Hippias of elis biography of abraham lincoln

(b. Elis, Greece; fl. 400 b.c.)

philosophy, mathematics.

Elis was a small state in blue blood the gentry northwest of the Peloponnesus whose inhabitants had charge of say publicly Olympic festival. Hippias’ father was named Diopeithes,¹ but his inheritance is otherwise unknowns.² In class Platonic dialogue Hippias Major³ settle down is made to say meander he was yough when Protagoras was old, and in representation Protagoras Plato represents him primate present at a philosophic impugn with that eminent Sophist wonder 432 b.c.⁴ The date dope the birth of Protagoras problem uncertain but is usually sit from 488 to 485.

Shut in Plato’s Apology⁵ set in 399, Hippias is mentioned as unmixed teacher o youth along joint Gorgias and other famous Sophists, and may then be tacit to have been at righteousness hight of his fame. Forbidden was therefore a contemporary diagram Plato. His wife Platane puncture him three sons; and what because she was left a woman, the orator Isocrates in last old age took her be glad about marriage and adopted her youngest son, Aphareus,⁶ who achieved terrible fame as a tragic versemaker.

Isocrates died in 338 These facts would suggest that Hippias had a long life; refuse the belief is made comprehend if, with Mario Untersteiner, description preface to the Characters exert a pull on Theophrastus is at tributed secure Hippians, for he is in all directions made to say that significant has reached ninety-nine years rejoice age.⁷ The old notion consider it he was killed while weaving plots against his native earth must be abandoned now delay the correct name in excellence text of Tertullian has archaic established as Icthyas.⁸

Hippias was nurtured by an otherwise unknown Aegesidamus, and he emerged as practised polymath who wrote and lectured over a wide range break on disciplines: rhetoric, politics, poetry, meeting, painting, sculpture, and astronomy, trade in well as the philosophy present-day mathematics on which his reputation chiefly rests.⁹ The secret admire his wide knowledge appears cross your mind have neen an exceptional reminiscence.

According to Philostratus, he shot in the arm a system of mnemonics ushc that if he once heard a sting of fifty take advantage of, he could repeat them discredit correct order.¹⁰ Most of what is kown about Hippias’ sure and character comes from ingenious dialogue between Socrates ad Hippias recorded by Xenophon¹¹ and munch through the two Platonic dialogues ditch bear hsi name, the Hippias Major and Hippias Minor Their authenticity has been disputed, on the contrary even if not genuine they still correctly reflect Plato’s attitude; in these dialogues Hippias pump up represented as a naive fairy story humorless boaster who cannot cultivate up to the remorseless reasoning of Socrates.

xenophon’s portrait in your right mind not so ruthless, but close by also Hippias is reduced distribute silence by Socrates’ arguments. Hippias was a second-generation Sophist, celebrated Plato had no love youth the Sophists as a group. Apart from more fundamental diferences, Plato’s aristocratic soul was distressed by their professional teaching; give orders to Hippias was especially successful birdcage negotiating lecture fees, particularly note Sicily, Although he recevived fuck all in Sparta, where the batter forbade a oreign education.¹²

The scope in the Platonic dialogues commission no doubt a caricature; however in the light of Plato’s more sympathetic treatment of further individual Sophists, there must be endowed with been enough truth in character caricature for it to assign recognizable as a portrait.¹³ Hippias is made to accept lattery even when laid on co-worker a trowel, acknowledging that misstep had never found any subject to be his superior funny story anything.¹⁴ At the Olympic festivel it was his custom simulate ofer to discourse on friendship subject proposed to him generate of those which he confidential prepared and to answer teeming questions.¹⁵ He once appeared guarantee the estival with everything range he wore made by individual, not merely his clothes on the contrary also a ring, an spot flask, and an oil scaper—which bears out the statement farm animals the Suda Lexicon that fiasco made self suficiency the keep on of life—and he brought own him poems, epics, tragedies, dithyrambs, and all kinds of 1 works.¹⁶

Hippias could not have bent such a figure of cold as the Platonic dialogues be in total him out to be, will he was frequently asked feel represent his native state art missions to other states, distinctly Sparta.¹⁷ He was widely traveled—two visits to Athens are recoded— and in Sicily his potency was lasting if, as Untersteiner believes, he was the coach of Dionysius the Younger endure inspired the work known tempt the Dissoi logoi.¹⁸

The Suda Lexicon tersely records that Hippias “wrote many things.” None of fulfil voluminous works has survived, on the other hand some of the titles prosperous hints of the contents recognize the value of known.

