p. 49: The essential term is the Italian virtù, which Leon Battista Alberti used in the fifteenth century for "those excelling gifts which God gave to the soul of man, greatest and preeminent above all other earthly animals." A man of virtù in Renaissance Italian, coming from the Latin virtus meaning power or capability, was a man with active intellectual power to command any situation, to do as he intended, like an architect producing a building according to his design; by contrast with someone at the mercy of fortuna, of chance or luck, of the accidents of fortuitous circumstance, unforeseen and hence out of control.

The conception of the man of virtù, the virtuoso aiming at reasoned and examined control alike of his own thoughts, intentions, and actions and also of his surroundings, points to the essence of the moral and intellectual commitments by which the Western scientific movement was generated. The conception of virtù embodied a program for relating man to the world as perceiver and knower and agent in the context of his integral moral, social, and cosmological existence. The program presupposed the stability of nature and mankind and of their relations; it entailed a commitment to an examined life of reasoned consistency in intellectual, practical, and moral life alike and it generated a common style in the mastery of self, or nature and of mankind alike by the rational anticipation of effects....

p. 57: Matching this rather with practical art than with natural philosophy in view, a contemporary asked Alberti "in what class of learned men" to put him. He answered: "Among the natural scientists [physici]....Certainly...he was born to investigate the secrets of nature. And what kind of mathematics does he not know? Geometer, arithmetician, astronomer, musician, he wrote marvellously better than anyone for many centuries on perspective.... He wrote on painting, on sculpture...and he not only wrote but also made with his own hands." Alberti explained in 1435: "In writing about painting...we will, to make our discourse clearer, first take from mathematicians those things which seem relevant to the subject. When we have learned thise, we will go on, to the best of our ability, to explain the art of painting form the basic principles of nature...We will now go on to instruct the painter how he can represent with his hand what he has conceived with his mind." Alberti exemplified in his account of the painter the active self-conscious man of virtù, the rational artist who made himself effective by means of knowledge, technique, and continual practice.... /p.58: He looked everywhere also for the issue of theory in practice and thereby its confirmation by observation. Thus moral like scientific virtù was to be cultivated by reasoned analysis of personal and contemporary experience, and by discourse with other men both present and past who recorded the experience and reflections of mankind. The ultimate aim of man in his natural life on this Earth was to cultivate himself by reason, technique, and letters as a well-composed and controlled work of art. This was an Aristotelian humanist ideal viewed perhaps with skepticism by some contemporaries engaged more roughly with the real world, but its principle of reasoned control in an examined life had long been made part of traditional Christian moral theory. For Alberti it was the basis of both the personal and the social responsibility that all huma activities and works entailed. Hence the necessity both for education and for that continual effort of practice in virtù, which alone could restrain the hazards of "unjust and malevolent fortuna". God had endowed man with an inborn virtù, and this it was our duty to cultivate both for our own sakes and by our work "so that times past and those present will be of service to those that have not yet come...." "Our first and proper use is to exert the power of our soul towards virtù," for: "To man alone among mortals is it given to investigate the causes of things, to examine how true are his thoughts and how good are his actions." At the same time he must live responsibly for the benefit of others, above all for "justice and truth."

All the practical arts proceeded then from a rational analysis of the subject matter and objectives of the art to their achievement in an appropriate representation or manipulation or use of the products of the analysis. Practical art like natural science became at once both highly intellectualized and precisely controlled. This was the intellectual bond uniting Alberti with his contemporaries, Nicolas of Cusa , Paolo dal Pozzo Toscanelli, Georg Peurbach, and Piero della Francesca, in their common search for a quantified geometrical space and techniques for its measurement in astronomy and cartography, optics and painting alike; and again later uniting Leonardo da Vinci and Albrecht Dürer, and likewise the musicians Franchino Gaffurino, Lodovico Fogliano, and their successors in their search for an arithmetically quantified music that accomodated the requirements /p. 59: of the human ear. When Dürer wrote that "a good painter is inwardly full of figures," which pour forth "from the inner ideas of which Plato writes," he was presenting the aesthetic theory of an artist with both philosophical education and technical knowledge of practical mathematics. The program became a commonplace. Thus Giorgio Valla: "the artist reasons when he wants something for himself, fashions and forms it inwardly, and accordingly makes an image for himself of everything that is to be portrayed." Marsilio Ficino "What is a work of art? The mind of the artist in matter separate from it. What is a work of nature? The mind of nature in matter united with it...And what is remarkable, human arts construct by themselves whatever nature herself constructs, as if we were not slaves of nature but rivals." But "not just anybody can discern by what principle and in what way the work of a clever artist, artistically constructed, is put together, but only he who has the same power of artistic genius [artis ingenium]....And he who discerns on account of similarity of genius could certainly construct the same things when he had recognized them, provided materials were no lacking." Since therefore man had seen and measured the order of the heavens, "who will deny that he has a genius (so to speak) almost the same as that of the Creator of the heavens and that he could in a certain way make the heavens if he obtained the instruments and celestial matter; since he makes them now, though of other matter, yet very similar in arrangement." Leonardo da Vinci: "Astronomy and the other sciences proceed by means of manual operations, but first they are mental as is painting, which is first in the mind of him who theorizes on it, but painting cannot achieve its perfection without manual operation." But "although nature starts from the reason and finishes as experience, for it is necessary to proceed the other way round, that is starting... from experience and with that to investigate the reason." "There is no effect in nature without reason: understand the reason and you do not need experiment." "Oh speculator on things, I do not praise you for knowing the things that nature through her order naturally brings about ordinarily by herself; but, I say, rejoice in knowing the end of those things which are designed by your own mind."