The text explains the concepts of Geometrical Plane and Perspective Plane. A geometrical plane is seen in its true form without distortion, while a perspective plane appears with foreshortening or distortion based on its orientation to the observer. The explanation includes instructions on how to visualize and experiment with these concepts using simple materials like a square of cardboard.
The Plane called Geometrical
Imagine a plane or flat figure of any shape, such as a piece of cardboard cut into a square. We are using a simple shape here to make the demonstration easier. If you place this plane on a table, in a vertical position, upright, and standing directly facing it, it is certain that you see this plane in its entirety, with all its right angles and equal sides. In short, you see it as it really is and as a geometer would define it in measuring. When a plane is placed to be seen in this entire manner, as it really is, it is said to be seen geometrically. This is what is meant by a Geometrical Plane. So when you have any object to draw from nature, you will first search to see if one of the faces is viewed by you in its entirety, as it truly is, and this face would be a geometric plane in relation to you, the artist or observer.
In general, when a face or one of the planes of an object is vertically positioned in relation to the observer, and parallel to the observer, this plane is seen geometrically. A plane in a horizontal position can also be seen geometrically, but you must be positioned horizontally for this to happen. For example, you might need to be lying down or bent precisely over the plane you are viewing.
The square ABCD (plate 3, fig. 1) is a geometric plane in relation to eye E, as it is evident that the rays projecting angles A, B, C, D, to eye E are equal to each other, and the sides AB, BC, CD, DA, which on the figure are not equal to each other, appear equal to the observer's eye E.
It is extremely easy and equally useful to replicate by a very simple experiment everything that has just been said about the Geometric Plane.
As stated earlier, get a square piece of cardboard and fix it vertically on any surface, like a table; then attach threads to each corner that you take to a point double or triple the length of the square's side from your eye. These threads will represent the visual rays (fig. 3), and they are equal. The sides AB, BC, CD, DA will then be equal. Your piece of square cardboard thus placed is a geometric plane.
The Plane called Perspective
Now imagine that the same square of cardboard is placed flat or horizontally instead of vertically in front of you. It is still the same square, but you will see it quite differently. You will not need much attention to recognize that the sides will no longer appear equal to you. Those further from you will certainly look shorter, which gives rise to the term 'foreshortening'. To judge foreshortening well, it is not only sufficient to see it, but you must think a little about what you see. This is what Perspective is; that is why it is agreed that when a plane presents itself to produce foreshortening, this plane is said to be a Perspective Plane, which means it is no longer seen as it truly is but rather as it appears, according to the rules of Drawing from Nature, which we will present in the following chapters.
Thus, the square ABCD (fig. 2) is this time a perspective plane concerning eye E because this plane is placed in such a way that the rays projecting angles to eye E are not equal among them, with E being smaller than BE and DE smaller than AE. Eye E sees BC not larger than Cf, as the point I covers point B for eye E. Similarly, eye E sees AD not larger than Dn.