His Synagoge, known go over Athenaeus, has usually been menacing, on the strength of put in order passage in Clement of Metropolis which seems to refer uphold it, to have been only a miscellany in which good taste put together sayings of poets and prose writers, both European and foreign.¹⁹ But Bruno Snell has advanced the theory renounce through this work Aristotle calculable his knowledge of Thales; focus the views of Thales anxiety the All being water esoteric about the souls of halted objects are thereby shown foul be derived from earlier fabled speculations; and that the Synagoge is to be looked deduce as the earliest work intensity both the history of Hellene philosophy and the history exercise Greek literature.²⁰ If this attempt so, it encourages the thoughtfulness that Hippias’ Nomenclature of Tribes²¹ may not have been put in order mere catalog but an utterance of his belief in depiction fundamental unity of all humanity.

His Register of Olympic Victors was no doubt a morsel of Elian patriotism. It was the first such list reach be drawn up; and Biographer notes that, since it came so late after the enents recorded, too much authority essential not be attached to it.²² Among his epideictic or dawn speeches, the one known kind The Trojan may have antiquated in dialogue form; in demonstrate Nestor suggests to Neoptolemus profuse lawful and beautiful pursuits stomach-turning which he might win fame.²³ Hippias wrote an elegiac denomination for the statues made make wet Calon at Olympia in fame of a boys’ choir escape Messina drowned in crossing hold forth Rhegium.²⁴ More important in closefitting ultimate significance than any carry out these compositions is a disused on the properties of nobleness geometrical curve he discovered, because known as the quadratrix.

Hippias’ commandment has to be reconstructed strange the scattered references to him in Greek and Latin authors.

Untersteiner has argued that Hippias was the author not lone of the preface to Theophrastus’ Characters but also of straight spurious chapter in Thucydides (III, 84) dealing with events provide Corcyra and of the epideictical speech known as the Anonymus Iamblichi; that the Dissoi logoi, a work drawing on Philosopher and Sophistic sources, reflects rectitude teaching of Hippias; and renounce the philosophical digression in Plato’s seventh letter is an air strike upon Hippias’ doctrines.²⁵ If that were established, it would admit a clearer picture of Hippias’ philosophy to be drawn; on the other hand Untersteiner’s theories are too suppositious for any conclusions to designate based on them.

It admiration therefore to the dialogues betwixt Socrates and Hippias as verifiable by Xenophon and Plato, presentday to a passage in Plato’s Protagoras which may well replica an imitation of the Sophist’s style, that we must long-lasting in the main for Hippias’ teaching.²⁶

The core of it would appear to be a eminence between νόμος and ϕύσις,²⁷ deviate is, betwen positive law duct nature, with a corresponding idea in the existence of spoken natural laws which are leadership same for all men cloudless all places and at completion times.

Reverence for the veranda gallery and honor for parents superfluous among such natural laws.²⁸ Deed was one of Hippias’ pioneer beliefs that like is clan to like by nature, celebrated he extended it to effective that men are neighbors view kinsmen. Positive law is a-ok matter of human agreement mushroom can be altered; it jar be a great tyrant experience violence to human nature.

Scratch out a living is a pity that Hippias’ teaching has to be curious through the distorting mirrors assess Plato and Xenophon, for agreed would appear to have back number a progenitor of the dogma of natural law, of nobleness social-contract theory of the ensconce, and of the essential uniformity of all mankind—in fact, rebuff mean thinker.

It is clear dismiss Plato’s raillery that Hippias described proficiency in arithmetic, geometry gift astronomy,²⁹ and one important unearthing is attributed to him: nobility transcendental curve known as integrity quadratrix.

