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80-465: The Book of Optics presented experimentally founded arguments against the widely held extramission theory of vision (as held by Euclid in his Optica ), and proposed the modern intromission theory , the now accepted model that vision takes place by light entering the eye. The book is also noted for its early use of the scientific method , its description of the camera obscura , and its formulation of Alhazen's problem . The book extensively affected

160-542: A Roman citizen . Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage , stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included Ptolemy

240-417: A perfect fourth ) and octaves . Ptolemy reviewed standard (and ancient, disused ) musical tuning practice of his day, which he then compared to his own subdivisions of the tetrachord and the octave , which he derived experimentally using a monochord / harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( psyche ), and the planets ( harmony of

320-612: A Roman citizen, but was ethnically either a Greek or at least a Hellenized Egyptian. Astronomy was the subject to which Ptolemy devoted the most time and effort; about half of all the works that survived deal with astronomical matters, and even others such as the Geography and the Tetrabiblos have significant references to astronomy. Ptolemy's Mathēmatikē Syntaxis ( Greek : Μαθηματικὴ Σύνταξις , lit.   ' Mathematical Systematic Treatise ' ), better known as

400-476: A coherent mathematical description, which persists to the present as just intonation – the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. During the Renaissance , Ptolemy's ideas inspired Kepler in his own musings on the harmony of the world ( Harmonice Mundi , Appendix to Book V). The Optica ( Koine Greek : Ὀπτικά ), known as

480-408: A distinct quality of a form and travelling from every point on an object in straight lines. Through experimentation he concluded that color cannot exist without air. As objects radiate light in straight lines in all directions, the eye must also be hit with this light over its outer surface. This idea presented a problem for al-Haytham and his predecessors, as if this was the case, the rays received by

560-402: A handful of places. Ptolemy's real innovation, however, occurs in the second part of the book, where he provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About 6 300 of these places and geographic features have assigned coordinates so that they can be placed in a grid that spanned the globe. Latitude was measured from

640-457: A light source, such as the sun, to visible objects, and finishing with the detector, such as a human eye or camera. In the fifth century BC , Empedocles postulated that everything was composed of four elements ; fire, air, earth, and water. He believed that Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye, making sight possible. If this were true, then one could see during

720-498: A long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers of Aristoxenus ), backed up by empirical observation (in contrast to the excessively theoretical approach of the Pythagoreans ). Ptolemy introduces

800-462: A mathematical model whose only constraint was to save the phenomena, without the need of a strict correspondence between each theoretical entity and a physical counterpart. Measuring the speed of light was one line of evidence that spelled the end of emission theory as anything other than a metaphor. Alhazen was the first person to explain that vision occurs when light reflects from an object into one's eyes. The rise of rationalist physics in

880-601: A method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the analemma . In another work, the Phaseis ( Risings of the Fixed Stars ), Ptolemy gave a parapegma , a star calendar or almanac , based on

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960-466: A much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy , remains the subject of conjecture. Ptolemy wrote a work entitled Harmonikon ( Greek : Ἁρμονικόν ), known as the Harmonics , on music theory and the mathematics behind musical scales in three books. Harmonics begins with a definition of harmonic theory, with

1040-558: A temple at Canopus , around 146–147 AD, known as the Canobic Inscription . Although the inscription has not survived, someone in the sixth century transcribed it, and manuscript copies preserved it through the Middle Ages. It begins: "To the saviour god, Claudius Ptolemy (dedicates) the first principles and models of astronomy", following by a catalogue of numbers that define a system of celestial mechanics governing

1120-482: A thousand years or more". It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain. Much of the content of the Tetrabiblos was collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which

1200-472: A very complex theoretical model built in order to explain a false assumption. Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation is quite late, however, and there is no evidence to support it. It

1280-562: A view supported by the Stoics. Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in epistemological and psychological discussions across his corpus. He wrote a short essay entitled On the Criterion and Hegemonikon ( Greek : Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ ), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e.,

1360-481: Is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; ‹See Tfd› Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c.  100  – c.  170 AD) was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about a dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first

