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Perseus

PERSEUS

(fi third cenrtury b.c. [?])

mathematics.

Perseus is known only from two passages in Proclus. In one passage his name is assciated with the incestigation if “Spiric” curves as that of Apollonius of Perga is with conies, Nicomedes with the conchoods, and Hippias of Elis with the quadratrices.1 In the second passage, derived from Gemintis, Proclus says that Perseus wrote an epigram upon his discovery, “Three lines upon five sections finding, Perseus made offering to the gods therefor.”2

In another place Proclus says that a spiric surface is thought of as generated by the revolution of a circle standing upright and turning about a fixed fixed point that is not its center; wherefore it comes about that there are three kinds of spiric surface according as the fixed point is on, inside, or outside the circumference.3 The spire surface is therefore what is known today as a “tore” in antiquity Hero of Alexandria gave it the name “Spire” or “ring.”4

These passages throw no light on the provenance of Perseus and leave wide room for conjecture about his dates. He must have lived before Geminus, as Proclus relies on that author; and it is probable before that the conic sections were advanced before the spiric curves were tackled. Perseus therefore probably lived between euclid Euclied and geminus say between 300 and 70 b.c., with a preference for the earlier date.

What Perseus actually discovered is also uncertain. In rather more precise language than that of Proclus, a spiric surface may be defined as the surface generated by a circle that revolves about a straight line (the axis of revolution) always remaining in a plane with it. There are three kinds of spiric surfaces, according as the axis of revoltution is outside the circle, tangential to it, or inside it (which are called by Proclus the “open,”, “continuous,” and “interlaced” and by Hero the “open”, continuous and “self-crossing”).

A spiric section on the analogy of a conic section would be a section of a spiric surface by a plane, which it is natural to assume is parallel to the axis in the first place. Proclus says that the sections are three in number corresponding to the three types of surface, but this is difficult it understand or to reconcile with the epigram. G. V. Schiaparelli showed how three different spiric curves could be obtained by a section of an open tore according as the plane of section was more or less distant from the axis of revolution,5 and Paul Tannery entered upon a closer mathematical analysis that led him to give a novel interpretation to the epigram.6 If r is the radius of the generating circle, a the distance of its center from the axis, and d the distance of the cutting plane from the axis, in the case of the open tore (for which a > r), the following five cases may be distinguished;

a + r > d > a (1)

d = a (2)

a > d > ar (3)

d = ar (4)

ar > d > 0 (5)

Of these the curve produced by (4) is Proclus’ first spiric curve, the “hippopede’ or “horse-fetter,” which is like a figure eight and had already been used by Eudoxus in his representation of planetary motion; (1) is Procls’ second broad in the middle; (3) is his third, narrow in the middel; (2) is a transition from (1)to (3); and (5) produces two symmetrical closed curves. If the tore is “Continous” (’closed” in modern terminolgy), a=r, hte forms (1),(2), and (3) remain as for the “open” tore, but (4) and (5) disapper and there is no new curve. If the tore is “interlaced” (“reentrant”) a.r. and the forms (4) and (5) do not exist; but there are three new curves corresponding to (1),(2),and (3), each with an oval inside it.

Tannery deduced that what the epigram means is that Perseus found three spiric curves in addition to the five sections. In this deduction he has been followed by most subsequent writiers, Loria even finding support in Dante.7 Although the interetation is not imposible, it putes a strain upon the Greek. It is simpler to suppose that Tannery has correctly identified the five sections, but that Perseus ignored (2) and (5) as not really giving new curves. Thus he found “three curves in five sections.” If we suppose that he took one of his curves from the five sections of the “open” tore, “Continuous”, and one from the sections of the “interlaced,” we could reconcile Prod us’ statement also, but it is simpler to suppose that Proclus writing centuries later, made an error.

NOTES

1. Proclus, In primum Euclidis, G. Fredlein, ed. (Leipzing, 1873; reper. Hildesheim, 1967), 356.6–12.

2.ibid pp. 11.23–112.2.

3.ibid p. 119.9–13.

4. Heron, Definitions 97, in J. L. Heiberg, ed., Heronis Alexandrini opera quae supersunt ominia iv (Leipzig, 1912), pp. 60.24–62.9.

5. G. V. Schiapaarelli, Le safere omocentriche di Eudosso, di Calippo e di Aristotele (Milan, 1875), pp. 32–34.

6. Paul Tannery, Mémoires scientifiques 11 (Toulouse-paris, 1912), pp. 26–28.

7. Gino Loria, Le scienze esatte nell’antica Grecia 2nd ed. (Milan, 1814), p. 417, n. 2.

BIBLIOGRAPHY

On Perseus or his works, see T. L. Health The Thirteen Books of Euclid’s 2nd ed. (Cambridge, 1926; repr. New York; 1956), I, 162–164; A History of Greek Mathemaics II (Oxford, 1921), 203–206; G. v.Schiaparelli, Le sfere omocentriche di Eudosso, di Calippo e di Aristotele (Milan, 1875), 32–34; and Paul Tannery, “Pour i’histoire des lines et de surfaces courbes dans I’antiquite,” in Bulletin des sciences mathematiques et astronomiques 2nd ser., 8 (Paris, 1884), 19–30; repr in Memoires secintifiques 2. (Toulouse-paris, 1912), 18–32.