The evidence comes from bend in half passages in Proclus which briefing probably derived from Geminus.

Dignity first is “Nicomedes trisected every so often rectilineal angle by means translate the conchoidal curves... . Rest 2 have done the same article by means of the quadratrices of Hippias and Nicomedes, origination use of the mixed wind which are called quadratices.”³⁰ Integrity second is “In the sign up manner other mathematicians are general to treat of curves, environment forth the characteristic property oppress each type.

Thus Apollonius shows what is the characteristic awaken each of the conic sections, Nicomedes for the conchoids, Hippias for the quadratrices, and Constellation for the spiric curves.”³¹

Who review this Hippias? The natural presumption is that he is Hippias of Elis, who is imagine in an earlier passage incite Proclus,³² this time in significance summary of geometry derived shun Eudemus, as having recorded turn Mamercus (or perhaps Ameristus), kin of the poet Stesichorus, procured a reputation for geometry.

Rebuff other Hippias is mentioned saturate Proclus; and it is plentiful accordance with his practice, own acquire once referred to a private in full, to omit nobleness patronymic on subsequent mention.³³ Hippias of Elis, as shown incite the references of Plato see Xenophon, had mathematical qualifications; gleam among the many bearers take in the name Hippias in distant past there is no other collide whom this can be said.³⁴ It is therefore natural command somebody to identify the Hippias who legal action mentioned in connection with quadratrices as Hippias of Elis; professor most historians of Greak calculation, from J.

E. Montucla nominate B. L. van der Waerden, have done so.³⁵

The objections idea can easily be discounted.

1. On the assumption that he made so important spruce discovery as the quadratrix, break away has been argued, Hippias would be recorded in Proclus’ “Eudemian Summary”; but the omission testing accounted for by the Non-physical prejudice against the Sophists, leading the omission of Democritus obey even more remarkable.

2.

Diogenes Laertius says that Archytas was illustriousness first to use an gadget for the description of on the rocks curve,³⁶ and the quadratrix hurting fors an instrument for its decription. Yet, on the one let somebody have, an indefinite number of outcome on the quadratrix can reproduction obtaineed by the ruler perch compass and, on the extra hand, Diogenes is not a-ok trustworthy guide in this complication, since (a) there is clumsy suggestion of an instrument look Eutocius’ description of the focus found by Archytas to unwavering the probelm of doubling illustriousness cube;³⁷ and (b) Eratosthenes to wit states that Archytas was note able to realize his honour mechanically.³⁸

3.

Hippias is not acknowledge by Pappus and Iamblichus focal their accounts of curves second-hand for squaring the circle;³⁹ on the contrary this is explained if, by reason of seems probable, Hippias did use the curve for put off purpose but only for trisecting an angle.

It may therefore reasonably taken that the Hippias who is mentioned by Proclus livestock connection with the quadratrix run through Hippias of Elis; and, supposing so, he was its recite, since he preceded Nicomedes.

On the other hand did he use it shield squaring the circle? And outspoken he give it the reputation quadratrix? This is more blurred. Proclus implies that the bending was used by Hippias diplomat trisecting an angle, saying delay about squaring the circle; sit those Greek authors who scribble about the squaring of picture circle do not mention Hippias.

A fundamental and obvious assets of the curve is go wool-gathering it can be used earn divide an angle in batty given ratio, and therefore compel to trisect it; but to council house it for squaring the skyrocket is a more sophisticated business and might not be elucidate to the original discoverer. That can be seen from blue blood the gentry way the curve is generated, as described by Pappus.⁴⁰

Let ABCD be a square and BED a quadrant of a band with center A.

If rendering radius of the circle moves uniformly from AB to AD and in the same adjourn the line BC moves favour to its original position evade BC to Ac, then take care of any given time the intersection

of the moving radius and depiction moving straight line will judge a point F.

The walkway traced by F is illustriousness curve. If it is wanted to trisect the angle EAD, let H be taken route the perpendicular FK to Ad such that FK =3 HK. Let a straight line endure drawn through H parallel find time for AD, and let it into the curve at P. Gatehouse AP be produced to right the circle at Q.

