Lawrence Wright gives a useful definition of perspective as follows:

Perspective is about the way we see things—or think we do—and about how we have tried to reproduce that visual concept on media such as diagrams, pictures, photographs, models, films and television, etc. Ergo, whatever the medium, if any degree of realism is intended, then some use of perspective theory, methods, and techniques is inevitable. 

Lawrence Wright, Perspective in Perspective, 1983

Patently, perspective is a broad subject that encompasses a vast range of theoretical methods, principles, techniques, which sometimes also involve one of a host of perspective instruments like the sextant, compass, camera, telescope, microscope, planisphere, pantograph, computer, satellite etc. 

Perspective is a fundamental topic; whereby we have identified three primary goals of Technical Perspective as (in human terms)—first viewing reality: observing spatial form directly; second, matching reality: surveying, measuring or modelling spatial form; and finally, making representations of reality: copying / constructing spatial forms.

Here on this site, we have avoided narrow definitions of perspective. For example, we sidestep the common tendency to assign perspective to be a series of techniques focussed on depicting depth through illusory effects produced by various means within pictures. Hence we do not place exaggerated emphasis on so-called Linear Perspective and related methods etc.

Perspective History

It is helpful to summarise key historical events that are pertinent to the historical development of Visual (Optical) and Symbolic Perspective.

Perspective in Ancient Times

Below are salient examples of perspective theories/inventions from ancient times.

Date(s)Person / Place OrganisationInventionDescriptionPerspective Category
15,000 BCCave PaintingCave paintings of animals show understanding of proto-perspectival effects, such as projected outline, varying scale with distance, and even a suggestion of relief by means of light and shade.Graphical
3500 BCAncient EgyptiansShadow ClocksEgyptian obelisks, constructed c. 3500 BC, are among the earliest shadow clocks.Natural,
Instrument, Mathematical
3000 BCAncient EgyptiansEgyptian Gauges and DialsFirst examples of gauges and dial markings are seen on Egyptian measuring instrument.Instrument, Mathematical
5000 BC – 3000 BCBabyloniansWritingScholars generally agree that the earliest form of writing appeared almost 5,500 years ago in Mesopotamia.Symbolic
2650 BCAncient EgyptiansRulerThe first ruler was a measuring rod made of copper alloy and it dated from 2650 BC.Instrument, Mathematical, Symbolic
2600 BCAncient EgyptiansEarly LensIt has been suggested that glass eye covers (natural crystal stones) are depicted in hieroglyphs from the Old Kingdom c. 2686–2181 BC), being functional simple glass meniscus lenses.Natural, Instrument
1534 BCAncient EgyptiansEarly Star ChartThe oldest dated star chart appeared in ancient Egyptian Astronomy.Natural, Graphical, Mathematical
1500 BCAncient EgyptiansWater ClockThe oldest description of a clepsydra, or water clock, is from the tomb inscription of an early 18th Dynasty Egyptian court official named Amenemhet.Natural, Instrument, Mathematical
1500 BCAncient Egyptians,  BabyloniansAncient SundialsThe earliest household clocks known, from the archaeological finds, are the sundials (1500 BC) in Ancient Egypt, and ancient Babylonian Astronomy.Natural, Instrument, Mathematical
1400 BCAncient EgyptiansProtractorSomething that can be described as a protractor or a forerunner of a protractor is found in a tomb of an ancient Egyptian architect Kha, dating from 1400 BC. The first real protractors were made around five hundred years ago.Instrument, Mathematical
1400 BCAncient EgyptiansPerspective like Drawing and Painting TechniquesThe standard work describing these methods is Schäfer (1974), who uses the term “perspective-like” (German aperspektivisch), a term also used by Jean Gebser, to describe Egyptian methods of spatial representation.Graphical
1000 BC – 300 ADAncient Greece, Rome, EgyptLinear PerspectiveThe basic question whether linear perspective was or was not known in Antiquity is still a matter of debate. However, no study of examples reveals the single vanishing point of linear perspective. Unfortunately, many classicists tend to use the term perspective very loosely to refer to a sense of depth, with no interest whether a vanishing point, a distance point, or other technicalities were involved.Graphical
600 – 700 BCPerspective PhenomenaPerspective Phenomena (Scale), Optical EffectsTablets from Assyria depict diminution of objects with increasing distance (including vanishing points). Similarly the so-called Nimrud Lens, a rock crystal artefact dated to the 7th C. BC, may have been used as a magnifying glass.Graphical
500 – 600 BCAncient GreeceCaliperThe earliest caliper has been found in the Greek Giglio wreck near the Italian coast. Many types of calipers permit reading out a measurement on a ruled scale, a dial, or a digital display. Some calipers can be as simple as a compass with inward or outward-facing points, but no scale.Instrument, Mathematical
500 BCBabyloniansMapNamed Imago Mundi Babylonian map, this is the oldest known world map, 6th C. BC Babylonia.Graphical, Mathematical
500 – 500 BCAncient IndiaTheories of LightIn Ancient India, from around the 6th–5th C. BC, Indian people developed theories on light. According to the Samkhya school, light is one of the five fundamental “subtle” elements (tanmatra) out of which emerge the gross elements.Natural, Visual (2nd Type)
400 BCChinaCamera ObscuraThe earliest known written account of a camera obscura was provided by a Chinese philosopher named Mo-tzu (or Mozi) in 400 BC. He noted that light from an illuminated object that passed through a pinhole into a dark room created an inverted image of the original object.Instrument, Mathematical
300 BCEuclidConics (lost), Divisions of Figures, Optics (lost), ElementsEuclidean Space of classical geometry is first defined by Euclid – (4 axioms on Surveying); an angle axiom denied simply relation between apparent size and distance.Natural, Visual (2nd Type), Mathematical
300 BCChinaArmillary Sphere (variations are known as spherical astrolabe, armilla, armil, or huntianyi (traditional Chinese: 渾天儀; simplified Chinese: 浑天仪).Being a model of objects in the sky, consisting of a spherical framework of rings, cantered on Earth or the Sun, that represent lines of celestial longitude and latitude; plus other astronomically important features, such as the ecliptic.Natural, Instrument, Mathematical
100 – 200 BCChinaCompass (magnetic directional)The compass was invented in China during the Han Dynasty between the 2nd C. BC and 1st C. AD where it was called the “south-governor” or “South Pointing Fish” (sīnán 司南). The magnetic compass was not, at first, used for navigation, but for geomancy and fortune-telling by the Chinese.Natural, Instrument, Mathematical
100 BCChina, GreeceAstrolabe (Ancient Greek: ἀστρολάβος astrolabos; Arabic: ٱلأَسْطُرلاب al-Asturlāb, Persian: ستاره‌یاب Setāreyāb)An ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclinometer and an analogue calculation device capable of working out several kinds of problems in astronomy. An early astrolabe was invented in Ancient Greece between 220 and 150 BC, often attributed to Hipparchus.Natural, Instrument, Mathematical
0 – 100 BCAncient GreeceThe Antikythera mechanismAn Ancient Greek hand-powered orrery, described as the oldest example of an analogue computer used to predict astronomical  positions and eclipses decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad.Natural, Instrument, Mathematical
300 – 400 ADGreece, RomeProto-Perspective Graphical TechniquesGreco-Roman efforts were linked with scenography (skaenographia). This resulted in a sense of depth usually through convergence along an axis of points (fish-bone perspective) and occasionally towards a central vanishing point.Natural, Graphical
60 ADRomeCrystal Magnifying GlassThe ancient Roman philosopher, Seneca, described, “letters could be magnified by a ball of crystal” about 2000 years ago.Natural, Instrument
150 ADEgyptQuadrantAn instrument that is used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings, such as longitude, latitude, and time of day. One of the earliest accounts of a quadrant comes from Ptolemy’s Almagest around AD 150.Natural, Instrument
Table 1: Perspective in Ancient Times (up to the fall of Roman Empire in 479 AD)

