Key People

RENAISSANCE, linear, or so-called one-point perspective is a geometrical construction method devised about 1415 by Italian Renaissance architect Filippo Brunelleschi [1377-1446] and documented in Della Pittura by architect Leon Battista Alberti [1404-1472] in 1435. The discovery of this form of linear perspective was an epochal moment in the Western artistic and scientific tradition(s). 

In subsequent times up to the present day, Renaissance perspective has been a key component of modern visual theory, spatial observation/representation methods, and related instruments/systems; thus, it has been a driver of fundamental progress across diverse subject areas.  But many other types/forms of perspective have been studied/developed, as with Piero della Francesca [1415-1492] and Leonardo da Vinci who were pioneers who had already experimented with various kinds of visual, linear, anamorphic, and even curvilinear perspective. 

In the 16th century, Nürnberg goldsmiths and jewellers depicted regular and semi-regular shapes in linear perspective as the method spread across Germany.  In the 18th century, linear perspective was increasingly applied to gardens and vast spaces, or space stretching out to a distant horizon.  Descriptive geometry claimed to provide universal principles for representation, leading to the idea that representation and human vision must align. 

Since the early 19th century, interest has shifted from geometrical representation to recording visual space, stimulating the exploration of alternative picture planes in perspective views.

Early Pioneers

In the following sections, we explore the innovations of pioneering perspectivists.

Abraham Bosse (1604-1676)

Abraham Bosse (1604–1676) was a French artist and theorist who was a leading figure in the development of perspective during the Baroque period. He was a strong advocate of the perspectival techniques of Girard Desargues, a mathematician. 

Treatise 

  • Traité des Pratiques Geometrales et Perspectives (1665): A treatise on perspective and mechanical drawing that was taught at the Royal Academy of Painting and Sculpture. 
  • Moyen universel de pratiquer la perspective sur les tableaux ou surfaces irrégulières (1653: A treatise on how to reproduce perspective on irregular surfaces, such as architectural walls. 

Drawings 

  • Les Perspecteurs: (1648) Drawings that illustrate perspective science. 
  • The Ages of Man: (1636) An engraving that is part of Bosse’s printmaking. 
  • The Marriage of Ladislas IV: (1645) Part of Bosse’s printmaking work. 

Albrecht Dürer (1471-1528)

Albrecht Dürer (1471 – 1528), was a German painter, printmaker, and theorist of the German Renaissance. Dürer’s vast body of work includes engravings, altarpieces, portraits and self- portraits, watercolours and books, which together secured his reputation as one of the most important figures of the Renaissance period. This is reinforced by his theoretical treatises, which involve principles of mathematics for linear perspective and body proportions. 

In 1525 Albrecht Dürer, in his illustration Man Drawing a Lute, shows an artist using a perspective machine to create a drawing. The machine consists of a wooden frame with a taut string running through it, representing the viewer’s line of sight. 

Aristotle (384-322 BC)

Aristotle (384–322 BC) was a Ancient Greek philosopher whose theory of definition outlines criteria for accuracy in definitions. Aristotle’s definition theory, found in Topics, Posterior Analytics, and Metaphysics, describes a subject’s essence through its genus and differentia. A proper definition is the essential starting point of scientific knowledge, identifying essence rather than just a name. 

Brooke Taylor (1695 – 1731)

In Taylor’s 1715 essay, Linear Perspective, he explains the principles of perspective in a more understandable way than earlier authors. But the work still suffered from brevity and obscurity, requiring further explanation in the treatises of Joshua Kirby (1754) and Daniel Fournier (1761). 

Claudius Ptolemy (100-170)

Claudius Ptolemy (90–168) was an Egyptian who proposed two map projections, and he is considered a pioneer of cartography: 

  • Conical projection
    A projection based on a cone that touches the Earth at the 36° parallel. In this projection, the meridians are straight lines that converge at a point north of the pole, while the parallels are concentric arcs. Ptolemy’s world map was drawn using this projection. 
  • Curved projection
    A more complex projection where both the latitudes and longitudes are curved, which better approximates the Earth’s spherical shape. Ptolemy used this projection for 26 regional maps, but used Marinus’s projection for his world map.

Ptolemy’s work revolutionised cartography in several ways:

  • He used perspective projection to depict the Earth’s sphere on a map. 
  • He introduced a coordinate system with parallels of latitude and meridians of longitude to accurately position geographic features. 
  • He included an index of place names with latitude and longitude coordinates. 
  • He oriented maps so that north is at the top and east is to the right. 
  • He provided detailed instructions on how to draw maps and source data. 

Euclid (300 BC)

Greek mathematician Euclid, from 300 BCE, developed an explanation of the geometry of vision, or visual perspective (2nd type, or retinal). In Antiquity, Euclid’s Optics first described the visual cone/ pyramid, recognised that parallel lines seem to converge, that further parts of the ground plane appear higher up, and explained foreshortening (optical type or reduction in size of receding dimensions, but there is no proof he understood true aspect foreshortening).

