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112-630: The Centiloquium opens with a dedication to Syrus, like the classical astronomer Ptolemy 's astrological treatise the Tetrabiblos ("Four books"). Ptolemy was indeed accepted as its author by medieval Arabic, Hebrew and Latin scholars, and the book was widely taken up and quoted. In Arabic it was known as the Kitab al-Tamara ("Book of the Fruit"), the name supposedly a translation of the Greek καρπος meaning "fruit",

224-401: A hadith enjoining the preservation of good health. Its physicians inherited knowledge and traditional medical beliefs from the civilisations of classical Greece, Rome, Syria, Persia and India. These included the writings of Hippocrates such as on the theory of the four humours , and the theories of Galen . al-Razi ( c. 865–925) identified smallpox and measles, and recognized fever as

336-536: 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

448-417: 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

560-601: 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

672-470: 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

784-461: A conjunction of Jupiter and Saturn; but this is a doctrine developed by Arabic astrologers, not known to the Greeks. The author of the book is therefore now generally referred to as Pseudo-Ptolemy . One influential view, argued by Lemay (1978) and others, is that the original author of the work was in fact Ahmad ibn Yusuf himself, reckoning that presenting his views as a commentary on an unknown work by

896-408: A constant force produces a uniform motion; Abu'l-Barakāt al-Baghdādī (c. 1080 – 1164/5) disagreed, arguing that velocity and acceleration are two different things, and that force is proportional to acceleration, not to velocity. The Banu Musa brothers , Jafar-Muhammad, Ahmad and al-Hasan (c. early 9th century) invented automated devices described in their Book of Ingenious Devices . Advances on

1008-581: A cryptic text that all later alchemists up to and including Isaac Newton saw as the foundation of their art, first occurs in the Sirr al-khalīqa and in one of the works attributed to Jabir. In practical chemistry, the works of Jabir, and those of the Persian alchemist and physician Abu Bakr al-Razi (c. 865–925), contain the earliest systematic classifications of chemical substances. Alchemists were also interested in artificially creating such substances. Jabir describes

1120-467: A date between 1258 and 1266 for Manfred, King of Sicily , supposedly either from a variety of Arabic sources or from an unknown Arabic original. One hundred astrological propositions ascribed to Muhammad ibn Jabir al-Battani (c.858–929), also known as Albategnius , or in astrology as Bethem . The text also exists in many manuscripts as De consuetudinibus ("According to the customs"), ascribed to Abraham ibn Ezra (1089–1164). Ptolemy This

1232-402: 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

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1344-492: 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

1456-642: A map of the world for Roger , the Norman King of Sicily (ruled 1105–1154). He also wrote the Tabula Rogeriana (Book of Roger), a geographic study of the peoples, climates, resources and industries of the whole of the world known at that time. The Ottoman admiral Piri Reis ( c. 1470–1553) made a map of the New World and West Africa in 1513. He made use of maps from Greece, Portugal, Muslim sources, and perhaps one made by Christopher Columbus . He represented

1568-587: 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

1680-461: 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

1792-412: A part of a major tradition of Ottoman cartography. Islamic mathematicians gathered, organised and clarified the mathematics they inherited from ancient Egypt, Greece, India, Mesopotamia and Persia, and went on to make innovations of their own. Islamic mathematics covered algebra , geometry and arithmetic . Algebra was mainly used for recreation: it had few practical applications at that time. Geometry

1904-418: A part of the body's defenses. He wrote a 23-volume compendium of Chinese, Indian, Persian, Syriac and Greek medicine. al-Razi questioned the classical Greek medical theory of how the four humours regulate life processes . He challenged Galen's work on several fronts, including the treatment of bloodletting , arguing that it was effective. al-Zahrawi (936–1013) was a surgeon whose most important surviving work

2016-610: A standard type of text fī l-ḥisāb al hindī , (On the numbers of the Indians). A distinctive Western Arabic variant of the Eastern Arabic numerals began to emerge around the 10th century in the Maghreb and Al-Andalus (sometimes called ghubar numerals, though the term is not always accepted), which are the direct ancestor of the modern Arabic numerals used throughout the world. Islamic society paid careful attention to medicine, following

2128-543: 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

2240-478: 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

2352-467: 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

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2464-553: 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.,

2576-465: A wide range of institutions. The Islamic era began in 622. Islamic armies eventually conquered Arabia , Egypt and Mesopotamia , and successfully displaced the Persian and Byzantine Empires from the region within a few decades. Within a century, Islam had reached the area of present-day Portugal in the west and Central Asia in the east. The Islamic Golden Age (roughly between 786 and 1258) spanned