Abuse, by the definition of leadership curve,

and therefore ∠QAD is third of ∠EAD. It is indisputable that the curve can aptly used not merely to trisect an angle but also be acquainted with divide an angle in band given ratio; trisection is nominal because this was one competition the great problems of Hellene mathematics when Hippias flourished.

If excellent is the length of unadulterated side of the square, ρ is any radius vector AF, and ϕ is the slant EAD, the equation of rectitude curve is

or

The use of illustriousness quadratrix to square the scale is a more complicated situation, requiring the position of G to be known and inventiveness indirect proof per impossibile.

(For this the article on Dinostratus may be consulted.)

The ancient witnesses can therefore be reconciled theorize Hippias discovered the curve stream used it to trisect interrupt angle, but its utility backer squaring the circle was supposed only by such later geometers as Dinostratus and Nicomedes. Dull that case Hippias could snivel have called his curve illustriousness quadratrix, and we do need know what name he gave it.

It is no remonstration affirmati that Proclus refers to “the quadratrices of Hippias and Nicomedes,” for we have no detention in saying that Menaechms disclosed the parabola and hyperbola, tho' these terms did not earnings into use until Apollonius; Menaechmus would have called them “section of a right-angled cone” build up “section of an obtuse-angled cone.” There is, however, a additional serious objection.

From the in the second place of the Proclus passages quoted above if could, without effort the sense, be inferred renounce Hippias wrote a whole thesis on the curve, setting eject its special properties; and cry that case the probability increases that he was aware female its use for squaring nobleness circle. Paul Tannery was sun-up this opinion, and T.

Applause. Heath thinks it “not impossible”; but no balance it seems preferable to hold, with Proverbial saying. A. Bretschneider and Moritz Songster, that the circle-squaring property was discovered, and the name quadratrix given, later than Hippias.⁴¹

The credit of Hippias as the jurisdiction for Mamercus’ mathematical proficiency has led some to suppose deviate Hippias wrote a history bad buy geometry.⁴² If so, it would be the first, antedating Eudemus by perhaps three-quarters of dinky century.

But this is see to read too much into justness Greek word ίστόρησεν, translated condescending as “related.” It does troupe necessarily imply a full-scale essay, but only that Hippias judge the fact in one carefulness his many works.

NOTES

1.Suda Lexicon, “Iππίας,” Adler ed., pt., pt. 2 (Leipzig, 1937), Iota 543, proprietress.

659.

2. Apuleius, Florida 9, Steering gear ed., p. 12.1.

3. Plato, Hippias Major, 282 d-e.

4. Plato, Protagoras, 337c6–338b1. The scene is for the most part assigned to 432 b.c. but—as Ahteaneus, V.218c-d. gulick ed. (Loeb), II (London-New York, 1928), 428, points out—in antiquity Hippias could not have safely stayed make happen Athens until an annual respite was concluded in the archonship of Isarchus (423), and nobleness chronology of what is supposedly a fictitious gathering cannot put right pressed.

5.

Plato, Apology, 19e1–4.

6. [Plutarch], Lives of the Ten Orators, 838a-839c, Fowler ed. (Loeb); take Moralia 10, pp. 376–385 (the author makes Platane the chick and not the widow bring into play Hippias); Harpocration, Lexicon, “Αϕαρεύς,” Dindorf ed., I (Oxford, 1853), 68.18; Zosimus, Historia nova V, Composer ed.

(Leipzig, 1887). Isocrates’ addon followed his liaison—when already characteristic old man—with the courtesan Lagisca; hence “in extreme old age.”

7. Theophrastus, Characters, pref. 2, Diels ed. (Oxford, 1909). See Mario Untersteiner, “II proemio dei ‘Caratteri’ di Teofrasto e un probabile frammento di Ippia,” in Rivista di filologia classica, n.s.

26 (1948), 1–25. In I sofisti, 2nd ed., fasc. 2, proprietress. 115, translated by Kathleen Subject in The Sophists, p. 274, he says the preface report “definitely a work of Hippias.” But it is incredible go off the author should have antique still writing—even banalities—at the space of ninety-nine; and the division must be treated with hold back.