Euclid focused on how things appear to the eye, now termed psychological optics, but he failed to note that vanishing points form when parallels are extended into depth, or to discover the basic size-distance law. Overall, Euclid introduced a quantitative dimension into an otherwise qualitative topic. Euclid also developed the rules of Euclidean geometry and space, and worked with an angle-based distance axiom. 

Filippo Brunelleschi (1377-1446)

Brunelleschi, the inventor of linear perspective (1412-1420), transformed Renaissance painting by systematically studying how objects appear from various angles. He utilised a grid to create accurate drawings, mathematically scaling objects to represent three-dimensions on a two- dimensional surface, resulting in precise linear perspective. 

Galileo Galilei (1564 – 1642)

Galileo Galilei’s artistic training and understanding of perspective helped him make scientific discoveries about the universe. His work combined art and science, and his discoveries supported the idea that the Sun was the centre of the universe. 

Galileo’s artistic training 

  • Galileo was a talented artist who studied perspective techniques from Italian artists. 
  • His artistic training helped him see light and shadow in a way that other astronomers couldn’t. 

Galileo’s perspective on the universe 

  • Supported the idea that the Sun was the centre of the universe, which was called heliocentrism. 
  • The universe is best understood through mathematics, which he called “the language of God”. 

Galileo’s discoveries 

  • The existence of mountains and craters on the moon 
  • The existence of sunspots on the sun, the phases of Venus 
  • The relationship between the pitch and frequency of sound waves 
  • The law of inertia, which states that an object in motion will stay in motion 

Giacomo Barozzi da Vignola (1507-1573)

Giacomo Barozzi[ da Vignola (1507 – 1573), often simply called Vignola, was one of the great Italian architects of 16th-century Mannerism. Vignola’s book Le Due Regole della Prospettiva Pratica is a treatise on perspective written by the artist and architect Jacopo Barozzi da Vignola in the 16th century. The book is considered a landmark of Renaissance architectural theory and illustration. 

Book contents [Le Due Regole della Prospettiva Pratica] 

  • The book explains the principles of perspective and how to apply them in art 
  • It includes a series of figures that illustrate different aspects of perspective science 
  • Shows how the observer’s viewpoint is important for understanding object perspectives

Why is it important? 

The book’s clarity made it one of the most popular books in architectural history. 

Girard Desargues (1591 – 1661)

Desargues’s Perspective Theorem, published in 1648, links 3-D and 2-D geometry, stating that two triangles are in perspective axially if and only if they are in perspective centrally. Desargues’s theorem is a cornerstone of projective geometry, influencing both classical mathematics and computer graphics. 

Detailed Explanation 

The contribution of Desargues to perspective consists of the definition of points and lines to infinity, found in his Brouillon Project. The theorem states that if two triangles ABC and A′B′C′, situated in three-dimensional space, are related to each other in such a way that they can be seen perspectively from one point (i.e., the lines AA′, BB′, and CC′ all intersect in one point), then the points of intersection of corresponding sides all lie on one line, provided that no two corresponding sides are parallel. 

Technical Note 

This concept is not only the fundamental principle of projective geometry, but is also an essential moment in the evolution of theory and practice of perspective, since it gives a general meaning to the punctum concursus (vanishing point). Put simply, Desargues brought understanding to infinity, and optical/technical perspective became an instrument capable of treating the infinite in finite terms. 

Ibn al-Haytham [Alhazen] (1000 BC)

Ḥasan Ibn al-Haytham latinised as Alhazen (965 – 1040) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Alhazen, also known as Ibn al-Haytham, pioneered the study of light and vision. His work influenced the development of perspective in painting and other artistic techniques during the Renaissance. He is said to have invented/tested the camera obscura, a precursor of the modern photographic camera. 

Light and vision 

  • Alhazen was the first to propose that light comes from objects, not the eye. 
  • He believed that light travels in straight lines from objects like lanterns. 
  • He described how the eye receives light reflected from objects. 
  • He believed that the image formed in the eye was inverted, but mistakenly thought that light entered the optic nerve upright (as did Leonardo da Vinci).

Mathematics and scientific methodology 

  • Alhazen believed in using mathematical and quantitative methods to study phenomena. 
  • He developed analytical geometry and scientific methodology. 
  • He used conic sections to solve Alhazen’s problem, which determines the point of reflection from a surface.
  • Alhazen accepted the geocentric model of the universe, but he eliminated the equant from Ptolemy’s models. An equant is a historical astronomical concept to explain planetary motion. 
  • He wrote The Model of the Motions of Each of the Seven Planets around 1038. 

Leon Battista Alberti (1404-1472)

Leon Battista Alberti (1404 – 1472) was an Italian Renaissance humanist, author, artist, architect, poet, priest, linguist, philosopher, and mathematician, and he epitomised the polymath. He is considered an important developer/recorder of the invention of linear perspective in drawing/painting, first developed by Brunelleschi around 1412-1420.

Panofsky’s (1927) interpretation of Alberti’s costruzione legittima method for producing a linear perspective graphical construction remains standard. 

Leonardo da Vinci (1452-1519)

Italian scientist, artist, and inventor Leonardo da Vinci [1452-1519] developed a comprehensive theory of perspective that includes definitions, principles, and explanations remarkably modern in form.