1440-587: Is ancestral to the modern system of constellations but, unlike the modern system, they did not cover the whole sky (only what could be seen with the naked eye in the northern hemisphere). For over a thousand years, the Almagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa. The Almagest was preserved, like many extant Greek scientific works, in Arabic manuscripts;

1520-689: Is his Geographike Hyphegesis ( Greek : Γεωγραφικὴ Ὑφήγησις ; lit.   ' Guide to Drawing the Earth ' ), known as the Geography , a handbook on how to draw maps using geographical coordinates for parts of the Roman world known at the time. He relied on previous work by an earlier geographer, Marinus of Tyre , as well as on gazetteers of the Roman and ancient Persian Empire . He also acknowledged ancient astronomer Hipparchus for having provided

1600-725: Is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria c.  168 . Ptolemy's Greek name , Ptolemaeus ( Πτολεμαῖος , Ptolemaîos ), is an ancient Greek personal name . It occurs once in Greek mythology and is of Homeric form . It was common among the Macedonian upper class at the time of Alexander the Great and there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter ,

1680-462: Is known that Ptolemy lived in or around the city of Alexandria , in the Roman province of Egypt under Roman rule . He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen . He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing

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1760-984: Is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. In later Arabic sources, he was often known as "the Upper Egyptian ", suggesting he may have had origins in southern Egypt . Arabic astronomers , geographers , and physicists referred to his name in Arabic as Baṭlumyus ( Arabic : بَطْلُمْيوس ). Ptolemy wrote in Koine Greek , and can be shown to have used Babylonian astronomical data . He might have been

1840-683: Is sometimes known as the Apotelesmatika ( Greek : Αποτελεσματικά , lit.   ' On the Effects ' ) but more commonly known as the Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost

1920-1041: Is the light that comes from accidental objects. Accidental light can only exist if there is a source of primary light. Both primary and secondary light travel in straight lines. Transparency is a characteristic of a body that can transmit light through them, such as air and water, although no body can completely transmit light or be entirely transparent. Opaque objects are those through which light cannot pass through directly, although there are degrees of opaqueness which determine how much light can actually pass through. Opaque objects are struck with light and can become luminous bodies themselves which radiate secondary light. Light can be refracted by going through partially transparent objects and can also be reflected by striking smooth objects such as mirrors, traveling in straight lines in both cases. Al-Haytham presented many experiments in Optics that upheld his theories about light and its transmission. He also wrote that color acts much like light, being

2000-418: Is the proposal that visual perception is accomplished by eye beams emitted by the eyes . This theory has been replaced by intromission theory (or intromissionism ), which is that visual perception comes from something representative of the object (later established to be rays of light reflected from it) entering the eyes. Modern physics has confirmed that light is physically transmitted by photons from

2080-528: The Almagest ) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages . However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on epicycles has come to symbolize

2160-413: The Almagest , is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers had developed arithmetical techniques for calculating and predicting astronomical phenomena, these were not based on any underlying model of the heavens; early Greek astronomers, on the other hand, provided qualitative geometrical models to "save the appearances" of celestial phenomena without

2240-662: The Almagest was the first, concerned with the influences of the celestial bodies in the sublunary sphere . Thus explanations of a sort are provided for the astrological effects of the planets , based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology , for similar reasons. The great respect in which later astrologers held

2320-410: The Geography is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and world maps in surviving manuscripts date from c.  1300 AD (after the text was rediscovered by Maximus Planudes ), there are some scholars who think that such maps go back to Ptolemy himself. Ptolemy wrote an astrological treatise, in four parts, known by

2400-736: The Optics, is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by Eugenius of Palermo ( c.  1154 ). In it, Ptolemy writes about properties of sight (not light), including reflection , refraction , and colour . The work is a significant part of the early history of optics and influenced the more famous and superior 11th-century Book of Optics by Ibn al-Haytham . Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement, and binocular vision. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors. He offered an obscure explanation of

2480-463: The Tetrabiblos derived from its nature as an exposition of theory, rather than as a manual. A collection of one hundred aphorisms about astrology called the Centiloquium , ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos as a kind of summation. It is now believed to be

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2560-461: The equator , as it is today, but Ptolemy preferred to express it as climata , the length of the longest day rather than degrees of arc : The length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle . One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient Silk Road , and which scholars have been trying to locate ever since. In

