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Article

Antikythera Mechanism  

Alexander Jones

The Antikythera Mechanism (National Archaeological Museum, Athens, inv. X 15087) was a Hellenistic gearwork device for displaying astronomical and chronological functions. Substantial but highly corroded remains of the instrument were recovered from an ancient shipwreck (see Figure 1).

The most complex scientific instrument to have survived from antiquity, it resembled the sphaerae or planetaria described by Cicero (1) and other Greco-Roman authors. The date of its construction is in dispute but must have been earlier than the middle of the 1st centurybce and can scarcely have been before the end of the 3rd centurybce. It is an invaluable witness for ancient mechanical technology at its most advanced level (see mechanics) as well as for Hellenistic astronomy.

Article

Antonius Musa  

J. T. Vallance

Antonius Musa, physician to *Augustus whom he cured of a grave illness (Suet. Aug. 59). *Pliny the Elder links him with *Themison and his hydropathic therapies may place him in the tradition of *Asclepiades (3) of Bithynia. He also wrote on *pharmacology; nothing survives, but he is cited by *Galen (e.

Article

Antonius Castor  

Antonius Castor, perhaps a freedman of M. *Antonius (2), was one of the elder *Pliny (1)'s sources for botany (HN 25. 9). Pliny mentions that he possessed his own botanical garden.

Article

Antyllus  

J. T. Vallance

Antyllus, 2nd cent. ce, physician, one of the *Pneumatists. He lived after *Archigenes, probably after Galen, and wrote treatises on *surgery, *dietetics, and therapeutics, none of which survives. Some of his work is cited by *Paul of Aegina, *Oribasius, and *Aetius (2) of Amida.

Article

Apollinarius  

G. J. Toomer

Apollinarius, astronomer (fl. ?1st cent. ce). From references in *Galen, *Vettius Valens, and others, he appears to have been one of the most important figures in Greek *astronomy between *Hipparchus (3) and *Ptolemy (4). He constructed lunar tables, based on the 248-day period used by the Babylonian astronomers, which became standard in Greek astronomy until superseded by Ptolemy's. A long quotation from a theoretical work is preserved in an astrological compilation, and treatises by him on solar *eclipses and *astrology are also cited.

Article

Apollodorus (4), of Alexandria, Greek author, 3rd cent. BCE  

John Scarborough

Apollodorus (4), of Alexandria (1), physician and zoologist of the beginning of the 3rd cent. bce. His major work, On Poisonous Animals, was a source for pharmacologists and toxicologists in later antiquity (e.g. *Numenius, *Heraclides (4) of Tarentum, *Nicander, *Sostratus, Sextius Niger, *Pliny (1), *Dioscorides (2), *Archigenes, *Aemilius Macer, and probably *Philumenus; see pharmacology).

Article

Apollonius (10) Mys  

Heinrich von Staden

Apollonius (10) Mys (fl. later 1st cent. bce?), Alexandrian physician of the ‘school’ of *Herophilus. Numerous fragments of his influential Εὐπόριστα (‘Common Remedies’), Unguents, and The School of Herophilus survive, some on papyrus.

Article

Apollonius  

Michael N. Fried

Apollonius of Perga (fl. 200 bce) was the youngest of the three leading mathematicians of the Hellenistic age, the other two being Euclid and Archimedes. His most significant work was Conics. Conics, comprising eight books, remained the most comprehensive treatment of the subject of conic sections until the 17th century. It was because of Conics that Apollonius was known in antiquity as the “Great Geometer.” Its first four books formed a “course in the elements” of conics, as Apollonius describes it. In these books, which are the only works of Apollonius extant in Greek, he shows how the parabola, ellipse, hyperbola, and opposite sections (what in the early 21st century are called the two branches of a hyperbola) could be obtained by sectioning an oblique double-napped cone; he specified their distinct properties, diameters, axes, tangents, and asymptotes. These books also include Apollonius’s solution to the three- and four-line locus. The later four books, of which only three survive in an Arabic translation, consider “special topics”: “maximum and minimum lines”; similarity and equality of conic sections; special theorems related to limits of possibility (diorismoi), involving diameters, conjugate diameters and the “figures” related to them; determinate problems in conics.

Article

Apollonius (3), chief minister of Ptolemy (1), 3rd cent. BCE  

Dorothy J. Thompson

Apollonius (3) (3rd cent. bce) served *Ptolemy (1) II as chief minister (dioikētēs) in Egypt and is best known as holder of a 10,000-aroura (2,750-ha: 6,800-acre) crown-gift estate near Philadelphia (1) in the *Fayūm. This estate formed the centre of a series of agricultural experiments (in *arboriculture, viticulture, crops, and livestock) and was managed by Zenon, a Carian immigrant from *Caunus, who came to the Fayūm in 256 and stayed on in the area after leaving Apollonius' service in 248/7. The collection of Zenon's papyri is the largest from the period and is now scattered throughout European and North American collections. It illustrates these and Apollonius' other interests: *textile-manufacturing at *Memphis, his contacts in *Alexandria (1), and commercial dealings, including slave-trading, in the Levant (see slavery).