According to Leonardo, the laws of perspective are an inalienable condition of the perception of objects in space. The eye sees objects in perspective automatically, because whenever it turns attention to a spatial scene, it sees the penetration by a transparent ‘perspective’ window of the so-called visual pyramid of rays, operating somewhat like an optical targeting system.

Leonardo goes on to explain fundamental axioms of perspective, such as object/scene geometry, point-of-sight, picture plane or perspective window, and perspective phenomena such as aspect, diminution of size, degradation of form, diminution of form, plus the formation of vanishing point(s) and a horizon line are also explained in detail, etc. 

Leonardo describes perspective as a rational demonstration of how objects convey their image to the eye, utilising converging lines that meet at a single point. Leonardo explains that perspective in dealing with distances employs two opposite ‘perspective’ pyramids: 

  • The Pyramid of Vision; which has its apex in the eye, and the base as distant as the horizon; whereby each body is full of infinite points, and every point makes a ray… and rays proceeding from the points of the surface of bodies form pyramids (throughout space). Thus each body fills the surrounding air by means of these rays with infinite images, each body becoming the base of innumerable and infinite pyramids… and the point of each pyramid has in itself the whole image of its base… and… the centre- line of the pyramid is full of infinite points of other pyramids, also: 
  • The Pyramid of Spatial Recession, with its base toward the eye and its apex at the horizon, whereby objects of equal size, situated in various places, will be seen by different pyramids, each smaller in proportion as the object is farther off. 

Lorenzo  Ghiberti (1378-1455)

Lorenzo Ghiberti (1378 – 1455), was an Italian Renaissance sculptor, best known as the creator of two sets of bronze doors of the Florence Baptistery, the later one called by Michelangelo the Gates of Paradise. His book of Commentarii contains important writings on art/perspective. 

Paolo Uccello (1397-1475)

Paolo Uccello (1397–1475) was an Italian Renaissance painter and architect, known for pioneering linear perspective and geometric precision. 

How did Uccello use perspective? 

  • Linear perspective: Uccello used linear perspective to create the illusion of depth on a flat surface. He used vanishing points and orthogonals (object space parallels) to create the illusion of distance. 
  • Grid-like patterns: Uccello created grid-like patterns by experimenting with the position and proportion of objects. 
  • Illusionism: Uccello used perspective to create illusions, such as in his work Sir John Hawkwood located in a Florence Cathedral.

Influence
Uccello’s work influenced other Renaissance artists, including Piero della Francesca, Leonardo da Vinci, and Albrecht Dürer. Uccello’s work demonstrated how scientific laws could be used to reconstruct 3-D objects. 

Piero della Francesca (1415-1492)

Piero della Francesca (1415–1492), an early Renaissance Italian painter and mathematician, is renowned for his art and theoretical study of perspective.

His surviving treatises—Abacus Treatise, On the Five Regular Solids, and On Perspective in Painting—cover arithmetic, algebra, and geometry, significantly influencing later works, particularly Luca Pacioli’s Divina proportione, illustrated by Leonardo da Vinci. 

Plato (428 – 423 BC)

Plato (428–348 BC) was an ancient Greek philosopher who is a foundational thinker in Western philosophy. Plato’s most famous contribution is the theory of forms (or ideas), which aims to solve the so-called problem of universals.

The problem of universals is a question from metaphysics: “Should the properties an object has in common with other objects, such as colour and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?”

Van Eyck (1390-1441)

Jan van Eyck’s paintings are known for their meticulous attention to detail and realism, but the question of perspective in his work has been debated for centuries. Some say he used perspective empirically, without understanding the underlying geometric laws. Others believe he used a device to create a more realistic representation of space. 

Empirical perspective 

  • Erwin Panofsky, a specialist in Flemish primitives, believed that van Eyck used perspective empirically, without understanding the underlying geometric laws. 
  • Panofsky thought that van Eyck tried to create the most realistic perspective possible.

Polyscopic perspective machine 

  • Some researchers believe van Eyck used a polyscopic perspective machine.
  • A 3-D reconstruction of the Arnolfini Portrait suggests van Eyck used a machine for more realistic space representation 
  • The machine may have had eyepieces placed at each end of the view axis, similar to the distance between the pupils of an adult man.

Atmospheric perspective 

  • Van Eyck’s paintings are some of the earliest examples of atmospheric perspective. 
  • In The Ghent Altarpiece, van Eyck paints objects in the background more blurred, with weaker colours and contrasts. 

Viator or Jean Pelerin (1445-1524)

The first diagram of two-point perspective is by Jean Pélérin in De Artificiali perspectiva (1505). Known as “Viator,” he transmitted rather than invented the method, noting that the central and two-tier points are on the eye-level horizon line. 

Vitelo (1270)

Known historically as Perspectiva (c. 1274), written by the Polish natural philosopher Witelo (or Vitello), this is a foundational text on the subjects of light, optics, and vision. It rests heavily on the earlier research of the Arab scholar Ibn al-Haytham regarding the physics of light, reflection, and refraction. Vitello’s optical and natural philosophy writings were highly influential and laid the crucial groundwork for later scientists and mathematicians, such as Johannes Kepler.