Perspective in the Middle Ages (5th – 13th Centuries)

While the mediaeval period largely abandoned geometrical depiction of pictorial space, it introduced a series of projection methods for systematic representation of space, notably, planisphere and astrolabe projections, as well as experimenting with the effects of camera obscuras.

801 – 873 ADArabiaTheory of LightIn a work known in the west as De radiis stellarum, al-Kindi developed a theory “that everything in the world … emits rays in every direction, which fill the whole world”.Natural
1000 ADArabiaTheory of LightScientist Ibn al-Haytham  (known in as Alhacen or Alhazen in Western Europe), writing in the 1010s, received both Ibn Sahl’s treatise and a partial Arabic translation of Ptolemy’s Optics. He produced a comprehensive and systematic analysis of Greek optical theories. He wrote about the effects of pinhole, concave lenses, and magnifying glasses in his Book of Optics.Natural, Instrument
10,000 ADPersiaAstrolabeSophisticated timekeeping astrolables with geared mechanisms were made in Persia.Natural, Instrument, Mathematical
1000 – 1200 ADEurope?Plano-Convex LensesBetween the 11th and 13th C. “reading Stones” were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively (with less aberrations/distortions). Natural, Instrument
1286EuropeEye-glassesPossibly in Pisa, Italy, the first pair of eyeglasses were made, although it is unclear who the inventor was.Natural, Instrument, Visual (2nd type)
5 – 12 C.EuropeOptical ThoeryWhile the mediaeval period largely abandoned geometrical depiction of pictorial space, it introduced a series of projection methods for systematic representation of space, notably, planisphere and astrolabe projections, as well as experimenting with the effects of camera obscuras.Natural, Mathematical, Graphical
Table 2: Perspective in the Middle Ages

Renaissance (14-17th Centuries)

The Renaissance was a fervent period of European cultural, artistic, political and economic “rebirth” following the Middle Ages. Generally described as taking place from the 14th century to the 17th century, the Renaissance promoted the rediscovery of classical philosophy, literature and art.