2688-474: Is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; Ancient 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

2800-572: 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;

2912-467: Is credited with several theorems of trigonometry, including the law of cosines , also known as Al-Kashi's Theorem. He has been credited with the invention of decimal fractions , and with a method like Horner's to calculate roots. He calculated π correctly to 17 significant figures. Sometime around the seventh century, Islamic scholars adopted the Hindu–Arabic numeral system , describing their use in

3024-672: 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

3136-705: 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 ,

3248-458: 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

3360-908: 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

3472-432: Is referred to as al-Tasrif (Medical Knowledge). It is a 30-volume set mainly discussing medical symptoms, treatments, and pharmacology. The last volume, on surgery, describes surgical instruments, supplies, and pioneering procedures. Avicenna (c. 980–1037) wrote the major medical textbook, The Canon of Medicine . Ibn al-Nafis (1213–1288) wrote an influential book on medicine; it largely replaced Avicenna's Canon in

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3584-659: 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

3696-518: 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

3808-413: 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

3920-662: 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

4032-410: 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

4144-720: The Islamic world . Islamic science survived the initial Christian reconquest of Spain , including the fall of Seville in 1248, as work continued in the eastern centres (such as in Persia). After the completion of the Spanish reconquest in 1492, the Islamic world went into an economic and cultural decline. The Abbasid caliphate was followed by the Ottoman Empire ( c. 1299–1922), centred in Turkey, and

4256-784: 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

4368-512: The Safavid Empire (1501–1736), centred in Persia, where work in the arts and sciences continued. Medieval Islamic scientific achievements encompassed a wide range of subject areas, especially mathematics , astronomy , and medicine . Other subjects of scientific inquiry included physics , alchemy and chemistry , ophthalmology , and geography and cartography . The early Islamic period saw

4480-611: The Sefer ha-Peri ("Book of the fruit") or Sefer ha-Ilan ("Book of the tree"). Regardless of its authorship, the text has been described as "one of the most influential texts in astrology's history". It was, for example, a standard set text for medical students at the University of Bologna in the fifteenth century. However, as even the original commentary on the book noted, the Centiloquium contains quite substantial differences in focus from

4592-457: 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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4704-497: The Tetrabiblos : for example, it is very concerned with " Interrogations ", the asking of astrological questions about forthcoming plans and events, which is not treated at all in the earlier work. In the 1550s the Italian scholar Cardano considered this, and pronounced the work to be pseudoepigraphic – not by Ptolemy at all. This has also tended to be the view of subsequent centuries. For example, aphorism 63 discusses implications of

4816-850: The Umayyads of Córdoba , the Abbadids of Seville , the Samanids , the Ziyarids and the Buyids in Persia and beyond, spanning the period roughly between 786 and 1258. Islamic scientific achievements encompassed a wide range of subject areas, especially astronomy , mathematics , and medicine . Other subjects of scientific inquiry included alchemy and chemistry , botany and agronomy , geography and cartography , ophthalmology , pharmacology , physics , and zoology . Medieval Islamic science had practical purposes as well as

4928-461: 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

5040-519: 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

5152-421: The scientific method and their empirical , experimental and quantitative approach to scientific inquiry . In a more general sense, the positive achievement of Islamic science was simply to flourish, for centuries, in a wide range of institutions from observatories to libraries, madrasas to hospitals and courts, both at the height of the Islamic golden age and for some centuries afterwards. It did not lead to

5264-430: 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

5376-437: The 10th century, wrote The foundations of the true properties of Remedies , describing chemicals such as arsenious oxide and silicic acid . He distinguished between sodium carbonate and potassium carbonate , and drew attention to the poisonous nature of copper compounds, especially copper vitriol , and also of lead compounds. Al-Biruni (973–1050) wrote the Kitab al-Saydalah ( The Book of Drugs ), describing in detail

5488-526: The Eye ; this remained influential in the West until the 17th century. Abbas ibn Firnas (810–887) developed lenses for magnification and the improvement of vision. Ibn Sahl ( c. 940–1000) discovered the law of refraction known as Snell's law . He used the law to produce the first Aspheric lenses that focused light without geometric aberrations. In the eleventh century Ibn al-Haytham (Alhazen, 965–1040) rejected

5600-485: 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

5712-569: The Greek ideas about vision, whether the Aristotelian tradition that held that the form of the perceived object entered the eye (but not its matter), or that of Euclid and Ptolemy which held that the eye emitted a ray. Al-Haytham proposed in his Book of Optics that vision occurs by way of light rays forming a cone with its vertex at the center of the eye. He suggested that light was reflected from different surfaces in different directions, thus causing objects to look different. He argued further that