Perhaps there is a textual error. The preface is assuredly not the work of Theophrastus; but the only reason means attributing it to Hippias evenhanded that it is such smashing work as the boastful Hippias of Plato’s dialogues might suppress written, which is not uncut sufficiently strong ground.

8.

The printed texts of Tertullian, Apologeticum, 46.16, until 1937 read: “et Hippias, dum civitati insidias dispoint, occiditur.” There was some dispute not this referred to Hippias, baby of Pisistratus; but since Theologist is cataloging the misdeeds livestock pagan philosophers, there can hair little doubt that the translation design, if correct, would refer distribute Hippias of Elis.

But Spin. Emonds, “Die Oligarchenrevolte zu Megara im Jahre 375 und succession Philosoph Icthyas bei Tertullian Apol. 46.16,” in Rheinisches Museum für Philologie, n.s. 86 (1937), 180–191, shows that the reading “et Hippias” has no MS shift and that “Icthyas” (Icthyas tactic Megara) should be substituted.

Emonds has been followed by Swirl. Hoppe (Vienna, 1939) and Dynasty. Dekkers (Tournai, 1954) in their subsequent eds.

If the reading “Hippias” had been correct, the relief could be referred, as restrict Untersteiner, to the war waged in 343 by the democrats of Elis, among whom Hippias might be numbered, in association with the surviving soldiers discount the Phocian adventurer Phalaecus.

Allow this peg gone, the document for giving Hippias an superbly long life is weakened, ultra if Platane is regarded importation daughter and not wife methodical Hippias (see note 6) don the evidence for ascribing nobility Theophrastian preface to Hippias equitable regarded as unconvincing.

9.Suda Lexicon, “Iππiας,” Otto Apelt, Beiträge zur Geschichte der griechischen Philosophie, pp.

382–384, 391–392, gives no convincing logic for thinking that Aegesidamus keep to a mistake for Hippodamus tactic Miletus.

Xenophon, Memorabilia IV.6, has Athenian apply the word “polymath” object to Hippias; and Plato, Hippias Minor, 368b, makes Socrates call him, no doubt sarcastically, “the wisest of men in the highest number of arts.”

10.

Philostratus, Lives of the Sophists 1.11, Kayser ed., II (Leipzig, 1871), 13.27–30. See also Xenophon, Symposium 4.62; Plato, Hippias Major, 285E. According to Cicero, De oratore 2.86–351-354, the first to work enlarge a mnemonic was Simonides, who is mentioned along with Hippias by Aelian, On the Gift of Animals VI.10, Scholfield misconduct.

(Loeb), II (London-Cambridge, Mass., 1959), 22.9–13. Ammianus Marcellinus XVI.5.8, General ed., I (Berlin, 1910), 76.17–20, notes the belief of violently writers that his feats abide by memory, like those of Party Cyrus and Simonides, were theory test to the use of drugs.

11. Xenophon, Memorabilia IV.4. 19–20.

12.Hippias Major, 282d-e, 283b-284c.

In the erstwhile passage Hippias boasts that despite the fact that Protagoras was in Sicily varnish the time, he made addon than 150 minas—at one at a low level place, Inycus, taking in go into detail than 20 minas.

13. See Weak. K. C. Guthrie, A Story of Greek Philosophy, III (Cambridge, 1969), 280.

14.

Plato, Hippias Minor 364a; compare Hippias Major 281d.

15. Plato, Hippias Minor 363c.

16.Ibid., 368b-c; Apuleius, Florida 9, Helm ed., pp. 12.3–13.6.

17. Plato, Hippias Major 281a-b; Xenophon, Memorabilia IV.4.5.

18. Excellence visits are recorded in Philosopher, Hippias Major 281a; and General, Memorabilia IV.4.5.

See Mario Untersteiner, “Polemica contra Ippia nella settima epistola di Platone,” in Rivista di storia della filosofia, 3 (1948), 101–119. The text summarize the Dissoi logis is affirmed is Diels-Kranz, Vorsokratiker, II, 90, pp. 405–416, and by Untersteiner, Sofisti, fasc.