1415EuropeInvention of Linear PerspectiveRenaissance perspective, while vaunted to be a rebirth of ancient methods, transformed its methods and goals, from imitation of general things to matching of specific objects. Brunelleschi’s first demonstrations using the Baptistery of San Giovanni and the Piazza dell Signoria in Florence are famous examples. Paradoxically, this did not lead immediately to a copying of the natural world. It led to idealized views (e.g. Baltimore, Berlin and Urbino panels).Natural, Graphical
15 C.GhibertiEssays on Linear Perspective.A series of essays on this artist’s role in the early history of linear perspective are conveniently collected in the acts of a conference on Lorenzo Ghiberti (1980). Graphical, Mathematical, Linear
15 C.BrunelleschiInvention of Linear PerspectuveEvidence of Brunelleschi’s perspectival experiments is limited to 6 lines of text by Manetti, his biographer. Nevertheless, because Brunelleschi has become a symbol of revolution in spatial representation there have been well over 100 articles written about these 6 lines in the past 50 years. Gioseffi’s (1957) interpretation remains important. Edgerton’s reconstruction using a camera (1973, 1975) has become one of the most popular interpretations of the experiment involving San Giovanni in Florence. Others are to be found in a conference on Brunelleschi (1980). A good summary of the chief interpretations is provided by Martin Kemp (1978). Recently, psychologists have also become interested in the implications of Brunelleschi’s experiment, as witnessed by Arnheim (1978) and Pastore (1979). Graphical, Mathematical, Linear
15 C.AlbertiDetails of Linear PerspectiveGrayson’s (1972) edition and translation of De pictura and Gambuti’s (1972) edition of Elementa picturae have made these sources more accessible. Panofsky’s (1927) interpretation of Alberti’s costruzione legittima remains standard. Even so the diagrams in the Lucca manuscript discovered by Arrighi (1972) raise new problems concerning the relationship between costruzione legittima and distance point construction, as discussed by Veltman. Graphical, Mathematical, Linear
15 C.MasaccioAnalysis of Masaccio’s paintings for evidence of Linear Perspective.Polzer’s (1971) careful analysis of perspectival lines in Masaccio’s Trinitá brings to light the importance of claims based on the actual work, rather than on photographs. Graphical, Mathematical, Linear
15 C.Domenico Veneziano?Holmes’ Courtauld thesis on the Pala di Santa Lucia raises new questions concerning the role of models in perspectival constructions. Battisti’s (1971) appendix, 5 written in collaboration with J. Ubans, remains one of the only published analyses of Veneziano’s perspective.Graphical, Mathematical, Linear
15 C.MantegnaFasolo’s (1965) analysis of Mantegna’s perspective remains basic. Battisti (1971) has discussed the 15th and 16th C. context of Mantegna’s interests. Smith (1974) has analysed the perspectival construction in Mantegna’s Dead Christ. Graphical, Mathematical, Linear
15 C.Antonella da MessinaTrutty-Coohill (1982) has drawn attention to the importance of light and shade in creating perspectival relief (eminentia). Leonardo terms this chiaroscuro. This important branch of perspective deserves much further study.Graphical, Mathematical, Linear
15 C.Piero della FrancescaDuring the Renaissance it was considered that Piero della Francesca had written three perspectival treatises: De prospectiva pingendi, De corporibus regularibus and Trattato d’abaco” (cf. E. Danti, introduction to his edition of Vignola’s Le due regole, 1583). Daly-Davis (1977) has thrown light on the connections between these works. Smedley (c. 1982), in an unpublished typescript, has made sculpted reconstructions of the heads described in Piero’s De prospectiva pingendi and has linked these with Platonic ideals of the time. Berry (Columbia, Missouri) made computerized reconstructions of diagrams in Piero’s treatise. Nonetheless, the De prospectiva pingendi still awaits an edition that takes into account the various manuscript versions. Graphical, Mathematical, Linear
15 C.Leonardo da Vinci At the instigation of and in consultation with Keele, Veltman has made a comprehensive study of Leonardo’s perspectival and optical writings. There have been a number of interpretations of the perspectival construction used in the Last Supper; some appear in Dalai-Emiliani (1980). Graphical, Mathematical, Linear
15 C.CorreggioCorreggio’s perspectival di sotto in su figures have been examined by Shearman (1980) and analysed by Battisti (1979). Graphical, Mathematical, Linear
15 C.Lotto(De) Vecchi (1978) has analysed the perspectival construction in Lotto’s Pala Martinengo.Graphical, Mathematical, Linear
15 C.DürerSchüritz (1919) remains a standard study of the perspectival constructions in Dürer’s paintings. Schröder’s (1980) book analyses several paintings and provides elegant projections for the Melencolia. Schröder rejects the possibility of number symbolism in the geometric body shown in the engraving. Since then Lynch (1982) has analysed the perspectival shape in Melencolia I independently and has produced a strong case to claim that number symbolism is involved, indeed that the irregular body is linked with the magic number square in the right hand of the engraving. Graphical, Mathematical, Linear
15 C.StevinSinisgalli’s (1978) edition and Italian translation of Stevin’s Latin treatise is of particular interest because of his introductory essay in which he produces three-dimensional reconstructions of Stevin’s abstract diagrams and relates these to diagrams of other major theorists notably Piero della Francesca, Giacomo Barozzi da Vignola, Frederico Commandino and Guidobaldo del Monte.Graphical, Mathematical, Linear
15 C.Veronese and TintorettoMarinelli (1974, 1980) has analysed perspectival constructions in the paintings of Veronese and Tintoretto respectively. Graphical, Mathematical, Linear
1440Johannes GutenbergPrinting Press In Germany, around 1440, goldsmith Johannes Gutenberg invented the printing press, which started the Printing Revolution. Symbolic
14 – 17 C.Linear perspective and the first perspective instruments In the Renaissance, artists used instruments such as the mirror and the perspectival window as a means of recording the visible world with linear perspective. Natural, Graphical, Mathematical 
15 – 16 C.Perspective experiments Piero della Francesca and Leonardo da Vinci were among the pioneers in exploring anamorphic effects, cases where extreme positions of a picture plane relative to objects caused dramatic distortions. Leonardo was also one of the early artists to explore the effects of applying the new method to cylindrical and spherical surfaces. In the 16th C., this was further explored by Carlo d’Urbino and Cigoli. In the 17th C., this theme became a regular feature of printed books: e.g. Dubreuil, 1642-1649 and Abraham Bosse, 1648. One reaction was to avoid near distance cases where distortion was extreme. This led to a narrowing of the field of vision.Natural, Graphical, Mathematical 