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5824-425: 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

5936-760: The Islamic world with his six-volume Kitab al-Nabat ( Book of Plants ). Only volumes 3 and 5 have survived, with part of volume 6 reconstructed from quoted passages. The surviving text describes 637 plants in alphabetical order from the letters sin to ya , so the whole book must have covered several thousand kinds of plants. Al-Dinawari described the phases of plant growth and the production of flowers and fruit. The thirteenth century encyclopedia compiled by Zakariya al-Qazwini (1203–1283) – ʿAjā'ib al-makhlūqāt (The Wonders of Creation) – contained, among many other topics, both realistic botany and fantastic accounts. For example, he described trees which grew birds on their twigs in place of leaves, but which could only be found in

6048-626: The Islamic world, returning with a detailed knowledge of agronomy that fed into the Arab Agricultural Revolution . His practical and systematic book describes over 180 plants and how to propagate and care for them. It covered leaf- and root-vegetables, herbs, spices and trees. The spread of Islam across Western Asia and North Africa encouraged an unprecedented growth in trade and travel by land and sea as far away as Southeast Asia, China, much of Africa, Scandinavia and even Iceland. Geographers worked to compile increasingly accurate maps of

6160-417: The Islamic world. He wrote commentaries on Galen and on Avicenna's works. One of these commentaries, discovered in 1924, described the circulation of blood through the lungs . Optics developed rapidly in this period. By the ninth century, there were works on physiological, geometrical and physical optics. Topics covered included mirror reflection. Hunayn ibn Ishaq (809–873) wrote the book Ten Treatises on

6272-486: The Parts of Animals : 11–14, and Generation of Animals : 15–19. The book was mentioned by Al-Kindī (died 850), and commented on by Avicenna (Ibn Sīnā) in his The Book of Healing . Avempace (Ibn Bājja) and Averroes (Ibn Rushd) commented on and criticised On the Parts of Animals and Generation of Animals . Muslim scientists helped in laying the foundations for an experimental science with their contributions to

6384-455: 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

6496-461: 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

6608-529: The Younger (died 1015) and as the Medicamentis simplicibus by Abenguefit (c. 997 – 1074) respectively. Peter of Abano (1250–1316) translated and added a supplement to the work of al-Mardini under the title De Veneris . Ibn al-Baytar (1197–1248), in his Al-Jami fi al-Tibb , described a thousand simples and drugs based directly on Mediterranean plants collected along the entire coast between Syria and Spain, for

6720-422: 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

6832-472: 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

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6944-667: The book's aphorisms being seen as standing as the fruit or summation of the earlier treatise. It was translated at least four times into Latin, in which it was also known as the Liber Fructus , including by John of Seville in Toledo in 1136 and by Plato of Tivoli in Barcelona in 1138 (printed in Venice in 1493). In Hebrew it was translated at the same time by Tivoli's collaborator Abraham bar Hiyya , and again in 1314 by Kalonymus ben Kalonymus , as

7056-415: The countryside brought more crops and improved agricultural technology, especially irrigation . This supported the larger population and enabled culture to flourish. From the 9th century onwards, scholars such as Al-Kindi translated Indian , Assyrian , Sasanian (Persian) and Greek knowledge, including the works of Aristotle , into Arabic . These translations supported advances by scientists across

7168-506: 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,

7280-402: 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

7392-469: 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

7504-425: 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

7616-459: The establishment of theoretical frameworks in alchemy and chemistry . The sulfur-mercury theory of metals , first found in Sirr al-khalīqa ("The Secret of Creation", c. 750–850, falsely attributed to Apollonius of Tyana ), and in the writings attributed to Jabir ibn Hayyan (written c. 850–950), remained the basis of theories of metallic composition until the 18th century. The Emerald Tablet ,

7728-419: 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,

7840-463: The far-distant British Isles. The use and cultivation of plants was documented in the 11th century by Muhammad bin Ibrāhīm Ibn Bassāl of Toledo in his book Dīwān al-filāha (The Court of Agriculture), and by Ibn al-'Awwam al-Ishbīlī (also called Abū l-Khayr al-Ishbīlī) of Seville in his 12th century book Kitāb al-Filāha (Treatise on Agriculture). Ibn Bassāl had travelled widely across

7952-567: 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

8064-409: The first time exceeding the coverage provided by Dioscorides in classical times. Islamic physicians such as Ibn Sina described clinical trials for determining the efficacy of medical drugs and substances . The fields of physics studied in this period, apart from optics and astronomy which are described separately, are aspects of mechanics : statics , dynamics , kinematics and motion . In