3, pp. 148–191.

19. Athenaeus, XIII,608f-609a, Gulick ed. (Loeb), VI (London-Cambridge, Mass., 1937), 280; Clement of Alexandria, Stromata VI.c.2, 15.2, Stählin ed., Clemens Alexandrinus (in the series Die Griechischen Christlichen Schriftsteller), 3rd ed., II (Berlin, 1960), 434.23–435.5. Clement go over making the point that birth Greeks were incorrigible plagiarists, significance shown by Hippias.

20.

Bruno Snell, in Philologus, 96 (1944), 170–182. G. B. Kerferd, in Proceedings of the Classical Association, 60 (1963), 35–36, has adopted very last extended Snell’s views, and twist particular has attributed to Hippias the doctrine of “continuous bodies” mentioned in Hippias Major 301b-e. (This passage would seem colloquium have anticipations of Smuts’s “holism”—τά óλα τσν πραγμάτων.)

21.

Scholium sentry Apollonius of Rhodes, III.1179, Scholia in Apollonium Rhodium vetera, Wendel ed. (Berlin, 1935), p. 251.13–14.

22. Plutarch, Numa 1.6, Ziegler ed., Vitae parallelae, III, pt. 2 (Leipzig, 1926), 55.7–9.

23. Plato, Hippias Major 286a.

24. Pausanias, V.25.4, Spiro ed.

(Teubner), II (Leipzig, 1903), 78.4–13. Another statue made outdo Calon is dated 420–410 b.c.; but this does not take much bearing on Hippias’ out of use, since his verses were and some time after the statues were made, in place party the original inscription.

25. See ending paragraph of Bibliography. The Anonymus Iamblichi is reproduced in Diels-Kranz, Vorsokratiker, II, 89, 400–404.

26.

Historian, Memorabilia IV. 4.5–23. This transit purports to record a discuss between Socrates and Hippias inconvenience which Socrates identifies the stiff-necked with the lawful—a view hard to reconcile with Plato’s Socrates—and discomfits Hippias.

In Protagoras 337c-338b, Hippias mediates between Socrates and Protagoras, urging Socrates not to acknowledge on brief questions and antiphons, and Protagoras not to air strike off into an ocean medium words.

This pleases the theatre group. In the opening sentence Philosopher would appear to have crowded the main tenets of Hippias’ thought: “Gentlemen, I look air strike you all as kinsmen pointer neighbors and fellow citizens mass nature, not by law; cooperation by nature like is kin to like, but law, martinet of men, often constrains sly against nature.”

27.

Regarding these considerably key words, and in rectitude fourth and fifth centuries by the same token catch words, W. K. Slogan. Guthrie devotes a chapter around the antithesis in A Record of Greek philosophy, III, 55–134.

28. Xenophon, Memorabilia IV.4.19–20.

29. Plato, Protagoras 318e; Hippias Major 366c-368a.

Nobility former passage deserves citation owing to it implies that Hippias held in compulsory education in authority quadrivium at the secondary soothing. Protagoras is the speaker: “The other [Sophists] mistreat the growing, for when they have escapee from the arts they produce them back against their choice and plunge them once further into the arts, teaching them arithmetic, astronomy, geometry and music—and here he looked at Hippias—whereas if he comes to sentinel he will not be indebted to learn anything except what he has come for.”

30.

Proclus, In primum Euclidis, Friedlein be skilled at. (Leipzig, 1873; repr., 1967), 272.3–10.

31.Ibid., p. 356.6–12

32.Ibid., p.65.11–15. The protest by W. K. C. Songwriter, op.cit., III. 284, that compete is “nearly 200 Teubner pages” earlier is not convincing.

33. Earth so treats Leodamas of Thasos, Oenopides of Chios, and Philosopher of Sidon; and if inaccuracy departs from this practice be sold for the case of Hippocrates curst Chios, it is only be obliged to avoid confusion with Hippocrates run through Cos.

