One of the main features of Piero's art was his accurate knowledge of perspective. He was, above all, a mathematician, well versed in arithmetic and geometry, and the author of several treatises on the science. He rejoiced in complicated problems of perspective, in long vistas of columns stretching away into the far distance, in mysterious hollows, in exquisite alcoves, curves, and embrasures, in the perfectly accurate drawing of roofs and rooms, and in the grouping of his figures in such geometric array and such careful receding proportion as made clear the charm that such mathematical arrangements had over the mind of the artist. There are, however, other characteristics of Piero's work, that must be carefully noted in making a survey of his style. There is a wonderful gravity and solemnity about his figures, a preoccupied look in most of their faces, and we trace also the very beginning of that power already mentioned, of linking figure to figure and group to group. Certainly, in the long processions that form so essential a part of the frescoes at San Francesco in Arezzo, there is a certain connection running through the group of figures which are arranged in processional order especially in the "Visit of the Queen of Sheba," the "Invention of the Cross," and the "Exaltation of the Cross," but individually the figures composing these groups are separate and distinct from one another, engaged in their own concerns and holding no converse one with the other. In these respects it was left for the later men, beginning with Perugino, to pull the picture together and make it one harmonious whole. When to this aloofness, this curious want of sympathy between the central group or scene in the picture and all the attendant groups or figures, we add a severe absence of emotion, an impassiveness in the faces of all the figures, together with a simple dignity of style and a power of delineation that is very attractive, we begin to understand Piero della Francesca. He never considered whether the faces of his figures were specially suited to the group in which he used them. He is quite unmoved by any ideas that the spectator may have as to fitness in the picture, and he never reveals his own views as to the scene and its appropriate presentation. Rage, pity, scorn, amazement, jealousy, passion, or even the depth of devotion, are no part of Piero's repertoire, but a quiet self-contained hauteur, a learned solemnity, and a religious calm characterise his figures, both men and women. There is abundance of dignity, stately form, earnest but impassive determination, but, even in the battle scenes, nothing of the _Sturm und Drang_ which would have been expected.