16 C.Fabrizio Mordente Compass  (reduction)The reduction compass  was invented by Fabrizio Mordente before 1567 as a drafting instrument. In use it was positioned on a piece of paper and its adjustable points could be used to transfer and compare dimensions and geometrical proportions.Natural, Graphical, Mathematical, Instrument 
1515Planispheres and Celestial GlobesThe first printed planispheres (representations of the celestial sphere on a flat surface) were produced in 1515, and printed celestial globes appeared at about the same time.Natural, Graphical, Mathematical 
1569Gerardus Mercator Mercator projectionThe Mercator projection (/mərˈkeɪtər/) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. … The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator.Natural, Graphical, Mathematical 
16 C.Optics linked with geometry [Urbino region] See work from the period including: Commandino, Benedetti, and Guidobaldo del Monte.Natural, Graphical, Mathematical 
17th C.Fabrizio MordenteCompass (proportional)Compass (proportional) or sector is developed by Fabrizio Mordente (1532 – ca 1608) an Italian mathematician who is best known for his invention of the “proportional eight-pointed compass” which has two arms with cursors that allow the solution of problems in measuring the circumference, area and angles of a circle.Natural, Graphical, Mathematical, Instrument 
16 C.Vanishing points. Roaming or Multiple Perspective(s).An important study by Sinisgalli (1981) demonstrates that Borromini’s corridor in the Palazzo Spada has 15 different vanishing points which accommodate the observers’ different viewpoints as they walk through it. Natural, Graphical, Mathematical 
17 C.Dutch PaintingsThe role of perspective in Dutch paintings in Delft in the period around 1650 has been the subject of doctoral dissertations by both Liedtke (1974) and Wheelock (1973, as book 1977). Wheelock’s work is important because it challenges recent assumptions concerning Vermeer’s use of camera obscuras in his painting practice. Both Wheelock and Liedtke have drawn attention to the role of theoretical treatises by Vredeman de Vries, Hondius and Marolois. Liedtke (1975-1976, cf. 1983) noted discrepancies between Saenredam’s perspectival sketches and his finished paintings. Ruurs (1980, 1982) has since analysed these discrepancies with greater precision. Outside the Delft scene, perspectival theory in the seventeenth C. remains largely unexplored.Natural, Graphical, Mathematical 
17 C.Rise of Centres (perspective movements)The seventeenth C. brought more than a list of new authors. It also brought a change in centres. Throughout the 15th and 16th centuries Urbino had been the meeting place of theoreticians concerned with the mathematical principles of linear perspective: to Urbino came Piero della Francesca, Luca Pacioli, Frederico Commandino, John Dee and Guidobaldo del Monte. During the 1630’s Paris had become the new European centre where mathematics and perspective were studied together. During this decade (1630- 1640) while Descartes was laying the foundations of co-ordinate geometry, Pascal was exploring the perspectival properties of conic sections, and Desargues was formulating the principles of perspéctival vanishing points geometrically. From the 1640’s onwards three levels of discussion can be traced. One is highly mathematical and continues at a high level with thinkers such as Brook Taylor, Lambert and Poncelet. A second level is still technical but more accessible. This involves names such as those listed above. A third level is popular, is initiated by Jesuit encyclopaedists such as Kircher, Bettini, Schott and Milliet de Chales and then adopted by others such as Schwenter, Le Clerc and Ozanam. A future history will need to trace how these three levels interact and yet maintain a certain independence. Natural, Graphical, Mathematical 
17 C.William OughtredSlide Rule  The slide rule was invented by William Oughtred in the 1600’s.Natural, Graphical, Mathematical, Instrument
17 C.Mathematical perspectiveParis became the world centre for mathematical perspective – for example with Aleaume, Desargues, Noceron, Bosse. Abraham Bosse, professor of perspective in French Academy urged students to draw what is there (Euclidean Geometry) and not what is seen (Euclidean theory of vision).Mathematical
1608Refracting TelescopeThe earliest known working telescopes were the Refracting Telescopes that appeared in the Netherlands  in 1608. Their inventor is unknown: Hans Lippershey applied for the first patent that year.Natural, Instrument
1609GalileoGalileo’s Telescope Galileo greatly improved upon telescope designs.Natural, Instrument
1620Compound MicroscopeThe earliest known examples of compound microscopes, which combine an objective lens  near the specimen with an eyepiece to view a real image, appeared in Europe around 1620.Natural, Instrument
1668Isaac NewtonReflecting Telescope Isaac Newton  is credited with constructing the first functional reflecting telescope in 1668, his Newtonian Reflector.Natural, Instrument
1600s – 1800s Vision and the principles of representation From the 1660’s to the 1820’s artists either a) chose limited conditions where the effects of vision and perspective coincided or b) spoke in general terms about (Euclidean) vision and (linear) perspective. The rise of descriptive geometry which claimed to offer universal principles for representation led to the first serious claims that representation and vision must be coincident. Natural, Graphical, Mathematical
17 C.Perspectival peep showSeventeenth C. artists developed a perspectival peep show (perpektyfkas) which invited viewers to use a “roving eye” to explore interiors. Natural, Instrument
17 C.The Magic LanternThe Magic Lantern – also known by its Latin name laterna magica, is an early type of image projector that used pictures—paintings, prints, or photographs—on transparent plates (usually made of glass), one or more lenses, and a light source. It was mostly developed in the 17th C. and commonly used for entertainment purposes. It was increasingly used for education during the 19th C.. Since the late 19th C., smaller versions were also mass-produced as toys. The magic lantern was in wide use from the 18th C. until the mid-20th C. when it was superseded by a compact version that could hold many 35 mm photographic slides: the  slide projector.Natural, Instrument
Table 3: Perspective in the Renaissance