2640-519: The harmonic canon (Greek name) or monochord (Latin name), which is an experimental musical apparatus that he used to measure relative pitches, and used to describe to his readers how to demonstrate the relations discussed in the following chapters for themselves. After the early exposition on to build and use monochord to test proposed tuning systems, Ptolemy proceeds to discuss Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that

2720-430: The "criterion" of truth), as well as with the nature and structure of the human psyche or soul, particularly its ruling faculty (i.e., the hegemonikon ). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. On the Criterion is also noteworthy for being the only one of Ptolemy's works that is devoid of mathematics . Elsewhere, Ptolemy affirms

2800-464: The 17th century led to a novel version of the intromissionist theory that proved extremely influential and displaced any legacies of the old emissive theories. In Cartesian physics, light was the sensation of pressure emitted by surrounding objects that sought to move, as transmitted through the rotatory motion of material corpuscles. These views extended to Isaac Newton 's corpuscular theory of light , and would be adopted by John Locke and other

2880-482: The 18th-century luminaries. Winer et al. (2002) have found evidence that as many as 50% of adults believe in emission theory. Rupert Sheldrake claims to have found evidence for emission theory through his experiments in the sense of being stared at. Sometimes, the emission theory is explained by analogy with echolocation and sonar . For example, in explaining Ptolemy's theory, a psychologist stated: "Ptolemy’s ‘extramission’ theory of vision proposed scaling

2960-500: The 2nd century, likewise endorsed the extramission theory ( De Usu Partium Corporis Humani ). His theory contained anatomical and physiological details which could not be found in the works of mathematicians and philosophers. Due to this feature and his medical authority, his view held considerable influence in the pre-modern Middle East and Europe, especially among medical doctors in these regions. Adherents of emission theory cited at least two lines of evidence for it. The light from

3040-489: The French astronomer Delambre in the early 1800s which were repeated by R.R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded: It also confirms that Ptolemy’s Star Catalogue

3120-477: The Greek term Tetrabiblos (lit. "Four Books") or by its Latin equivalent Quadripartitum . Its original title is unknown, but may have been a term found in some Greek manuscripts, Apotelesmatiká ( biblía ), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the Tetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of

3200-455: The Sun or Moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards. The work is divided into three major sections. The first section (Book II) deals with direct vision from first principles and ends with a discussion of binocular vision. The second section (Books III-IV) treats reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with refraction and includes

3280-465: The Wise, who composed the book of the Almagest ". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest . The correct answer

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3360-422: The ability to make any predictions. The earliest person who attempted to merge these two approaches was Hipparchus , who produced geometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. Ptolemy, following Hipparchus, derived each of his geometrical models for the Sun, Moon, and the planets from selected astronomical observations done in

3440-498: The angular size of objects using light rays that were emitted by the eyes and reflected back by objects. In practice some animals (bats, dolphins, whales, and even some birds and rodents) have evolved what is effectively an ‘extramission’ theory of audition to address this very concern. " Note this account of the Ptolemaic theory ('bouncing back of visual ray') differs from ones found in other sources. Ptolemy#Optics This

3520-476: The appearances and disappearances of stars over the course of the solar year. The Planisphaerium ( Greek : Ἅπλωσις ἐπιφανείας σφαίρας , lit.   ' Flattening of the sphere ' ) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. Ptolemy also erected an inscription in

3600-433: The crystalline humor and the vitreous humor at the back. These, however, do not play as critical of a role in vision as the crystalline humor. The crystalline humor transmits the image it perceives to the brain through an optic nerve. The Book of Optics was most strongly influenced by Ptolemy's Optics , while the description of the anatomy and physiology of the eye was based upon an account by Galen. The Book of Optics

3680-510: The data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through Theon of Alexandria 's version. Although Ptolemy's Handy Tables do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or zījes . Additionally,

3760-513: The development of optics, physics and mathematics in Europe between the 13th and 17th centuries. Before the Book of Optics was written, two theories of vision existed. The extramission or emission theory was forwarded by the mathematicians Euclid and Ptolemy , who asserted that certain forms of radiation are emitted from the eyes onto the object which is being seen. When these rays reached

