(_α_) The _first_ of these of importance is the _linear perspective._ This is introduced as necessary, because painting has only the superficies at its disposal and no longer, as was the case with the bas-relief of antique sculpture, can extend its figures side by side on one and the same plane, but has to proceed to a mode of presentation, which finds it necessary to make the remoteness of its objects in all their spatial dimensions merely appear as such to our senses. For the art of painting has to unfold the content it selects, to place the same in its various movement before our eyes, and to associate in different ways its figures with the landscape of external Nature, its buildings and so forth, in a wholly distinct grade of literalness to that which sculpture in the relief is able to secure. And that which painting in this respect cannot place before us in its actual degree of remoteness in the realistic manner of sculpture it must present under the illusion of reality. What we have first to notice here consists in this that the _single_ surface which confronts painting is divided into distinct planes, apparently remote from one another, and by this means the contrasts of a near foreground and a remote background are secured, which furthermore are linked together by means of a middle distance. Inasmuch as the objects are, the more distant they are from the vision, proportionately reduced in size, and this deduction follows in Nature itself optical laws capable of mathematical determination, the art of painting, too, has on its part to follow the same rules, which, by virtue of the fact that objects are set forth on one surface, are applicable here in a particular way. And this is the rational ground of the so-called linear or mathematical perspective in the art of painting, whose more detailed exposition, however, it is not our business here to discuss.