On the geometric game.

a - b m c. Drawing 16 portions from this circular ring, its remainder is worth the greatest square that can fit within that ring.

These are worth the 4 greatest portions.

The bird that beats its wings with equal motion, without any beat of the tail, will have straight motion; but if one of the wings dips more than the other, then the straight motion will change into a curved one, and it will wheel around a low point, toward which the lowered wing is directed.

The life of the painter in the countryside. To the painter are necessary the mathematics belonging to painting, and the deprivation of company alien to their studies; and a mind changeable according to the direction of the objects that present themselves before it, and remote from other cares. And if, in the contemplation and definition of one case, a second case interposes itself, as happens when the object stirs the sense, then of such cases one must judge which is of more laborious definition, and follow that one to its final clarity, and then follow the definition of the other. And above all be of a mind equal to the nature of the mirror's surface, which transforms itself into as many various colours as are the colours of its objects. And let his companions have a likeness to him in such studies; and, not finding them, let him keep company with himself in his contemplations, for in the end he will find no more useful company. On colours. Of colours of equal whiteness, that one will show most bright which is on a darker ground, and black will show most dark which is on a ground of greater whiteness. Red will show more fiery which is on a yellower ground, and so will do all the colours surrounded by their directly contrary colours.

On painting in landscapes. If between the eye and the horizon there interposes the slope of a hill declining toward the eye, the eye being about the middle of the height of that slope, then such a hill will acquire darkness in every degree of its length. It is proved by the seventh [proposition] of this [book], which says: that plant will show darker which is seen more from below. Therefore the proposition is verified, because such a hill shows, from the middle downward, all its plants in the parts as much illuminated by the brightness of the sky as the part shaded by the darkness of the earth; for which reason such plants must be of moderate darkness; and from that place toward the roots of the hill such plants keep growing brighter, by the converse of the seventh; and by that seventh, the more such plants approach the summit of the hill, the more they must become darker. But such darkness is not proportional to the distance, by the eighth of this [book], which says: 'that thing will show darker which is found in thinner air'; and by the tenth: 'that will show darker which borders on a brighter ground.'