18-19th Centuries

The 18th and 19th Centuries saw the birth and development of a host of new technological inventions including optical instruments, photography, cinema, electricity, radio and even an early form of television; whereby all of these innovations would lay the foundations of the incredible progress seen in science and technology in the 20th and 21st Centuries. Once again a huge variety of perspective theories, methods, techniques, forms, applications, etc., were a vital part of in these incredible achievements.

1731SextantA Sextant is a doubly-reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon  for the purposes of celestial navigation. The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749).Natural, Instrument, Mathematical
17 C.Concept of photographic imageEnglish photographer and inventor Thomas Wedgewood is believed to have been the first person to have thought of creating permanent pictures by capturing camera images on a material coated with a light-sensitive chemical. He originally wanted to capture the images of a camera obscura, but found they were too faint to have an effect upon the silver nitrate solution that was recommended to him as a light-sensitive substance. Wedgwood did manage to copy painted glass plates and captured shadows on white leather, as well as on paper moistened with a silver nitrate solution. Natural, Instrument, 
18 C.Practical applications of perspectiveMeanwhile, the eighteenth C. increasingly applied perspective to gardens, and large spaces stretching as far as the horizon. Some spaces were calculated to make distances look closer, others to make it look further away. Space became something to be manipulated: the eye a sense to be tricked. This often led to a widening of the field of vision, and occasionally to a narrow peephole as in Piranesi’s gate of Knights of Malta in the Santa Sabina hill in Rome.Natural, Graphical, Mathematical
1700 – 1800Perspective practical texts explode in number Pirenne (1970) has explored the relationship between Pozzo’s seventeenth C. practice and theory as expressed in his 1707 treatise. The perspectival views of Bibiena and Piranesi are fairly well known, although precise studies are few. For the most part, however, our knowledge of the 18th C. perspectival theory remains minimal. General histories may mention the name Brook Taylor. But no one has yet studied the 30 editions and adaptations produced by Kirby, Highmore, Fournier, Malton, Cowley, Rivoire and Jacquier. The same holds true for a long list of authors of eighteenth C. perspectival treatises such as Bernard Lamy, Leonard Sturm, Gravesande, Jean Courtonne, J.J. Schübler, Paul Heinecke, John Peele, Abbé Deidier, J.A. von Segner, Georg Heinrich Werner, Caspar Philips Jacobszoon, Claude Lagardette, Johann Adam Breysig or John Wood. None of these authors has yet been studied in detail, although the majority of the names have been mentioned by experts. Natural, Graphical, Mathematical
19 C.Basic forms of space recognised (Visual, Geometric), dawn of Psychological OpticsThe19th C. saw new attention to properties of geometry and optics. Von Helmholtz explored the possibility that optical space within the retina might entail Riemannian rather than Euclidean space. In the latter 19th C., theoreticians such as Herdman (1863) outlined the possibilities of (cylindrical) curvilinear perspective.Natural, Graphical, Mathematical
1800-1900Links to Art / Photography – arguments over sources / discoveryThere has been some recent work on the history of perspective in the 19th C.. In this connection Wenzel (1979) has written on a transformation in French landscape painting from Valenciennes to Corot, 1787 to 1827. Marcussen (1977) has also studied Corot’s perspectival interests and has subsequently (1980) given an outline of French treatises on perspective in the nineteenth C.. There has been some study of how nineteenth C. painters used alternatives to linear perspective, as, for instance, Adams’ (1975) essay on Cézanne or Rewald’s work on Van Gogh, adapted by Heelan (1983). There has also been considerable polemic concerning the relationship between latter nineteenth C. painting, impressionism in particular, and photography. One side, epitomized by Scharf (1974) claims that photography introduced new ways of seeing which inspired the so called innovations of the impressionists. Perucchi-Petri’s (1976) study of Bonnard, Vuillard and Denis accepts that both Japanese art and photography were influences.Natural, Graphical, Mathematical, Instrument
1800-1900Perspective theoretical textsThe number of theoretical treatises increases dramatically. In the period 1800-1825 more than 100 treatises appear. Between 1825 and 1850 there are more than 200. From 1850 to 1875 there are more than 300. From 1875 to 1900 there are more than 400. In short, between 1800 and 1900 there appeared upwards of 1000 treatises. (By contrast in the period 1400- 1500, one perspectival treatise was actually published).Natural, Graphical, Mathematical
19 C.Mechanical televisionPrior to electric televisions, we had mechanical televisions. These early televisions started appearing in the early 1800s. They involved mechanically scanning images then transmitting those images onto a screen. Compared to electronic televisions, they were extremely rudimentary.Natural, Instrument
1801PhotogramsFrench balloonist, professor and inventor Jacques Charles is believed to have captured fleeting negative photograms of silhouettes on light-sensitive paper at the start of the 19th C., prior to WedgwoodNatural, Instrument
19 C.Non-euclidean spaceMathematicians explored various alternatives to (rectilinear) Euclidean space. Meanwhile, physiologists became aware of serious problems with earlier analogies between the eye and camera obscura (Leonardo, Kepler, Scheiner).Mathematical
1805Camera Lucidia The camera lucida was patented in 1806 by the English chemist William Hyde Wollaston. The basic optics were described 200 years earlier by the German astronomer Johannes Kepler in his Dioptrice (1611), but there is no evidence he or his contemporaries constructed a working camera lucida.Natural, Instrument
1826First photographThe world’s first photograph made in a camera was taken in 1826 by Joseph Nicéphore Niépce. This photo, simply titled, “View from the Window at Le Gras,” is said to be the world’s earliest surviving photograph.Natural, Instrument
1830First silvered mirrorsThe silvered-glass mirrors found throughout the world today first got their start in Germany almost 200 years ago. In 1835, German chemist Justus von Liebig developed a process for applying a thin layer of metallic silver to one side of a pane of clear glass.Natural, Instrument
1832Sir Charles WheatstoneStereoscopeThe earliest stereoscopes, “both with reflecting mirrors and with refracting prisms”, were invented by Sir Charles Wheatstone and constructed for him by optician R. Murray in 1832.Natural, Instrument
1839Alphonse Giroux First photographic cameraThe first photographic camera developed for commercial manufacture was a daguerreotype camera, built by Alphonse Giroux in 1839. Natural, Instrument
1843TelegraphIn 1843, Morse built a telegraph system from Washington, D.C., to Baltimore with the financial support of Congress. On May 24, 1844, the first message, “What hath God wrought?” was sent.Symbolic
1850DaguerreFirst practical photographic method for general-purpose usage Daguerre made the pivotal discovery that an invisibly slight or “latent” images produced on such a plate by a much shorter exposure could be “developed” to full visibility by mercury fumes. This brought the required exposure time down to a few minutes under optimum conditions. A strong hot solution of common salt served to stabilise or fix the image by removing the remaining silver iodide. On 7 January 1839, this first complete practical photographic process was announced at a meeting of the French Academy of Sciences, and the news quickly spread. Known as the daguerreotype process, it was the most common commercial process until the late 1850s when it was superseded by the colloidal process.Natural, Instrument
1861James Clerk Maxwell First color photographThe first colour photograph was taken by the mathematical physicist, James Clerk Maxwell. Maxwell created the image of a tartan ribbon by photographing it three times through red, blue, and yellow filters, then recombining the images into one colour composite in 1861. Natural, Instrument
1878Motion photography  (zoetrope) – Horse in MotionThis groundbreaking motion photography was accomplished using multiple cameras and assembling the individual pictures into a a single motion picture. it’s something that you could do today, using a few cameras that are set to go off at an exact moment (in a timed series). The movie was made to scientifically answer a popularly debated question during this era: Are all four of a horse’s hooves ever off the ground at the same time while the horse is galloping? The video proved that they indeed were and, more importantly, motion photography was born.Natural, Instrument
1888Earliest surviving motion pictureRounday Garden Scene – The world’s earliest surviving motion-picture film, showing actual consecutive action is called Roundhay Garden Scene. It’s a short film directed by French inventor Louis Le Prince. While it’s just 2.11 seconds long, it is technically a movie. According to the Guinness Book of Records, it is the oldest surviving film in existence.Natural, Instrument
1888EdisonKinetographIn 1888 in New York City, the great inventor Thomas Edison and his British assistant William Dickson worried that others were gaining ground in camera development. The pair set out to create a device that could record moving pictures. In 1890 Dickson unveiled the Kinetograph, a primitive motion picture camera. In 1892 he invented the Kinestoscope, a machine that could project the moving images onto a screen. In 1894, Edison initiated public film screenings in recently-opened “Kinetograph Parlors.”Natural, Instrument
1895Early cinema Although the advent of film as an artistic medium is not clearly defined, the commercial, public screening of ten of lumiere brothers short films in Paris on 28 December 1895 can be regarded as the breakthrough of projected cinematographic motion pictures.Natural, Instrument
19 C.Optical illusions The nineteenth C. drew attention to a series of geometrical optical illusions. Natural, Instrument, Forced
1895MarconiRadioMarconi is credited with being the first person to transmit radio signals, doing so over a distance of a mile and a half in 1895 in Lavernock Point in the Vale of Glamorgan in Wales.Symbolic
Table 4: Perspective in the 18th and 19th Centuries

20th Century

The 20th century was dominated by significant events that defined the modern era: Spanish flu pandemic, World War I and World War II, nuclear weapons, nuclear power, microchips, and space exploration, nationalism and decolonization, the Cold War and post-Cold War conflicts, and other technological advances, etc. As explained elsewhere on this site, various kinds of perspective underpinned and played a huge role in many of these advancements.

