본 논문은 L.B. 알베르티의 회화론을 중심으로 고전 그리스 광학의 전통과 초기 르네상스 선 원근법 이론 사이의 관계를 고찰한다. 선 원근법의 기술적 측면에 초점을 맞추었던 동시대 이론서들과 달리 알베르티의 논문은 수학적 논리가 지닌 형이상학적 가치를 중요하게 다루었는데, 이러한 성격은 유클리드의 광학으로부터 직접적으로 계승되었다고 할 수 있다. 유클리드가 수학적 정의와 명제들로써 증명했던 시각적 세계는 대상과 이미지 사이의 비례적 관계로 이루어진 추상적 공간이었다. 그리고 이러한 추상적 합리성이야말로 알베르티가 자신의 ‘거리점 작도법’의 궁극적인 가치로 주장했던 바로서, 보는 주체와 보여지는 대상 사이의 기하학적 근거에 따라서 실제 세계의 시각 피라미드와 회화 세계의 시각 피라미드를 합치시키고자 했던 것이다

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term ‘vanishing point’. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of ‘vanishing points’. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.