Ivor Bulmer-Thomas

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Perseus (in Greek mythology)

Perseus (pûr´sēəs, –sŏŏs), in Greek mythology, son of Zeus and Danaë. His grandfather, Acrisius, had been warned by an oracle that his grandson would kill him and therefore put Perseus and his mother in a chest and threw it into the sea. It drifted to Seriphus, where King Polydectes befriended the two. After a time Polydectes fell in love with Danaë but was embarrassed by the presence of her full-grown son. He sent Perseus to fetch the head of the Gorgon Medusa, thinking that Perseus would die in the attempt. The gods, however, loved Perseus. Hermes gave him a curved sword and winged sandals, Athena a mirrorlike shield, and Hades a helmet that made Perseus invisible. Thus armed, Perseus slew Medusa. While fleeing the other Gorgons, Medusa's sisters, Perseus asked Atlas for help. Atlas refused, and Perseus, by means of the Medusa head, promptly turned him into a mountain of stone. On his way home Perseus rescued Andromeda from a sea monster and married her. When he arrived in Seriphus, he killed Polydectes and his followers. He then gave the Medusa head to Athena. He went with his mother and his wife to Argos. There, while competing in a discus contest, Perseus accidentally killed his grandfather. Thus the prophecy was fulfilled. Perseus was the father of Electryon, who was the grandfather of Hercules. The famous figure of Perseus by Benvenuto Cellini stands in the Loggia dei Lanzi in Florence.

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Perseus (king of Macedon)

Perseus, c.212–166 BC, last king of Macedon (179–168 BC), son and successor of Philip V. He intrigued against his younger brother, Demetrius, eventually bringing about the latter's execution by Philip V. As king, his involvement in Greek politics excited the fears of Eumenes II of Pergamum, who, thinking that Pergamum's position was being endangered, went to Rome to provoke war against Perseus by pointing to alignments of Macedon with anti-Roman factions in Greece. The resultant Third Macedonian War (171–168) began with a Macedonian cavalry victory and then dragged on indecisively. Finally Aemilius Paullus took command of the Roman forces and soundly defeated (168) Perseus at Pydna on the Gulf of Thessaloníki. Perseus died in captivity.

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Perseus

Perseus

In Greek mythology, Perseus was the heroic slayer of the Gorgon Medusa* . His mother was Danaë, daughter of King Acrisius of Argos. Before Perseus's birth, an oracle predicted that Danaë would bear a child who would one day kill his grandfather. Terrified by this prophecy, Acrisius imprisoned his daughter in a tower. However, Danaë received a visit in the tower from Zeus* , who had taken the form of a shower of gold, and she became pregnant.

After Danaë gave birth to Perseus, Acrisius had his daughter and her child locked in a box, which he threw into the sea. The box came ashore on the island of Seriphos and was found by Dictys, a fisherman. Dictys sheltered Danaë and Perseus in his home, and they remained with him for many years.

When Perseus had grown into a young man, King Polydectes of Seriphos fell in love with Danaë and tried to persuade her to marry him. Danaë refused, and Perseus protected his mother from the unwanted advances. Hoping to rid himself of Perseus, Polydectes set him a seemingly impossible task. Perseus was to obtain the head of Medusa* , a monster so hideous that anyone who even glanced at her face turned to stone.

Perseus received gifts from the gods to help him in his task: a pair of winged sandals, a sword, a helmet that made the wearer invisible, and a bronze shield from Athena* that was polished to shine like a mirror. Perseus then visted the Graeae, three old hags who were sisters of the Gorgons and who shared a single eye. Seizing their eye, he demanded to know where he could find the Gorgons. When they told him, Perseus threw the eye into a lake so that the Graeae could not warn their sisters.

With the winged sandals, Perseus flew to the home of the Gorgons. When he reached their cave, he advanced toward Medusa using Athena's shield as a mirror to avoid looking directly at the monster. Then he took the sword and cut off Medusa's head, which he placed in a bag. Drops of Medusa's blood that touched the ground changed into the winged horse Pegasus. Wearing the helmet that made him invisible, Perseus flew off on Pegasus.

Gorgon one of three ugly monsters who had snakes for hair, staring eyes, and huge wings

oracle priest or priestess or other creature through whom a god is believed to speak; also the location (such as a shrine) where such words are spoken

prophecy foretelling of what is to come; also something that is predicted

nymph minor goddess of nature, usually represented as young and beautiful

On his way home, Perseus came upon the giant Atlas* , who held up the sky. Atlas tried to stop Perseus, but the hero took out the head of Medusa and turned the giant to stone. Next Perseus saw a beautiful woman chained to a rock. This was Andromeda, left as a sacrifice to a sea monster after her mother, Cassiopea, had boasted of her beauty and offended the sea nymphs known as the Nereids. Perseus killed the sea monster, rescued Andromeda, and asked her to marry him.