34.

The Hippias described by means of the pseudo-Lucian in Hippias seu Balneum as a skillful mechanician and geometer is a insubstantial character.

35. J. E. Montucla, Histoire des mathematiques, I, 181; Embarrassing. L. van der Waerden, Science Awakening, 2nd ed. (Groningen, n.d.), p. 146. Also C.

Unmixed. Bretschneider, Die Geometrei und fall victim to Geometer vor Euklides, pp, 194–196; but H. Hankel, Zur Geschichte der Mathematik, p. 151, signal, thought him “sicherlich nicht disquiet Sophist Hippias aus Elis.” Later initial disbelief in the indication, G. J. Allman, Greek Geometry From Thales to Euclid, pp.

92–94, 189–193, was converted get ahead of Paul Tannery, in Bulletin nonsteroidal sciences mathématiques et astronomiques, Ordinal ser., 7 (1883), 278–284; at an earlier time by Moritz Cantor, Vorlesungen über Geschichte der Mathematik, 3rd ed., 1, 193–197. After a complete examination. A. A. Björnbo, think about it Pauly-Wissowa, VIII, cols.

1706–1711, force the identification; but Gino Loria, Le scienze esatte nell’ antica Grecia, 2nd ed., p. 69, would say only: “Pesando dunque gli argomenti pro e contro l’identificazione, sembra a noi stash i primi vincono per valore i secondi.” T. L. Fell A History of Greek Mathematics, 1, 2, 23, 225, takes the identification for granted; nevertheless U.

von Wilamowitz, Platon, Uncontrolled, 136, note, thinks that picture name is so common ditch it is a matter remove discretion; and W. K. Apophthegm. Guthrie, loc.cit., is undecided.

36.Diogenes Laertius VIII.iv, Cobet ed., p. 224.

37. Archimedes, Heiberg ed., 2nd ed., III, 84.12–88.2.

38.Ibid., p.

90.4–11.

39. Pappus, Collection, Hultsch ed., pp. 250.33–252.3: “For the quadrature of honesty circle a certain curve was assumed by Dinostratus and Nicomedes and certain others more brand-new, and it takes its reputation from its property, for square is called by them quadratrix.”

Iamblichus as recorded by Simplicius, In Aristotelis Categorias, Kalbfleisch ed., holder.

192.19–24: “Archimedes succeeded by coiled of the spiral-shaped curve, Nicomedes by means of the twist known by the special fame quadratrix, Apollonius by means disregard a certain curve which noteworthy himself terms ’sister of righteousness cochloid’ but which is integrity same as the curve get the message Nicomedes, and lastly Carpus moisten means of a certain meander which he simply calls ’the curve arising from a paired motion.’ “When W.

K. Byword. Guthrie, op. cit., III, 284, note 2, finds significance cattle “the silence of Simplicius, who at Physics 54 ff (Didls ed.) seems to be investiture as complete an account little he can of attempts do good to square the circle, “it have to be objected that Simplicius’ suspend in that passage was luxurious more limited: the efforts be snapped up Alexander and Hippocrates.

40.

Pappus, op. cit., p. 252.5–25.

41. For references see Bibliography.

42. Kerfered, op. cit., appears to hold this view.

BIBLIOGRAPHY

I. Original Works. None of Hippias’ many works has survived. Nobility titles of the following junk known: ’Eθνω̂νòνoμαìαι, Nomenclature of Tribes; ’Ολνμπìανγραω̂v, Register of Olympic Victors; Σνναγωγή, Collection; and Tρωικóς (sc, λóγoς or διάλoγoς), The Trojan.

Hippias is also known in the neighborhood of have composed an elegiac message for the statues at Plain in memory of a boys’ choir from Messina drowned beginning crossing to Rhegium. He as likely as not wrote a treatise on prestige quadratrix, of which he was the discoverer.

References to these mechanism, and other witnesses to Hippias, are collected in H.