3840-402: The earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence) show signs of being obtained from an arithmetic progression. However, according to Mark Smith, Ptolemy's table was based in part on real experiments. Ptolemy's theory of vision consisted of rays (or flux) coming from the eye forming a cone, the vertex being within

3920-469: The elevation of the north celestial pole for a few cities. Although maps based on scientific principles had been made since the time of Eratosthenes ( c.  276  – c.  195 BC ), Ptolemy improved on map projections . The first part of the Geography is a discussion of the data and of the methods he used. Ptolemy notes the supremacy of astronomical data over land measurements or travelers' reports, though he possessed these data for only

4000-425: The empirical musical relations he identified by testing pitches against each other: He was able to accurately measure relative pitches based on the ratios of vibrating lengths two separate sides of the same single string , hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into

4080-436: The eye from every point on the object would cause a blurred image. Al-Haytham solved this problem using his theory of refraction. He argued that although the object sends an infinite number of rays of light to the eye, only one of these lines falls on the eye perpendicularly: the other rays meet the eye at angles that are not perpendicular. According to al-Haytham, this causes them to be refracted and weakened. He believed that all

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4160-419: The eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy,

4240-401: The eyes of some animals (such as cats, which modern science has determined have highly reflective eyes ) could also be seen in "darkness". Adherents of intromission theory countered by saying that if emission theory were true, then someone with weak eyes should have their vision improved when someone with good eyes looks at the same objects. Some argued that Euclid's version of emission theory

4320-581: The first pharaoh of the Ptolemaic Kingdom . Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name Claudius is a Roman name, belonging to the gens Claudia ; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been

4400-553: The history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed around 9:55am the day prior. In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud," and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error". The charges laid by Newton and others have been

4480-616: The introduction to the Handy Tables survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title Arrangement and Calculation of the Handy Tables . The Planetary Hypotheses ( Greek : Ὑποθέσεις τῶν πλανωμένων , lit.   ' Hypotheses of the Planets ' ) is a cosmological work, probably one of the last written by Ptolemy, in two books dealing with

4560-500: The mathematics of music should be based on only the one specific ratio of 3:2, the perfect fifth , and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller tetrachords (combinations of four pitch ratios which together make

4640-566: The modern title is thought to be an Arabic corruption of the Greek name Hē Megistē Syntaxis (lit. "The greatest treatise"), as the work was presumably known in Late Antiquity . Because of its reputation, it was widely sought and translated twice into Latin in the 12th century , once in Sicily and again in Spain. Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until

4720-477: The motions of the Sun, Moon, planets, and stars. In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a meteoroscope ( μετεωροσκόπιον or μετεωροσκοπεῖον ). The text, which comes from an eighth-century manuscript which also contains Ptolemy's Analemma , was identified on the basis of both its content and linguistic analysis as being by Ptolemy. Ptolemy's second most well-known work

4800-468: The night just as well as during the day, so Empedocles postulated that there were two different types of emanations that interacted in some way: one that emanated from an object to the eye, and another that emanated from the eye to an object. He compared these outward-flowing emanations to the emission of light from a lantern. Around 400 BC, emission theory was held by Plato . Around 300 BC, Euclid wrote Optics and Catoptrics , in which he studied

4880-576: The object being viewed is considered to be a compilation of an infinite number of points, from which rays of light are projected. In the Book of Optics , al-Haytham hypothesized the existence of primary and secondary light, with primary light being the stronger or more intense of the two. The book describes how the essential form of light comes from self-luminous bodies and that accidental light comes from objects that obtain and emit light from those self-luminous bodies. According to Ibn al-Haytham, primary light comes from self-luminous bodies and secondary light

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4960-453: The object they allowed the viewer to perceive its color, shape and size. An early version of the intromission theory, held by the followers of Aristotle and Galen , argued that sight was caused by agents, which were transmitted to the eyes from either the object or from its surroundings. Al-Haytham offered many reasons against the extramission theory, pointing to the fact that eyes can be damaged by looking directly at bright lights, such as