1920John Logie Baird, Charles Francis JenkinsEarly televisionOne of the first mechanical televisions used a rotating disk with holes arranged in a spiral pattern. This device was created independently by two inventors: Scottish inventor John Logie Baird and American inventor Charles Francis Jenkins. Both devices were invented in the early 1920s.Natural, Instrument
1927First electronic televisionThe world’s first electronic television was created by a 21 year old inventor named Philo Taylor Farnsworth. That inventor lived in a house without electricity until he was age 14. Starting in high school, he began to think of a system that could capture moving images, transform those images into code, then move those images along radio waves to different devices. Farnsworth was ahead of any mechanical television system invented to-date. Farnsworth’s system captured moving images using a beam of electrons (basically, a primitive camera). The first image transmitted by television was a simple line. Later, Farnsworth transmitted a dollar sign using his television after a prospective investor asked “When are we going to see some dollars in this thing, Farnsworth?”Natural, Instrument
1947Hologram theoryHolography dates from 1947, when scientist Dennis Gabor developed the theory of holography while working to improve the resolution of an electron microscope. Gabor coined the term hologram from the Greek words holos, meaning “whole,” and gramma, meaning “message”.Natural, Instrument
1962First holograms developedThe development of the laser enabled the first practical optical holograms that recorded 3D objects to be made in 1962 by Yuri Denisyuk in the Soviet Union, and by E. Leith and J. Upatnieks in the USA.Natural, Instrument
1965Satellite Communications The world’s first commercial communications satellite, Intelsat1, or Early Bird, launched April 6, 1965.Natural, Instrument, Mathematical, Symbolic
1965Theodor Holm NelsonHypermediaTheodor Holm Nelson (born June 17, 1937) coined the terms hypertext and hypermedia and published them in 1965 (World Wide Web was a partial implementation of Ted’s ideas).Symbolic
20 C.Debate over Physical vs Visual SpaceMach explored this distinction in his Analysis of Sensations and devoted a chapter to it in his Knowledge and Error (1905). The emergent schools of psychology focussed on different aspects of this distinction. The Berlin school, later the Gestalt school, emphasized geometrical space. The Leipzig school (Wundt, Titchener) emphasized visual space. In the twentieth C. this distinction has remained with physiologists such as Doesschate. Sometimes the names for the elements have changed. Sir Ernst Gombrich, for example, referred to visual space as the optical world or the mirror and to geometrical space as the physical world, the experienced world or the map. Natural, Mathematical
20 C.Supposed death of perspectiveRhetorically, there has been an attack on perspective in the 20th C., to the extent that some have spoken of the death of perspective. In practice, there have been more publications than ever, along with a radical increase in alternative methods. Jobin (1932) was interested in curvilinear methods in connection with skyscrapers. Barre & Flocon (1967) were interested in where it corresponded to perception of the eye.Ever since Novotny’s (1938) book, it has become a commonplace to assume that linear perspective died with Cézanne and that its impact on twentieth C. artists has therefore been absent. Recent work points to a more complex situation. Holländer (1973) notes links between the tradition of anamorphic perspective and the surrealists. Clair (1977-1978) documents very carefully how Duchamp’s painting builds on seventeenth C. exemplars by Nicéron and Dubreuil. Henderson (1983) documents how early twentieth C. artists, responding to developments in both mathematics and science, were attempting to integrate a fourth dimension in space and not simply abandon space altogether.As yet we have no clear picture of what was happening at the level of perspectival theory. In terms of textbooks published there was a decline. Between 1900 and 1925 there were only c. 300 published and between 1925 and 1950 there were but 200 new texts on perspective published, i.e. only half of that published in the heyday of Impressionism (1875-1900). Between 1950 and 1975 the amount has again risen to 350. In all, from 1900 to the present, upwards of 900 treatises on linear perspective have been published. Hence contrary to Novotny’s claims perspective is alive and well and living. Natural, Mathematical
1960 – 1980Goals of art / representationOne of the enduring contributions of Sir Ernst Gombrich has been to emphasise multiple functions or goals of art: e.g. magic (which used to be termed primitive art); pattern (Sense of Order), mimesis (Art and IllusionImage and the EyeIllusion in Nature and Art), expression and abstraction (Meditations on a Hobbyhorse) and symbolism (Symbolic Images). In this approach some functions of art do not need, and sometimes even preclude, perspective, while others encourage its use. Natural, Mathematical
1967IMAX CinemaIMAX is a proprietary system of high-resolution cameras, film formats, film projectors, and theaters known for having very large screens with a tall aspect ratio and steep stadium seating. Graeme Ferguson, Roman Kroitor, Robert Kerr, and William C. Shaw were the co-founders of what would be named the IMAX Corporation (founded in September 1967 as Multiscreen Corporation, Limited), and they developed the first IMAX cinema projection standards in the late 1960s and early 1970s in Canada. It all began when a small group of Canadian experimental filmmakers came together to produce a multi-screen film installation at EXPO ‘67 in Montreal. The installation was part of a competition to create the first truly large-screen film experience. The filmmakers did it by syncing nine projectors together.Natural, Instrument
1967MandelbrotFractalsThis article was entitled “How long is the coast of Britain? Statistical self-similarity and fractional dimension”, from Science, vol. 155, p. 636-638, where the author questions the validity of Technical Perspective (for example linear perspective). One of the fundamental tenets of Renaissance perspective was the inverse size-distance law which stated that if one doubled the distance the represented size was one half, if one trebled the distance the size was one third and so on. Mandelbrot’s article about the size of the coast of Britain implicitly introduced a spanner into this assumption by showing that size was a function of scale as well as distance. In a sense we have been vaguely aware of this ever since the seventeenth C.. The shape of an ordinary image is transformed entirely when we change the scale of its image radically in in a telescope or a microscope.Fractals may have brought this problem into focus, but fractals assume a principle of iteration, i.e. their basic patterns are repeated and hence remain independent of scale. Hence they do not solve the problem which they have raised. What is needed is a new approach to perspective that takes into account scale as well as distance, whereby any given shape only applies within a given range of scales. This is important in a world where we travel between scales with greater frequency.Natural, Instrument
