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It is generally agreed upon that the architect Brunelleschi was the one that discovered the rules for perspective in the early 15th century. I have perused books like "On Painting" by Leon Battista, another early 15th century practitioner of perspective and the terms don't appear there. I am wondering, when did these n-point perspective terms come into use that are so common in perspective books and art classes of the 20th and 21st century?
The oldest reference I find is surprisingly recent, 1878. These specific terms seem to have been assumed specifically by the architectural community in the late 1800s. From the 1878 American Architect and Architecture, vol 3-4:
151 The last paper discussed the phenomena of Parallel Perspective in which of the three sets of lines that define a rectangular object two are parallel to the picture and have their vanishing points accordingly at an infinite distance the third alone has its vanishing point in the plane of the picture This may be called accordingly One Point Perspective since it employs only one vanishing point
152 In the previous papers only one of the principal sets of lines namely the vertical lines were parallel to the picture both sets of horizontal lines being inclined to it at an angle one to the right and one to the left This may accordingly be called Angular Two Point Perspective two vanishing points being employed
We now come to a third case that in which all three of the lines of a rectangular object are inclined to the picture the object presenting towards the eye a solid corner In this case all three vanishing points are employed and the drawing may be said to be made in Oblique or Three Point Perspective Plate VII illustrates this case Figs 24 25 and 26 presenting examples in which though the object is vertical the plane of the picture is inclined while in Fig 27 the picture is vertical as usual but the cubical on the floor the two covers of the box in the foreground and the chair are all tipped so that all their edges are inclined to the picture They are accordingly drawn in Three Point Perspective Fig 24 shows a post at the corner of a fence as it appears or
This terminology is repeated by Ware, 1882, Modern Perspective: A Treatise Upon the Principles and Practice of Plane and Cylindrical Perspective
For in One Point Perspective the vanishing point C being given the station point may be anywhere upon the Axis the line passing through C in a direction perpendicular to the plane of the picture In Two Point Perspective the vanishing points VR and V being given the station point S must be somewhere on the circumference of a semicircle whose diameter lies between those points and which is itself in a horizontal plane perpendicular to the plane of the picture any point in this semicircle will do In Three Point Perspective it must in like manner lie somewhere in the circumference of each of three semicircles whose diameters are the three sides of the triangle formed by the three vanishing points