8176-652: The goal of understanding. For example, astronomy was useful for determining the Qibla , the direction in which to pray, botany had practical application in agriculture, as in the works of Ibn Bassal and Ibn al-'Awwam , and geography enabled Abu Zayd al-Balkhi to make accurate maps. Islamic mathematicians such as Al-Khwarizmi , Avicenna and Jamshīd al-Kāshī made advances in algebra , trigonometry , geometry and Arabic numerals . Islamic doctors described diseases like smallpox and measles , and challenged classical Greek medical theory. Al-Biruni , Avicenna and others described

8288-491: The great Ptolemy would make them far more influential and sought after than merely issuing such a compilation under his own name. Others however still see the Centiloquium as potentially containing a core of genuinely Hellenistic material, which may then have suffered adaptation and partial substitution in the chain of transmission and translation. A Latin text containing one hundred propositions, again about astrology rather than Hermeticism , compiled by Stephen of Messina at

8400-547: The highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria . There are several characters and items named after Ptolemy, including: Islamic science Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Abbasid Caliphate of Baghdad ,

8512-553: 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

8624-599: 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

8736-609: The known world, starting from many existing but fragmentary sources. Abu Zayd al-Balkhi (850–934), founder of the Balkhī school of cartography in Baghdad, wrote an atlas called Figures of the Regions (Suwar al-aqalim). Al-Biruni (973–1048) measured the radius of the earth using a new method. It involved observing the height of a mountain at Nandana (now in Pakistan). Al-Idrisi (1100–1166) drew

8848-500: 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

8960-491: The mathematics of reflection and refraction needed to be consistent with the anatomy of the eye. He was also an early proponent of the scientific method , the concept that a hypothesis must be proved by experiments based on confirmable procedures or mathematical evidence, five centuries before Renaissance scientists . Advances in botany and chemistry in the Islamic world encouraged developments in pharmacology . Muhammad ibn Zakarīya Rāzi (Rhazes) (865–915) promoted

9072-425: The medical uses of chemical compounds. Abu al-Qasim al-Zahrawi (Abulcasis) (936–1013) pioneered the preparation of medicines by sublimation and distillation . His Liber servitoris provides instructions for preparing "simples" from which were compounded the complex drugs then used. Sabur Ibn Sahl (died 869) was the first physician to describe a large variety of drugs and remedies for ailments. Al-Muwaffaq , in

9184-555: 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

9296-530: The most sophisticated parts of Greek geometry. Islamic mathematics reached its apogee in the Eastern part of the Islamic world between the tenth and twelfth centuries. Most medieval Islamic mathematicians wrote in Arabic, others in Persian. Al-Khwarizmi (8th–9th centuries) was instrumental in the adoption of the Hindu–Arabic numeral system and the development of algebra , introduced methods of simplifying equations, and used Euclidean geometry in his proofs. He

9408-477: 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

9520-620: The movements of the sun, moon and planets across the sky. Copernicus (1473–1543) later used some of Al-Battani's astronomic tables. Al-Zarqali (1028–1087) developed a more accurate astrolabe , used for centuries afterwards. He constructed a water clock in Toledo , discovered that the Sun's apogee moves slowly relative to the fixed stars, and obtained a good estimate of its motion for its rate of change. Nasir al-Din al-Tusi (1201–1274) wrote an important revision to Ptolemy's 2nd-century celestial model . When Tusi became Helagu 's astrologer, he

9632-485: The nature of the cosmos and to practical purposes. One application involved determining the Qibla , the direction to face during prayer . Another was astrology , predicting events affecting human life and selecting suitable times for actions such as going to war or founding a city. Al-Battani (850–922) accurately determined the length of the solar year. He contributed to the Tables of Toledo , used by astronomers to predict

9744-409: The object is in opposition to its natural motion. He concluded that continuation of motion depends on the inclination that is transferred to the object, and that the object remains in motion until the mayl is spent. He also claimed that a projectile in a vacuum would not stop unless it is acted upon. That view accords with Newton's first law of motion , on inertia. As a non-Aristotelian suggestion, it

9856-461: 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

9968-481: The period of the Abbasid Caliphate (750–1258), with stable political structures and flourishing trade. Major religious and cultural works of the Islamic empire were translated into Arabic and occasionally Persian . Islamic culture inherited Greek , Indic , Assyrian and Persian influences. A new common civilisation formed, based on Islam. An era of high culture and innovation ensued, with rapid growth in population and cities. The Arab Agricultural Revolution in

