and bulls are baited before they are killed for eating."-Op. Maj. p. 470. 20 Op. Maj. p. 473. special virtue of these stones and their hexagonal figure; let therefore the experimenter go on, and he will find the same in other transparent stones, in dark ones as well as in light-colored. He will find the same effect also in other forms than the hexagon, if they be furrowed in the surface, as the Irish crystals are. Let him consider too, that he sees the same colors in the drops which are dashed from oars in the sunshine; and in the spray thrown by a mill-wheel;-and in the dewdrops which lie on the grass in a meadow on a summer morning;and if a man takes water in his mouth and projects it on one side into a sunbeam; and if in an oil lamp hanging in the air, the rays fall in certain positions upon the surface of the oil;-and in many other ways, are colors produced. We have here a collection of instances, which are almost all examples of the same kind as the phenomena under consideration; and by the help of a principle collected by induction from these facts, the colors of the rainbow were afterwards really explained. "With regard to the form and other circumstances of the bow he is still more precise. He bids us measure the height of the bow and of the sun, to show that the centre of the bow is exactly opposite to the sun. He explains the circular form of the bow,-its being independent of the form of the cloud, its moving when we move, its flying when we follow, by its consisting of the reflections from a vast number of minute drops. He does not, indeed, trace the course of the rays through the drop, or account for the precise magnitude which the bow assumes; but he approaches to the verge of this part of the explanation; and must be considered as having given a most happy example of experimental inquiry into nature, at a time when such examples were exceedingly scanty. In this respect, he was more fortunate than Francis Bacon, as we shall hereafter see. "We know but little of the biography of Roger Bacon, but we have every reason to believe that his influence upon his age was not great. He was suspected of magic, and is said to have been put into close confinement in consequence of this charge. In his work he speaks of Astrology, as a science well worth cultivating. But,' says he, 'Theologians and Decretists, not being learned in such matters, and seeing that evil as well as good may be done, neglect and abhor such things, and reckon them among Magic Arts.' We have already seen, that at the very time when Bacon was thus raising his voice against the habit of blindly following authority, and seeking for all science in Aristotle, Thomas Aquinas was employed in fashioning Aristotle's tenets into that fixed form in which they became the great impediment to the progress of knowledge. It would seem, indeed, that something of a struggle between the progressive and stationary powers of the human mind was going on at this time. Bacon himself says," 'Never was there so great an appearance of wisdom, nor so much exercise of study in so many Faculties, in so many regions, as for this last forty years. Doctors are dispersed everywhere, in every castle, in every burgh, and especially by the students of two Orders (he means the Franciscans and Dominicans, who were almost the only religious orders that distinguished themselves by an application to study)," which has not happened except for about forty years. And yet there was never so much ignorance, so much error.' And in the part of his work which refers to Mathematics, he says of that study," that it is the door and the key of the sciences; and that the neglect of it for thirty or forty years has entirely ruined the studies of the Latins. According to these statements, some change, disastrous to the fortunes of science, must have taken place about 1230, soon after the foundation of the Dominican and Franciscan Orders.24 Nor can we doubt that the adoption of the Aristotelian philosophy by these two Orders, in the form in which the Angelical Doctor had systematized it, was one of the events which most tended to defer, for three centuries, the reform which Roger Bacon urged as a matter of crying necessity in his own time." It is worthy of remark that in the Opus Majus of Roger Bacon, as afterwards in the Novum Organon of Francis Bacon, we have certain features of experimental research pointed out conspicuously as Prarogativa: although in the former, this term is employed to designate the superiority of experimental science in general to the science of the schools; in the latter work, the term is applied to certain classes of experiments as superior to others. 21 Quoted by Jebb, Pref. to Op. Maj. 22 Mosheim, Hist. iii. 161. 24 Mosheim, iii. 161. I Nicolas of Cus. WILL quote the passage, in the writings of this author, which bears upon the subject in question. I translate it from the edition. of his book De Docta Ignorantia, from his works published at Basil in 1565. He praises Learned Ignorance-that is, Acknowledged Ignorance—as the source of knowledge. His ground for asserting the motions of the earth is, that there is no such thing as perfect rest, or an exact centre, or a perfect circle, nor perfect uniformity of motion. "Neque verus circulus dabilis est, quinetiam verior dari possit, neque unquam uno tempore sicut alio æqualiter præcisè, aut movetur, aut circulum veri similem, æqualem describit, etiamsi nobis hoc non appareat. Et ubicumque quis fuerit, se in centro esse credit." (Lib. i. сар. xi. P, 39.) He adds, "The Ancients did not attain to this knowledge, because they were wanting in Learned Ignorance. Now it is manifest to us that the Earth is truly in motion, although this do not appear to us; since we do not apprehend motion except by comparison with something fixed. For if any one were in a boat in the middle of a river, ignorant that the water was flowing, and not seeing the banks, how could he apprehend that the boat was moving? And thus since every one, whether he be in the Earth, or in the Sun, or in any other star, thinks that he is in an immovable centre, and that every thing else is moving; he would assign different poles for himself, others as being in the Sun, others in the Earth, and others in the Moon, and so of the rest. Whence the machine of the world is as if it had its centre everywhere and its circumference nowhere." This train of thought |