Article

Apollonius (8), of Citium, Alexandrian physician, c. 90–15 BCE?  

Heinrich von Staden

Apollonius (8), of Citium (c. 90–15 bce?), Alexandrian physician. Extant in an illustrated 10th-cent. manuscript, his commentary on the Hippocratic (see hippocrates (2)) treatise Περὶἀρθρῶν (‘On Joints’), offers invaluable evidence of the early state of the Hippocratic text, of orthopaedic *surgery, and of Empiricist polemics. His works on Hippocratic lexicography and on therapeutics are lost.

Article

Aratus (1) poet, of Soloi in Cilicia, c. 315–c. 240 BCE  

Emma Gee

Aratus is said to have studied philosophy in Athens, probably coming into contact with Zeno, founder of the Stoic school; subsequently, in 276 bce, he arrived at the court of Antigonus (2) ‘Gonatas’ of Macedon. Little can be independently proven, since the extant lives probably all derive from a single Hellenistic commentator.1Aratus ranks among the finest Hellenistic poets, beside Callimachus (3) and Apollonius (1) Rhodius. He wrote many other works, most of which are lost.2 His sole surviving poem, the Phaenomena, which comprises more than a thousand lines in epic hexameters, describes the positions and motions of the constellations and teaches the reader how to recognize signs of impending weather on earth. The Phaenomena is written in an idealized version of the Archaic language of Homer and Hesiod, and contains mythological material in the form of aitia for some constellations.3 It falls into two parts, the ‘.

Article

arboriculture  

Robert Sallares

Tree cultivation. In the first millennium bce there was a remarkable expansion of fruit-tree cultivation in the Mediterranean from east to west. The productivity of Mediterranean *agriculture was significantly increased because trees were often intercropped with cereals and legumes, increasing total yields per unit area. These developments laid the economic foundations for the prosperity of Greek and Roman civilization and made diets more diverse and more nutritious. The most important of the trees in question were the *olive, vine (see wine), *fig, apple, pear, plum, pistachio, walnut, chestnut, carob, date-palm, peach, almond, pomegranate, sweet and sour cherry-trees. The cultivation of many of these species of trees depended on the spread of the technique of grafting. The date of the establishment of citrus trees in the Mediterranean is disputed. They were probably not important until after the end of the classical period. The Roman agronomists provide us with information about arboriculture. Trees were also very important in the ancient economy for *timber.

Article

Archigenes  

William David Ross and V. Nutton

Archigenes, of Apamea in Syria, pupil of *Agathinus; well-known physician at Rome in the time of Trajan (98–117 ce). He was an eclectic, but was chiefly influenced by the doctrines of the Pneumatic school (see pneumatists). The leading principle of his therapeutics was to combat the eight δυσκρασίαι (bad temperaments).

Article

Archimedes, mathematician, c. 287–212/211 BCE  

Reviel Netz

Born at *Syracuse, son of an astronomer Phidias, and killed at the sack of the city by the Romans under M. *Claudius Marcellus (1), he was on intimate terms with its king *Hieron (2) II. He may have visited Egypt, but lived most of his life at Syracuse, corresponding with *Conon (2), *Dositheus (1), *Eratosthenes, and others. He became a figure of legend and popular history (see Plut. Marc. 14–19) knew him as the inventor of marvellous machines used against the Romans at the siege of Syracuse, and of devices such as the screw for raising water (κοχλίας); for his boast ‘give me a place to stand and I will move the earth’ (Simpl. In Phys. 1110. 5); for his determination of the proportions of gold and silver in a wreath made for Hieron (εὕρηκα, εὕρηκα, ‘Eureka! I have discovered it!’ Vitr.

Article

Archytas of Tarentum  

Carl Huffman

Archytas led the democratic Greek city-state of Tarentum and served as a successful general. He was a leading mathematician in the first half of the fourth century bce and a prominent Pythagorean philosopher. He famously sent a ship to save Plato from the Tyrant Dionysius I of Sicily, although his relationship to Plato was complex. Only four fragments of his genuine writings survive, but many fragments of works forged in his name are found among the Pythagorean pseudepigrapha. He solved the famous mathematical puzzle known as the duplication of the cube and gave a celebrated argument for the infinity of the universe. He was the foremost Pythagorean music theorist and devised mathematical descriptions of the musical scales of his day. He championed the four mathematical sciences that became the quadrivium of the Middle Ages. Anecdotes about him convey an ethics that values reason over pleasure and praises self-control.Archytas is most famous in the modern world for having sent a trireme to rescue .

