As it is comprehensively stated in Encyclopaedia Britannica, the “Linear perspective is a system of creating an illusion of depth on a flat surface. All parallel lines (orthogonals) in a painting or drawing using this system converge in a single vanishing point” on the composition`s horizon line”. It is believed that the concept of linear perspective was known by architects of Greek and Roman periods but no written records exist from that time. However it is clear the linear perspective concept was discussed around the 5th centre BCE by the painter Agatharcus of Athensas and others as a part of subject – skenographia in theatrical sets. For the first time the concept was formally described as implemented in 1415 by Italian Renaissance architect Fillipo Brunelleschi and later by another architect and writer Leon Batista Alberti in 1435. Leonard Da Vinci and Albrecht Durer obviously mastered the concept as well. At this point it is worth to mention the linear perspective had not been applied in earlier periods of art such as for example in Egyptian and Byzantine art where drawings and paintings are often shown in a profile on a two dimensional surface while applying of the linear perspective is a technique which transforms the painted reality into realistic three dimensional objects. Since 14th century of early Renaissance the concept of Linear Perspective have been evolving through time. Many artists and architects of Florentine Renaissance took ideas of Fillipo Brunelleschi further into fresco paintings such as “Holy Trinity” by Masaccio and to further scientific details by Leon Batista Alberti and Lorenzo Ghiberti. The principles of Linear Perspective were further explored during the High Renaissance by Raphael and the concept had become a part of a core curriculum in art schools and fine art academies in Europe. The Linear perspective evolved further in 18th century onwards in cityscapes and Cubism which emerged in late 1900. The most powerful and spectacular features and advances of this technique have come during the 20th century with computers.
The concept of “linear perspective” (LP) consists of 3 key points: parallel lines – “orthogonals”, the horizon line and a vanishing point. The place were orthogonals meet is called the “vanishing point”. Since the concept of LP was discovered and formalised it was considered as revolutionary because it was a tool to create an illusion of depth and distance from a single view point in painting /drawing.
Types of Linear Perspective:
1) One Point Perspective contains a one vanishing point along the horizon line. This type of LP is usually used for drawing/painting all sorts of railroads, hallways or room interiors.
Gustave Caillebotte, “Le Pont de l`Europe”, 1876, image via pininterest.com

2) Two Point Perspective, also refereed to as three quarter perspective or angular perspective contains two vanishing points on the horizon line. This technique is usually applying in city/town scapes drawings/paintings, for example to show a corner of the street.
Gustave Caillebotte, “Paris Street, Rainy day” (1877); image via pininterest.com

3) Atmospheric perspective or Aerial Perspective is also a technique of creating an illusion of depth on a two dimensional surface but instead of using horizon lines and vanishing points it primarily uses colours. This effect was first noted by Leonardo da Vinci who observed the fact that colours “… became weaker in proportion to their distance from the person who is looking at them”. It can by said in other words – objects that are further away have blurry edges and appear in a lighter colour.
J.M.W. Turner,” Rain.Steam and Speed”, (1844); image via pininterest.com

Who broke the rules of classical Linear Perspective?
Cubism. Since the Renaissance in the 15th century European Art appreciated an illusion of three dimensional space achieved with applying a LP and Tonal Gradation technique. However such artists as Georges Braque and Pablo Picasso at some stage around 1907-1908 invented a totally new style of painting – cubism. Cubism aims to show a viewer an object as it really is but not just as it looks like.Cubism uses a flat geometric shapes to represent the different sides and angles of the object. Basically, cubism breaks down the object into geometric shapes. Cubists insist that the painting should not pretend to as it is a “window” onto reality but it should be as it is – a flat surface and should behave like one.
Georges Braque, “Glass on Table”, 1909-1910, image via Tate.org.uk;

Paul Cézanne.
Paul Cézanne, a French artist and Post Impressionist painter (1839-1906), had his own theory about how objects in artworks can be painted/drawn: he insisted that painting was not just bringing on canvas the visual experience but also a “sensational” experience. He believed that painting should be reduced to “seeing” things but it had to be sensationally inclusive to a whole experience any artist had observing them. His words about some of his objects in his artworks explain his artistic approach: “… I paint as I see, as I perceive”, “Look, that tree trunk: between us and it there is a space, an atmosphere,I grant you that. But then again it is this palpable, resistant trunk, this body ….. See like someone who just been born!”. I should include here the abstract from the article of Paul Smith about Cezanne`s understanding of painting the perspective in Art Bulletin:
”The Perspective “distortions” commonly observed in Cézanne`s paintings can be seen as the expression of “blind” visuomotor experiences as well as conscious visual perceptions. They thus correspond not to actual movements but to “virtual” movements internal to acts of perception of a kind described by Merleau-Ponty which allow the perceiving subject a fuller sense of the physicality of things. Cézanne conveyed this form of engagement with things, alongside the appearances they present, buy using varieties of parallel projection, often in disguise. His repudiation of perspective implies a repudiation of spectacle as the normative form of visual experience in modern life.”
To illustrate unique approach and mastery of this artist I put the following of his paintings with art experts comments.
Paul Cézanne, “Still Life with Apples and a Pot of Primroses”, (1890), oil on canvas; image via metmuseum.org

This painting above, according to James Voorhies, Department of European Paintings, the Metropolitan Museum of Arts, is: “… a mature work from about 1890, reveals Cezanne`s artistic evolution and mastery of his style building forms completely from colour and creating scenes with distorted perspectival space. The objects in this painting, such as the fruit and tablecloth, are rendered without use of light or shadow, but through extremely subtle gradations of colour.”
Paul Cézanne, “Dish of Apples”, (1876-1877); image via metmuseum.org;

In the artwork above and in his landscapes as James Voorhier says in his article: “Cézanne ignores the laws of classical perspective, allowing each object to be independent within the space of a picture while the relationship of one object to another takes precedence over traditional single point perspective”. In the landscape “Gardanne” he painted the landscape with intense volumetric patterns of geometric rhythms most pronounced in the houses. This pictures anticipates the Cubism of Georges Braque (1882-1963) and Pablo Picasso (1881-1973)”.
In the landscapes below Paul Cézanne used an organised system of layers to construct a series of horizontal planes, which build dimension and draw viewer into the landscape.
Paul Cézanne, “Mont Saint-Victoire and the Viaduct of the Arc River Valéry”,(1882-1885), oil on canvas; image via metmuseum.org;

Paul Cézanne, “The Gulf of Marseille Seen from L`Estaque”,oil on canvas, (1880-1885); image via metmuseum.org;

Paul Cézanne, “Gardanne”, oil on canvas, (1885-1886); image via metmuseum.org

Reference list:
1) “Linear Perspective” by Naomi Blumberg, art/Britannica, britannica.com;
2) “Linear Perspective” by Aleid, 1st of July 2016 on Head for Art, art for the everyday on headforart.com;
3) “Understanding a Linear Perspective in Art”, last updated on 08.07.2019 on invaluable.com;
4) “Linear Perspective in Renaissance Art: Definition and Examples Works”, chapter 2, lesson 9; on study.com;
5) “Linear Perspective in Painting”, Drawing/Painting Technique: Definition, Types and History on visual -arts-cork.com;
6) “All about Cubism. Discover the radical 20th Century Art movement…” on Tate.org.com;
7) “Cezanne`s “Primitive perspective”, or the View from Everywhere”, Paul Smith, the Art Bulletin; March 2013on jstor.org;
8) “Paul Cezanne” by James Voorhies, the Metropolitan Museum of Art, October 2004, metmuseum.org;
