In two equal parts, by marking point E. Through point E, middle of AB, draw a line to the convergence point V. This line dividing ABCD gives two squares EADF, EFCB. In the latter, draw the diagonal BF, extending it to meet point G on line AV. From point G, drop the perpendicular GI. In square CFH, draw diagonal CH extending to L, from where lower the perpendicular LM; from point L, draw diagonal IS to point N, from which drop NP, and so forth. In this manner, the diminishing of several windows and spaces between them is achieved. In reality, these windows are all the same size, but they appear to diminish because they are on the vanishing side of the house and move away from the observer's eye.

The preceding operation applies to a multitude of objects, such as a row of trees, as represented near the house in fig. 8. After comparing the height of the first tree with that of the house, determine this height by a vertical line, such as line AB, fig. 8. Compare the distance from one tree to another with the height of the first. This distance is marked by a point on which you raise a vertical, like line CD. From the two ends A and B of line AB, representing the first tree, draw lines to the convergence point V. Divide AB into two equal parts at E; draw EV to the convergence point, and find the places of the other trees by means of diagonals, as above. Then compare the height of the tree trunk, from the ground to where the branches start, with the total height. On height AB, representing the first tree, you mark the height of the trunk by a point: from this point, draw a line to the convergence point, which gives you, on the other verticals, the height of each trunk of the trees represented by lines AB, DC, GI, etc.

The operation just demonstrated assumes that trees are well and regularly planted at equal distances from each other, and trimmed so that the branching begins at a uniform height from the ground. It is understood that if there are noticeable deviations, for height or otherwise, when drawing from life, adjustments are made accordingly by deviating more or less from the lines determined by the preceding operation. A colonnade or row of pillars, and even a procession, is drawn in the same way as we have shown. The convergence of columns, pillars, or people walking in long lines is found by the same operation as for trees in avenues. These various objects are equally distant from each other, but appear to come closer as they move away.

Simple experiment to observe that objects seem closer together the further they move from the observer.

We assume here AC, BD (Fig. 10.), the lines of two rows of trees or other objects; Y the observer's eye; CD a pane of glass through which the observer looks, on which he draws what he sees. The two rays CY and HY close to the eye form a larger angle and intersect on line CD a portion larger than rays HY and GY; GY and FY make an even smaller angle, and so on: thus, points 1, 2, 3, 4, 5, etc., representing H, G, F, etc., appear to come together as H, G, F, move away from the eye.

By the same means, it can be assured that the height of objects diminishes to our eye, in proportion to the distance they move away from us. If you calculate, on the glass, the height of a man of five feet, placed ten feet away from you, and that of the same man placed twenty feet away, he appears, the second time, half of what he looked like initially. If two men, one placed ten feet, the other twenty feet from you, appear the same size, it is because the second is twice as tall as the first: he will be ten feet if the first is five.

Translation Notes

• "Vanishing side" refers to perspective technique where objects appear to diminish as they recede into distance.
• "Convergence point" is a concept in perspective drawing where lines appear to converge at a distant point.