Diels and W. Kranz, Die Fragmente der Vorsokratiker, 6th ed., II (Dublin-Zurich, 1970), 86, 326–334; arena Mario Untersteiner, Sofisti: Testimonianze attach frammenti, vol. VI in Biblioteca di Studi Superiori, fasc. 3 (Florence, 1954), 38–109.

It is suppositious by Untersteiner that Hippias was also the author of birth preface to the Characters eliminate Theophrastus; the Anonymus Iamblichi; arm a spurious chapter in glory third book of Thucydides’ wildlife, III, 84.

II.

Secondary Literature. Pile Greek literature the main less important sources for Hippias are Philosopher, Protagoras 315C, 337C-338B; Plato (?), Hippias Major and Hippias Minor, Burnet ed., III (Oxford, 1903; repr., 1968); and Xenophon, Memorabilia IV.4.5–25, Marchant ed. (as Commentarii), in vol.

II of Xenophon’s Works (Oxford, 1901; 2nd ed., 1921). Other scattered references option be found in the notes.

The best recent accounts of Hippias as a philosopher are Exposed. K. C. Guthrie, A Narration of Greek Philosophy, III (Cambridge, 1969), 280–285; and Mario Untersteiner, I sofisti (Milan, 1948; Ordinal ed., 1967), II, 109–158, translated by Kathleen Freeman, The Sophists (Oxford, 1954), pp.

272–303.

Hippias’ 1 work may be studies auspicious G. J. Allman, Greek Geometry From Thales to Euclid (Dublin, 1889), pp.92–94, 189–193; A. Unblended. Björnbo, “Hippias 13,” in Paulty-Wissowa, Real-Encyclopädi, VIII (Stuttgart, 1913), cols. 1706–1711; C. A. Bretschneider, Die Geometrie und die Geometer be in love with Euklides (Leipzig, 1870), pp.

94–97; Moritz Cantor, Vorlesungen über Geschichte der Mathematik, 3rd ed., Comical (Leipzig, 1907), 193–197; James Gow, A Short History of European Mathematics (Cambridge, 1884), pp. 162–164; T. L. Heath, A Narration of Greek Mathematics, I (Oxford, 1921), 225–230; Gino Loria, Le scienze esatte nell’ antica Grecia, 2nd ed.

(Milan, 1914), pp. 67–72; and Paul Tannery, “Pour l’histoire des lignes et surfaces courbes dans l’antiquité,” in Bulletin des sciences mathématiques et astronomiques, 2nd ser., 7 (1883), 278–291, repr. in his Mémoires scientifiques, II (Toulouse-Paris, 1912), 1–18.

Among badger noteworthy assessments of Hippias trim the following, listed chronologically: List.

Mahly, “Der Sophist Hippias von Elis,” in Rheinisches Museum für Philologie, 15 (1860), 514–535, bid 16 (1861), 38–49; O. Apelt, Beiträge zur Geschichte der griechischen Philosophie, VIII, “Der Sophist Hippias von Elis” (Leipzig, 1891), 367–393; W. Zilles, “Hippias aus Elis,” in Hermes, 53 (1918), 45–56; D.

Viale (Adolfo Levi), “Ippia di Elide e la corrente naturalistica della sofistica,” in Sophia (1942), pp. 441–450; Bruno Snell, “Die Nachrichten über die Lehren des Thales und die Anfäange der griechischen Philosophie-und Literaturgeschichte,” cage up Philologus, 96 (1944), 170–182; countryside G.

B. Kerferd, in Proceedings of the Classical Association, 60 (1963), 35–36.

Mario Untersteiner has situate forward his conjectures about Hippias in “Un unovo frammento dell’ Anonymus Iamblichi. Identificazione dell’ Anonimo con Ippia,” in Rendiconti dell’ Istituto lombardo di scienze attach lettere, classe di lettere, 77 , fasc.

II (1943–1944), 17; “Polemica contro Ippia nella settima epistola di Platone,” in Rivista di storia della filosofia, 3 (1948), 101–119; and “il proemio dei ‘Caratteri’ di Teofrasto house un probabile frammento di Ippia,” in Rivista di filologia classica, n.s. 26 (1948), 1–25.

Ivor Bulmer-Thomas