Article

Aretaeus  

William David Ross

Aretaeus, of *Cappadocia, medical author, a contemporary of *Galen (c. 150–200 ce), wrote in Ionic in imitation of Hippocrates (2). Works (extant but incomplete): On the Causes and Symptoms of Acute and Chronic Diseases; On the Cure of Acute and Chronic Diseases; (lost) On Fevers; On Female Disorders; On Preservatives; Operations.

Article

Aristarchus (1), of Samos, Greek astronomer, mathematician, 3rd century BCE  

Nathan Camillo Sidoli

Aristarchus, often called the “mathematician” in our sources, is dated through a summer solstice observation of 280bce attributed to him by Ptolemy (Alm. 3.1). He is said to have been a student of Straton of Lampsacus, who succeeded Theophrastus as the head of the Peripatetic school in 288/287bce (Stob. Ecl. 1.16.1); and he is most famous for having advanced the heliocentric hypothesis, although his only surviving work in mathematical astronomy assumes a geocentric cosmos.According to Archimedes, Aristarchus hypothesized that the fixed stars and sun are unmoved, while the earth is carried around the sun on a circle, and that the sphere of the fixed stars is so large that the ratio of the circle about which the earth moves to the distance of the stars is that which a centre has to the surface of a sphere (Sand Reckoner, 4–5). We do not know how Aristarchus understood or utilized this hypothesis, which Archimedes claims is strictly impossible, but Archimedes himself reinterprets it to mean that the ratio of the diameter of the earth to the diameter of the earth’s orbit is the same as that of the diameter of the earth’s orbit to the diameter of the cosmos. Furthermore, Plutarch says that Aristarchus supposed that the earth rotates about its own axis (De fac.

Article

Aristides Quintilianus  

Andrew Barker

Aristides Quintilianus (3rd cent. ce ?), author of a lost Poetics and an ambitious De musica. Musical issues are classified as theoretical (‘technical’ and ‘physical’) and practical. Book 1 (technical) expounds harmonics, rhythmics, and metrics, mainly from Aristoxenian sources (see aristoxenus), incorporating valuable material otherwise unknown. Book 2 (practical) discusses music's educational and psychotherapeutic uses with verve and style, ingeniously integrating older ideas (some attributed to *Damon (2)) with engaging reflections of Aristides' own, notably on solmization and on the *soul. Book 3 (physical), exploiting Pythagorean harmonic analyses, links musical phenomena through numerology, mathematics, and natural science with the overall structure of reality. The work is impressively detailed, and unified, despite inconsistencies, by a near-Neoplatonist vision (see neoplatonism) of cosmos, soul, and music as manifestations of a single divine order. See music §§ 5–6.

Article

Aristoxenus  

Andrew Barker

Aristoxenus, of *Tarentum (b. c.370 bce), best known for musical writings but also a philosopher, biographer, and historian. He was trained in *music, possibly to professional standards, by his father Spintharus and Lampon of Erythrae (perhaps while living in *Mantinea). Later, probably at Athens, he studied with the Pythagorean (see pythagoras) Xenophilus, pupil of *Philolaus, before joining *Aristotle's Lyceum. Here his success made him expect to inherit the headship; and when Aristotle bequeathed it to *Theophrastus instead, his remarks about Aristotle (according to the Suda, our main biographical source) were memorably rude. The waspishness of criticisms levelled at others in his writings makes this believable; but his intellectual orientation is unmistakably Aristotelian, and his one surviving reference to Aristotle (Harm. 31. 10–16) is also the one unqualified compliment paid to anyone in that work. Nothing is known of him after 322 bce.

Article

arithmetical tables  

Giuseppina Azzarello

Greek arithmetical tables are systematic series of calculations written on papyrus and other light materials such as potsherds, wooden and wax tablets, and paper. About 150 items stemming from Egypt and covering a wide chronological range (4th century bce–13th century ce) have been published. Calculations are normally written in columns and separated by vertical and horizontal lines. They consist of addition, multiplication, squares and division, which are expressed in form of fractions (4: 2 = 2 is expressed as ½ of 4 = 2), and their results are given as the addition of juxtaposed unit fractions, a feature originating in Egyptian mathematics. Every kind of operation presents different patterns and features which can be of help in determining chronology and context. It is particularly challenging to establish the context of the tables, as they can belong to reference books used by professional accountants or be school texts. Material, handwriting, spelling, and the presence of other inscriptions on the same item, such as drawings, personal names, or even school exercises, can shed light on this point.