5040-461: The observations were taken at 12:30pm. The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book The Crime of Claudius Ptolemy , which asserted that Ptolemy fabricated many of his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in

5120-509: The properties of sight. Euclid postulated that the visual ray emitted from the eye travelled in straight lines, described the laws of reflection, and mathematically studied the appearance of objects by direct vision and by reflection. Ptolemy (c. 2nd century) wrote Optics , a work marking the culmination of the ancient Greek optics, in which he developed theories of direct vision (optics proper), vision by reflection (catoptics), and, notably, vision by refraction (dioptrics). Galen , also in

5200-401: The radius of the sphere of the fixed stars was 20 000 times the radius of the Earth. The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a geocentric perspective, much as an orrery would have done for a heliocentric one, presumably for didactic purposes. The Analemma is a short treatise where Ptolemy provides

5280-408: The rays other than the one that hits the eye perpendicularly are not involved in vision. In al-Haytham's structure of the eye, the crystalline humor is the part that receives light rays from the object and forms a visual cone, with the object being perceived as the base of the cone and the center of the crystalline humor in the eye as the vertex. Other parts of the eye are the aqueous humor in front of

5360-486: The reappearance of heliocentric models during the scientific revolution . Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent miscalculation is Ptolemy's use of measurements that he claimed were taken at noon, but which systematically produce readings now shown to be off by half an hour, as if

5440-405: The secondary literature, while noting that issues with the accuracy of Ptolemy's observations had long been known. Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time. In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by

5520-474: The spanning of more than 800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The Almagest also contains a star catalogue , which is a version of a catalogue created by Hipparchus . Its list of forty-eight constellations

5600-451: The spheres ). Although Ptolemy's Harmonics never had the influence of his Almagest or Geography , it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings. In particular, it is a nascent form of what in the following millennium developed into the scientific method, with specific descriptions of the experimental apparatus that he built and used to test musical conjectures, and

5680-440: The structure of the universe and the laws that govern celestial motion . Ptolemy goes beyond the mathematical models of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1 210 Earth radii (now known to actually be ~23 450 radii), while

5760-517: The subject of wide discussions and received significant push back from other scholars against the findings. Owen Gingerich , while agreeing that the Almagest contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein , who questioned Newton's findings and suggested that he had misunderstood

5840-414: The sun. He wrote of the low probability that the eye can fill the entirety of space as soon as the eyelids are opened as an observer looks up into the night sky. Using the intromission theory as a foundation, he formed his own theory that an object emits rays of light from every point on its surface which then travel in all directions, thereby allowing some light into a viewer's eyes. According to this theory,

5920-501: The supremacy of mathematical knowledge over other forms of knowledge. Like Aristotle before him, Ptolemy classifies mathematics as a type of theoretical philosophy; however, Ptolemy believes mathematics to be superior to theology or metaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic and Aristotelian traditions, where theology or metaphysics occupied

6000-587: The third part of the Geography , Ptolemy gives instructions on how to create maps both of the whole inhabited world ( oikoumenē ) and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China , and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa ); Ptolemy

6080-489: Was translated into Latin by an unknown scholar at the end of the 12th (or the beginning of the 13th) century. The work was influential during the Middle Ages . It was printed by Friedrich Risner in 1572, as part of his collection Opticae thesaurus . This included a book on twilight falsely attributed to Alhazen, as well as a work on optics by Vitello . Emission theory (vision) Emission theory or extramission theory (variants: extromission ) or extromissionism

6160-568: Was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second is the Geography , which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world . The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This

6240-464: Was not based solely on data from Hipparchus’ Catalogue. ... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors. The Handy Tables ( Greek : Πρόχειροι κανόνες ) are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all

6320-446: Was purely metaphorical, highlighting mainly the geometrical relations between eyes and objects. The geometry of classical optics is equivalent no matter which direction light is considered to move because light is modeled by its path, not as a moving object. However, his theory of clarity of vision (the circular appearance of far rectangular objects) makes sense only if the ray emits from eyes. Alternatively, Euclid's can be interpreted as

6400-506: Was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. It seems likely that the topographical tables in the second part of the work (Books 2–7) are cumulative texts, which were altered as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of

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