and sixteenth centuries. His arguments, however, to prove the identity of the least and the greatest (maximum, minimum) in each order of existence, and finally the union of all maxima and minima in the absolute unity of God, may seem a juggling with scantily veiled fallacies.25 But there can be no doubt of the earnestness of his endeavor to think God, and adjust his own existence to that absolute potency and actuality. We cannot really know God, because we must know by connecting the unknown with the known, and the infinite cannot thus be reached through the finite. Therefore since the Greatest, being veritas infinita, cannot be absolutely known by us, we reach it incompraehensibiliter, which is through the way of docta ignorantia. Mathematics also may help us along to our apprehension of the absolute union of opposites. An infinite line is at once triangle, circle, and sphere, and contains actually (actu― here we seem back with Thomas and Aristotle) everything that finite lines are in potentia. Likewise everything that lies in potentia in every least and simplest thing, exists actually in the greatest being: thus opposites disappear. The Greatest exceeds substance and accidents; but is more like substance (as Dionysius says) : i. e. it is supersubstantialis rather than superaccidentalis. Surely this man had not cut loose from scholasticism; nor did he do so in applying his reasonings to the universe of concrete and finite things. Yet for himself he argues (at the opening of the second book of Docta ignorantia) that these must be known through the nature of their prototype and creator, and since that cannot be known (save incompraehensibiliter) we fall back on the method. of docta ignorantia. Cusa's third chapter of Book II proceeds to show how the Greatest embraces or comprehends (complicet) and then evolves (explicet) all things in a way that we may somehow apprehend. The Infinite Unity is the complicatio of all things, holds them all within its unity; but God is also the explicatio or evolution of all things. Everything in him (as complicatio) is himself, and as explicatio he is in all things what they 25 See e. g. the arguments of De dọcta ignorantia, I, 4. are.26 Conversely finite things in their contracted or concrete way have whatever the Greatest has in its greatest way. Only the Absolute Greatest is infinite; the Universe, the world of concrete things is not the Absolute Greatest, which is God. The Universe therefore is not infinite; but neither is it finite, for it has no limit. Since there is nothing absolute and self-existent save God, the Universe is obviously from Him. Through the Universe as a whole the absolute Unity of God transfuses itself into the plurality of created things. Matter, which is the potentiality of the Universe, could not exist without the form in which it shall reach a non-absolute actuality. Nor could that form exist but for the potentiality which is matter. That form is the soul of the world. Matter is predisposed toward it, is impregnated with desire for actualization in it. Reciprocally that form, which is the World-soul, is drawn to its potentiality which is matter, without which it could not be. This desire for each other, this living bond uniting them, is as the Holy Spirit uniting Father and Son: and the Universe of concrete things is the reflex, the explicatio, of the Tri-une God. The microcosm, man, is constituted as the macrocosm. The union between matter and the World-soul is reproduced in the union between the human body and the human soul. The life of man on earth hangs on the mutual drawing together and realization of the two in this union. Cusa was deeply interested in physical speculation, even in observation and experiment; but his thoughts upon natural phenomena always trailed his metaphysics. There was metaphysics, if not mysticism, in his explanation of the movement of bodies. It was affected by his conception of the union of the World-soul with matter, and the relationship of one and both to God. Soul, spirit, is the universal motor. Involved in matter, it im 26 Lib. II, cap. 3 has the title - Quomodo maximum complicet et explicet omnia intellectibiliter. Maximum autem est, cui nihil potest opponi, ubi et minimum est maximum. Unitas igitur infinita est omnium complicatio. Hoc quidem dicitur unitas, quae omnia unit. . . . scias Deum omnium rerum complicationem et explicationem, et, ut est complicatio, omnia in ipso esse ipsum, et, ut est explicatio, ipsum in omnibus esse id quod sunt. Cf. Uebinger, Die Gotteslehre des Nikolaus Cusanus (Munster, 1888). parts ceaseless motion, which thus becomes an attribute of the visible Universe. God is omnipresent in all that is. He moves it all. Matter, impregnate with the World-soul, moves. Through the human soul, the human body moves. All things move; nothing is at rest. The earth is not the center of the Universe (centrum Mundi), neither can it ever lack manifold movement. Although Cusa did not discard the theory of the spheres, the earth is not for him the centre of the sphere of the fixed stars, but moves like the planets. Nor can either sun or moon or earth in its motion describe a true circle, cum non moveantur super fixo.27 Cusa's thoughtful interest did not merely follow the grand lines of physical speculation; it was also turned upon an indefinite number of the problems of physics or mechanics.28 The quite sufficiently original mind of Cusa was also stored with learning. He had read and assimilated so very much and from such diverse sources. He had read, for instance, the famous Lully, and taken from him certain thoughts built round the phrase quodlibet in quolibet, everything in everything; he was filled with Neoplatonism, drawn from Plotinus, from the Hierarchies of Pseudo-Dionysius, and from a certain later Neoplatonic Theologia Aristotelis; he had also borrowed from many others much physical speculation.29 In turn he influenced many and diverse men, among whom probably Leonardo da Vinci, and certainly the restless Bruno a century later. It suggests the continuity between mediaeval thought and that of the fifteenth and sixteenth centuries, to find Leonardo working with ideas which were close to those of Cusa's own fashioning and with others which Cusa had drawn from mediaeval men; or to find Leonardo making use of ideas which he might, or even may, have taken from such a fourteenth century Occamist and physicist as Albertus of Saxonia.30 Appar 27 De doc. ig. II, 11. See Max Jacobi, Das Universum, etc., in den Lehren des Nicolaus von Cusa. (Berlin, 1904.) 28 See generally Duhem's articles in Bulletin Italien. 29 This is shown at length by Duhem, "Nicolas de Cues et Leonardo da Vinci," Bulletin Italien, VII (1907), pp. 87-134; ib. pp. 181-220. 30 See Duhem, Bulletin Italien, VII (1907), pp. 314-329; ib. VIII, pp. ently the thoughts of Cusa and Albertus affected Keppler and even the Copernican theory in general, for which Cusa's reasonings were suited to prepare men's minds." 212 sqq.; 312 sqq., where Leonardo's direct indebtedness to Cusa is asserted positively. 31 Duhem, Bulletin Italien, VIII, pp. 18-55. CHAPTER XXXI LEONARDO DA VINCI THE philosophy of Cusa exemplifies how the mediaeval and antique past furnished much of the thought of even so constructive mind as his. The same will be true of the most original philosophies and physical investigations of the fifteenth and sixteenth centuries. But though that period drew masterfully upon its ancient sources, men had become restive under the authority of the past, and greater numbers than before were turning their thoughts directly to the world of nature. Criticism became more audacious, and novel shapings of opinion more in vogue. If the training of the past made possible these novelties, still the breath of life, which always is of the present, was in the latter. Many ideas drawn probably from the writings of previous men were made good use of in the eminently living and original works of the mind and hands of Leonardo da Vinci, who was twelve years old when Nicholas of Cusa died. Leonardo's personality was complex beyond the verge of mystery. It seems possible to discern the master motives of his nature; but to name the chief among them were perilous; and perilous the attempt to find a unity of effort, of purpose, in his life. Perhaps no single motive unified those energies which pursued a confederacy of intellectual interests, or dispersed themselves through different provinces of investigation. Yet it was one Leonardo who became absorbed in science and in art. He, and not a part of him, was at the same time or successively, artist and engineer, investigator and writer, his faculties co-operating in the accomplishment of what might be a means or an end according to the purpose in his mind. Constantly, in his earlier life at least, he studied nature for the purpose of art, as when he dis |