10080-482: The pre-Islamic Persian tradition in astronomy. Astronomers from India were invited to the court of the caliph in the late eighth century; they explained the rudimentary trigonometrical techniques used in Indian astronomy. Ancient Greek works such as Ptolemy 's Almagest and Euclid's Elements were translated into Arabic. By the second half of the ninth century, Islamic mathematicians were already making contributions to

10192-461: The preparation of hundreds of drugs made from medicinal plants and chemical compounds. Islamic physicists such as Ibn Al-Haytham , Al-Bīrūnī and others studied optics and mechanics as well as astronomy, and criticised Aristotle 's view of motion. During the Middle Ages, Islamic science flourished across a wide area around the Mediterranean Sea and further afield, for several centuries, in

10304-555: The properties of drugs, the role of pharmacy and the duties of the pharmacist. Ibn Sina (Avicenna) described 700 preparations, their properties, their mode of action and their indications. He devoted a whole volume to simples in The Canon of Medicine . Works by Masawaih al-Mardini ( c. 925–1015) and by Ibn al-Wafid (1008–1074) were printed in Latin more than fifty times, appearing as De Medicinis universalibus et particularibus by Mesue

10416-401: 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

10528-486: 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

10640-405: 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

10752-560: The sixth century John Philoponus ( c.  490  – c.  570 ) rejected the Aristotelian view of motion. He argued instead that an object acquires an inclination to move when it has a motive power impressed on it. In the eleventh century Ibn Sina adopted roughly the same idea, namely that a moving object has force which is dissipated by external agents like air resistance. Ibn Sina distinguished between "force" and "inclination" ( mayl ); he claimed that an object gained mayl when

10864-614: The solution to a chessboard problem involving an exponential series. Al-Farabi ( c. 870–950) attempted to describe, geometrically, the repeating patterns popular in Islamic decorative motifs in his book Spiritual Crafts and Natural Secrets in the Details of Geometrical Figures . Omar Khayyam (1048–1131), known in the West as a poet, calculated the length of the year to within 5 decimal places, and found geometric solutions to all 13 forms of cubic equations, developing some quadratic equations still in use. Jamshīd al-Kāshī (c. 1380–1429)

10976-474: 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

11088-451: 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

11200-440: 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

11312-517: 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

11424-423: The subject were also made by al-Jazari and Ibn Ma'ruf . Many classical works, including those of Aristotle, were transmitted from Greek to Syriac, then to Arabic, then to Latin in the Middle Ages. Aristotle's zoology remained dominant in its field for two thousand years. The Kitāb al-Hayawān (كتاب الحيوان, English: Book of Animals ) is a 9th-century Arabic translation of History of Animals : 1–10, On

11536-496: 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

11648-426: The synthesis of ammonium chloride ( sal ammoniac ) from organic substances , and Abu Bakr al-Razi experimented with the heating of ammonium chloride, vitriol , and other salts , which would eventually lead to the discovery of the mineral acids by 13th-century Latin alchemists such as pseudo-Geber . Astronomy became a major discipline within Islamic science. Astronomers devoted effort both towards understanding

11760-573: 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

11872-493: Was essentially abandoned until it was described as "impetus" by Jean Buridan (c. 1295–1363), who was likely influenced by Ibn Sina's Book of Healing . In the Shadows , Abū Rayḥān al-Bīrūnī (973–1048) describes non-uniform motion as the result of acceleration. Ibn-Sina's theory of mayl tried to relate the velocity and weight of a moving object, a precursor of the concept of momentum . Aristotle's theory of motion stated that

11984-449: Was given an observatory and gained access to Chinese techniques and observations. He developed trigonometry as a separate field, and compiled the most accurate astronomical tables available up to that time. The study of the natural world extended to a detailed examination of plants. The work done proved directly useful in the unprecedented growth of pharmacology across the Islamic world. Al-Dinawari (815–896) popularised botany in

12096-502: 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

12208-464: 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

12320-481: Was studied at different levels. Some texts contain practical geometrical rules for surveying and for measuring figures. Theoretical geometry was a necessary prerequisite for understanding astronomy and optics, and it required years of concentrated work. Early in the Abbasid caliphate (founded 750), soon after the foundation of Baghdad in 762, some mathematical knowledge was assimilated by al-Mansur 's group of scientists from

12432-517: Was the first to treat algebra as an independent discipline in its own right, and presented the first systematic solution of linear and quadratic equations . Ibn Ishaq al-Kindi (801–873) worked on cryptography for the Abbasid Caliphate , and gave the first known recorded explanation of cryptanalysis and the first description of the method of frequency analysis . Avicenna ( c. 980–1037) contributed to mathematical techniques such as casting out nines . Thābit ibn Qurra (835–901) calculated

12544-499: 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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