Arriving back in Seriphos, Perseus found that his mother had taken refuge in the temple of Athena to avoid the advances of Polydectes. Furious, Perseus used Medusa's head to turn Polydectes and his soldiers to stone. Perseus returned the winged sandals, helmet, and shield to the gods and gave the head of Medusa to Athena, who placed it on her shield. He then took Andromeda to Argos, the kingdom of his grandfather Acrisius.

discus heavy, circular plate hurled over distance as a sport

Hearing that Perseus had arrived, Acrisius fled to Thessaly, mindful of the prophecy made years before. Later, however, Perseus took part in an athletic contest there and threw a discus that accidentally killed Acrisius. The prophecy was fulfilled.

See also Andromeda ; ATHENA ; Atlas ; Cassiopea ; DANA ; GORGONS ; HEROES ; Medusa ; Pegasus .

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Perseus (in astronomy)

Perseus, in astronomy, northern constellation lying E of Cassiopeia and N of Taurus. It contains the bright star Mirfak (Alpha Persei) and Algol (Beta Persei), a visible variable star of the type known as an eclipsing variable. Perseus contains two star clusters (NGC 869 and NGC 884) that are visible to the naked eye, as well as an open cluster (M34) that is barely visible. A meteor shower known as the Perseids appears to radiate from a star in Perseus; this shower can be seen every year for several nights beginning Aug. 10, after midnight. In 1901 a brilliant nova was observed in the constellation. Perseus reaches its highest point in the evening sky in late December.

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Perseus

Perseus in Greek mythology, the son of Zeus and Danae, a hero celebrated for many achievements. Aided by gifts from the gods (a helmet which conferred invisibility from Pluto, wings for his feet from Hermes, and a mirror so that he could look indirectly at the gorgon from Athene) he cut off the head of the gorgon Medusa and gave it to Athene; riding the winged horse Pegasus which sprang from the gorgon's blood, he rescued and married Andromeda, and he became king of Tiryns in Greece.

A prophecy had said that he would kill his grandfather; this happened in Thessaly when his grandfather, who was attending some games there, was accidentally killed by a discus thrown by Perseus.

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Perseus

Perseus In Greek mythology, son of Danaë and Zeus. Perseus beheaded the snake-haired gorgon Medusa, turned Atlas to stone and rescued the princess Andromeda from being sacrificed to a sea monster.

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Perseus

Perseus In astronomy, a prominent northern constellation. Perseus is a rich constellation, crossed by the Milky Way.

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Perseus

PerseusBierce, fierce, Pearce, Peirce, pierce, tierce •Fabius, scabious •Eusebius •amphibious, Polybius •dubious • Thaddeus • compendious •radius • tedious •fastidious, hideous, insidious, invidious, perfidious •Claudiuscommodious, melodious, odious •studious • Cepheus •Morpheus, Orpheus •Pelagius • callipygous • Vitellius •alias, Sibelius, Vesalius •Aurelius, Berzelius, contumelious, Cornelius, Delius •bilious, punctilious, supercilious •coleus • Julius • nucleus • Equuleus •abstemious •Ennius, Nenniuscontemporaneous, cutaneous, extemporaneous, extraneous, instantaneous, miscellaneous, Pausanias, porcellaneous, simultaneous, spontaneous, subcutaneous •genius, heterogeneous, homogeneous, ingenious •consanguineous, ignominious, Phineas, sanguineous •igneous, ligneous •Vilnius •acrimonious, antimonious, ceremonious, erroneous, euphonious, felonious, harmonious, parsimonious, Petronius, sanctimonious, Suetonius •Apollonius • impecunious •calumnious • Asclepius • impious •Scorpius •copious, Gropius, Procopius •Marius • pancreas • retiarius •Aquarius, calcareous, Darius, denarius, gregarious, hilarious, multifarious, nefarious, omnifarious, precarious, Sagittarius, senarius, Stradivarius, temerarious, various, vicarious •Atreus •delirious, Sirius •vitreous •censorious, glorious, laborious, meritorious, notorious, uproarious, uxorious, vainglorious, victorious •opprobrious •lugubrious, salubrious •illustrious, industrious •cinereous, deleterious, imperious, mysterious, Nereus, serious, Tiberiuscurious, furious, injurious, luxurious, penurious, perjurious, spurious, sulphureous (US sulfureous), usurious •Cassius, gaseous •Alcaeus • Celsius •Theseus, Tiresias •osseous, Roscius •nauseous •caduceus, Lucius •Perseus • Statius • Propertius •Deo gratias • plenteous • piteous •bounteous •Grotius, Photius, Proteus •beauteous, duteous •courteous, sestertius •Boethius, Prometheus •envious • Octavius •devious, previous •lascivious, niveous, oblivious •obvious •Vesuvius, Vitruviusimpervious, pervious •aqueous • subaqueous • obsequious •Dionysius

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