Mathematics, such as appertain to painting, are necessary to the painter, also the absence of companions who are alien to his studies: his brain must be versatile and susceptible to the variety of objects which it encounters, and free from distracting cares. And if in the contemplation and definition of one subject a second subject intervenes,--as happens when the mind is filled with an object,--in such cases he must decide which of the two objects is the more difficult of definition, and pursue that one until he arrives at perfect clearness of definition, and then turn to the definition of the other. And above all things his mind should be like the surface of the mirror, which shows as many colours as there are objects it reflects; and his companions should study in the same manner, and if such cannot be found he should meditate in solitude with himself, and he will not find more profitable company. [Sidenote: Perspective & Mathematics] 57. In the study of natural causes and reasons light affords the greatest pleasure to the student; among the great facts of mathematics the certainty of demonstration most signally elevates the mind of the student. Perspective must therefore be {108} placed at the head of all human study and discipline, in the field of which the radiant line is rendered complex by the methods of demonstration; in it resides the glory of physics as well as of mathematics, and it is adorned with flowers of both these sciences. The laws of those sciences which are capable of extensive analysis I will confine in brief conclusions, and according to the nature of the material I will interweave mathematical demonstrations, at times deducing results from causes, and at times tracing causes by results. I will add to my conclusions some which are not contained in these, but which can be deduced from them, if the Lord, the Supreme Light, illuminates me, so that I may treat of light. [Sidenote: Of the Method of Learning] 58. When you will have thoroughly mastered perspective and have learnt by heart the parts and forms of objects, strive when you go about to observe. Note and consider the circumstances and the actions or men, as they talk, dispute, laugh or fight together, and not only the behaviour of the men themselves, but that of the bystanders who separate them or look on at these things; and make a note of them, in this way, with slight marks in your little note-book. And you should always carry this note-book with you, and it should be of coloured paper, so that what you {109} write may not be rubbed out; but (when it is used up) change the old for a new one, since these things should not be rubbed out, but preserved with great care, because such is the infinity of the forms and circumstances of objects, that the memory is incapable of retaining them; wherefore keep these sketches as your guides and masters. 59.