This chapter discusses how circles appear as ellipses when viewed from different planes using perspective. It explores how varying the observer's position above a circle influences the degree of foreshortening and changes its appearance from a circle to an ellipse. Practical demonstrations illustrate these changes in perspective, emphasizing the difference in diameters as perceived by an observer.
Chapter II
Drawing Natural Circular or Spherical Forms.
A circle can be placed on a horizontal plane, a vertical plane seen from the side, or an oblique plane relative to the observer. In all three scenarios, the circle appears, due to perspective, as an ellipse.
Consider the circle ABCD (plate 4, fig. 1), viewed geometrically, with two diameters AC and BD; these two diameters appear equal because the circle is positioned vertically in relation to you and is seen directly. For you, it forms a geometrical plane without any foreshortening, appearing as a circle. However, if we place the same circle horizontally, such as AÈCA, the diameter AG, being parallel to the observer, won't experience foreshortening, whereas the diameter bd, now a receding line, will be more or less foreshortened based on the observer's height relative to the circle. Thus, there are a longer and shorter diameter, and instead of being seen as a circle, it appears as a flattened or reduced circle, or as we call in perspective, an ellipse.
Demonstration of the Circle viewed in perspective.
Let's assume the eye L (fig. 1) looks at the circle AÈCA, placed horizontally relative to this eye L, the diameter AG will appear foreshortened. Indeed, if two rays are assumed to extend from points A and C to the eye L, this eye will see the diameter AG no larger than Cl or bd (see plate 3, fig. 5). Conversely, the diameter bd appears foreshortened to us, being parallel to the eye or observer L, and will be seen geometrically and in full size by this eye. This circle AÈCA will be seen by the observer L in perspective, as an ellipse; with its two unequal diameters bd and AC.
It is understood that the higher one is above a circle, the more open the ellipse appears, as the receding diameter then undergoes various degrees of foreshortening. The closer this circle is to eye level, the more closed the ellipse seems.
If this same circle is placed horizontally above the observer, the ellipse will be seen below. (Plate 3, fig. 4.)
Translation Notes:
Géométralement: refers to seeing in a strictly geometric way, i.e., without perspective distortion.
Raccourci: foreshortening, a technique used in perspective to represent an object extending back in space.