1979J.J. GibsonJ.J. Gibson and the Visual Field J. J. Gibson called visual space the visual field and linked geometrical space with the visual world. There is more to this change of terms than is at first apparent. In the nineteenth C. it was generally assumed that visual space was subjective and geometrical space was objective. In Gibson’s approach both are susceptible to measurement and hence in some sense objective. In Gibson’s formulation there is also no opposition between vision and geometry. Geometry applies to both physical space and to (psychological) visual space. The question remains whether the same branch of geometry applies to both kinds of spaceNatural, Instrument
1983InternetJanuary 1, 1983 is considered the official birthday of the Internet. Prior to this, the various computer networks did not have a standard way to communicate with each other. A new communications protocol was established called Transfer Control Protocol/Internetwork Protocol (TCP/IP). This allowed different kinds of computers on different networks to “talk” to each other. ARPANET and the Defense Data Network officially changed to the TCP/IP standard on January 1, 1983, hence the birth of the Internet. All networks could now be connected by a universal language.Symbolic
1990World Wide WebEnglish scientist Tim Berners-Lee invented the World Wide Web in 1989. He wrote the first web browser in 1990 in Geneva, Switzerland.Symbolic
1990Medical ImagingMedical Imaging – New kinds of ‘transparent’, multi-layer, multi-view, and multi-scale perspective views, and associated visualisation technologies, receive prominence in medical work; and ever since the development of the first x-ray and various types of microscopes. Later technologies such as computed tomography, magnetic resonance imaging, and sonography further expanded the range of medical imaging techniques. These technologies allow for the visual exploration and representation of the body using new perspective views and images that vastly extend the capacities of human sightNatural, Instrument, Mathematical
20 C.New goals of art/representationOne goal might might be termed exploring, which can be subdivided into the mental world, the perceptual world and chance. The third of these, of which Jackson Pollock is an excellent example, aims to remove any clear one-to-one correspondence between artist and art. This goal, which results in abstract painting, was for a time frequently identified with modern art. It is becoming ever more obvious, however, that the other two areas of exploring, namely, the mental and the perceptual world, have inspired a much richer repertoire of images. Exploration of the mental world has led to depiction of dreams, phantasies and other psychological dimensions. As a result realism has been applied to new realms and in the process it has been transformed into surrealism, magic-realism, super-realism, hyper- realism.Natural, Instrument, Graphical
20 C.Artistic experiments Linear perspective continues to play a significant role in artistic explorations. But it is often used in conjunction with other methods. Delvaux frequently uses curved perspective in his streets. Dali moves subtly between regular perspective and anamorphosis. Magritte uses what appears to be linear perspective but then deliberately plays with its underlying principles of occlusion and transparency. Implicit in these experiments is an insistence that artists are not bound to a one-to-one correspondence between object and representation.Natural, Graphical
20 C. David Hockney David Hockney’s experiments with perspectiveHockney’s combinations of photography and painting are a further expression of these trends. He uses photo-montages to create multiple viewpoints within a single photo-assembly, depictions which work somewhat like cubist art. In Hockney’s case there is also another explicit concern. Linear perspective, he claims, created a wall between the viewer and the object represented. Inverted perspective, according to Hockney, offers a way of removing that wall and integrating both viewer and representation within the same space Natural, Graphical
20 C.Recording Visual SpaceSince the early nineteenth C. there has been a growing fascination with recording visual space as opposed to geometrical space, and this has been an important stimulus for the exploration of alternative picture planes. The most obvious versions entail imitating the convex surface of the eye as in the work of Barre and Flocon that was made accessible through an excellent translation by Robert Hansen, who developed his own method of hyperbolic perspective and subsequently explored the history of the subject. Natural, Graphical
20 C.Alternative picture planesOther artists, Hockney among them, are explicitly searching for means to incorporate the dimension of time into their representations of space. This new interest in the dynamic aspects of vision accounts for many of the recent experiments with alternative picture planes using spherical perspective, cylindrical perspective, hyperbolic, fisheye, tetraconic, polyconic and many another variants.Natural, Graphical, Instruments
20 C.Photogrammetry and Satellite ImagingHow does one translate a view of the spherical earth from space onto the flat surface of a map? Precise mathematical methods have been developed to exactly solve this problem.Natural, Graphical, Instruments
20 C.Computer screens – first interactive computer display developed In 1963, Ivan Sutherland engineered a revolution in computer graphics with his highly-interactive program Sketchpad. It enabled users to design and draw in real time directly on the computer display, using a light pen.Natural, Graphical, Instruments
20 C.Virtual Reality In the latter twentieth C., images of the mirror and the looking glass continue to be used, now in the context of the computer screen, and with a new goal of seeing the hitherto invisible. As Ivan Sutherland put it: “We lack corresponding familiarity with the forces on charged particles, forces in non-uniform fields, the effects of non-projective geometric transformations, and high energy, low friction motion. A display connected to a digital computer gives us a chance to gain familiarity with concepts not realizable in the physical world. It is a looking glass into a mathematical wonderland. Virtual reality is introducing new, dynamic interplays between egocentric and exocentric viewpoints, including the ability to move through both walls and windows enabling seamless transitions between interiors and exteriors”.Natural, Graphical, Instruments
20 C.Artist Dick TermesDick Termes is an American artist who uses a six point perspective system that he devised to create unique paintings on large spheres called Termespheres. He is the world’s leading spherical artistNatural, Graphical, Instruments
Table 5: Perspective in the 20th Century

21st Century

The 21st Century is ushering in the era of Digital Perspective. A host of new technologies are being applied to a huge variety of problems in terms of New Media systems, whereby amazing new perspective techniques are being used in digital filmmaking, Motion Capture, real-time and online gaming, so-called Metaverse systems, plus Virtual, Augmented, Extended Reality systems, etc.

21 C.Paul Debevec (computer modelling and generation of different kinds of perspective image/view)New principles, forms, applications of Technical PerspectiveIf perspective is defined in a narrow sense as linear perspective then one of the major reasons for its continued popularity is a growing historical awareness which seeks both to understand methods developed in the Renaissance and apply new technologies in the analysis thereof. Yet there are significant contrasts between Renaissance methods and modern developments.The Renaissance paid lip service to equations between perspective and vision, while at the same time linking perspective increasingly with geometry and committing themselves to recording geometrical space of the physical world. Some twentieth C. artists have continued this tradition in their explorations of realism, hyper-realism, and surrealism. Others have abandoned this commitment and focussed increasingly on the exploration of visual space, both exterior and interior. This has led to new goals of art in terms of exploring perceptual, mental, dream, psychological and even psycho-pathological states.As a result, whereas Renaissance artists focussed attention on linear picture planes, modern C. artists explored many alternative shapes of picture planes. They also contradicted the traditional transparency-occlusion principles of perspective in their quest for artistic freedom. Hence whereas Renaissance artists established a one-to-one correspondence between object and representation, twentieth and twenty-first C. artists strive to demonstrate the contrary. Natural (Environmental), Natural (Visual), Natural (Environmental), Graphical, Mathematical
21 C.YouTube, Netflix, Faecbook, Instagram Rise of broad-band communications, networked systems and digital streamingNew Media systems allow access to millions of television and Internet channels; along with capability of individuals to broadcast content from mobile phones etc.Natural (Environmental), Natural (Visual), Graphical, Mathematical, Instrument, Media
21 C.Super-high-resolution digital cameras and networked TelevisionsSuper-high-resolution digital cameras; plus super-high-resolution digital monitors/televisions (4k, 8k, and 16k display pixels in widest aspect). High definition televisions combined with access to millions of channels (many with live content).Natural (Environmental), Natural (Visual), Graphical, Mathematical, Instrument, Media
21 C.New Media and Multi-view, Multi-scale, Multi-time Perspective(s)As defined on this site, we have Media Perspective, which refers to the particular imaging capabilities, and visual transformations provided by a new media system. Said media perspective, typically consists of multiple networked instances of other instrument/media perspectives. Examples of technologies that fit under the umbrella of media perspectives include: Internet and Web-based information systems, networked digital television systems, smartphones, and networked devices, satellite imaging systems, GPS, plus Virtual Reality (VR), Augmented Reality (AR), Mixed Reality (MR), and Extended Reality (XR) systems, etc. Whereby, in the case of a highly developed media perspective system, views from one or more of the other categories of perspective (listed above), may be connected/linked together and then ordered, constructed, matched, mixed, explored, and cross-matched, etc. The result is the formation of a new class of Multi-view Perspective. Henceforth, a new era is emerging, of multiple and all-encompassing virtual ‘worlds’!  Natural (Environmental), Natural (Visual), Graphical, Mathematical, Instrument, Media
21 C.James Cameron3-D movies, Virtual Reality, Motion Capture, Stagecraft and Avatar 1& 2 movie making systems.Stagecraft Motion Capture System: Virtual Environments: New ways to blend Virtual-Space Cinema Production with Real-Space Production. Use of real-time ray-tracing and real-time computer graphical rendering systems to project (in real-time) real on the virtual and vice-versa (Unreal Engine etc). Similar techniques used to produce the Avatar 1 and 2 movies. Three-dimensional (3D) and stereoscopic camera systems become ubiquitous: plus 3D televisions, 3D headsets to view and interact with 3D content, etc.Natural (Environmental), Natural (Visual), Graphical, Mathematical, Instrument, Media
Table 6: Perspective in the 21st Century


In the nineteenth century perspective was primarily of interest to historians of science (notably Poudra, Cremona) who saw therein a forerunner of descriptive geometry. This culminated in Gino Loria’s standard history.

Meanwhile, for art historians such as Doehlemann (1906) perspective appeared to hold a key to debates concerning chronology. Panofsky was stimulated by such ideas, but focussed attention on links between philosophical systems, theories of vision and methods of representation. He himself never analysed the perspectival construction of a single painting. His fellow art historians remained even more wary of perspective, the assumption being that if art be a question of genius and inspiration, it cannot have to do with technical laws. 

Looking back on the past decades, however, it is the impact of psychologists on the study of perspective that is most striking. Art historians may not agree with their sometimes facile notions of the development of perspective in art. Nonetheless, the psychologists have challenged us all to think anew about spatial perception. If the laws of linear perspective apply to both the natural world and painting do we perceive both differently or do we not? 

In the nineteenth century perspective still appeared of incidental interest in explaining a branch of mathematics or a school of paintings. In the twentieth century perspective emerged as a central problem of perception, as a basic factor in the debate how we perceive pictures, in how we define pictures. And if pictures are uniquely human, perspective promises new insight into our human uniqueness. 



Kim Henry Veltman (1980 - 2017).
Alan Stuart Radley (2023).


Radley, A.S. (2023) 'Perspective Category Theory'. Published on the Perspective Research Centre (PRC) website 2020 - 2023.

Veltman, K.H. (1994) 'The Sources of Perspective' - published as an online book (no images). Later published with images as 'The Encyclopaedia of Perspective' - Volumes 1, 2 - (2020) by Alan Stuart Radley at the Perspective Research Centre.

Veltman, K.H. (1994) 'The Literature of Perspective' - published as an online book (no images). Later published with images as 'The Encyclopaedia of Perspective' - Volumes 3, 4 - (2020) by Alan Stuart Radley at the Perspective Research Centre.

Veltman, K.H. (1980s-2020) 'The Bibliography of Perspective' - began as a card index system in the 1980s; before being transferred to a dBASE-3 database system on an IBM PC (1990s). Later the bibliography was made available on the web on the SUMS system (2002-2020). In 2020 the Bibliography of Perspective was published as part of'The Encyclopaedia of Perspective' - Volumes 6, 7, 8 - by Alan Stuart Radley at the Perspective Research Centre.

Copyright © 2020-23 Alan Stuart Radley.
All rights are reserved.