Blog. 7. mathematics. 610–626. 25. 1. It is likely that when Hippocrates took up mathematics, he addressed himself to the problem of squaring the circle, which was much in vogue; it is evident that in the course of his researches he found he could square certain lunes and, if this had not been done before him, probably effected the two easy quadratures described by Alexander as well as the more sophisticated ones attributed to him by Eudemus. who lived about 450 B.C. With the passage should be studied Epinomis 990bs-991b4, Burner ed. It is a sufficient condition for the lune to be squarable that sector OAFB = sector CAEB, for in that case the area will be equal to Δ CAB−Δ OAB, that is, the quadrilateral AOBC. 290 BC) - astronomy, spherical geometry He adds that mathematics came to be divulged by the Pythagoreans in the following way: One of their number lost his fortune, and because of this tribulation he was allowed to make money by teaching geometry. To construct a trapezium such that one of the parallel sides shall be equal to the greater of two given lines and each of the three remaining sides equal to the less. There is an obvious fallacy here, for the lune which was squared was one standing on the side of a square and it does not follow that the lune standing on the side of the hexagon can be squared. Early life Hippocrates was born on the Aegean island of Cos, just off the Ionian coast near Halicarnassus (island of Greece) during the end of the fifth century B.C.E. Thus, doubling the cube reduces a three-dimensional problem of doubling the cube to a one-dimensional problem of finding two lengths. He then went to Athens for litigation and taught mathematics there for his livelihood from 450 BC to 430 BC. Like other details about Hippocrates, we really know very little beyond the fact that he is considered a great physician and … Hippocrates’s book gave geometrical solutions to quadratic equations and methods of integration. Leonardo’s admiration for mathematics was unconditional, and found expression in his writings in such statements as “No certainty exists where none o…, Archimedes 1. 2, Hayduck ed. In it he explains about the discovery of Lunes by Hippocrates. There is confirmation in Eutocius, who in his commentary on Archimedes’ Measurement of a Circle notes that Archimedes wished to show that a circle would be equal to a certain rectilinear area, a matter investigated of old by eminent philosophers before him.23 “For it is clear,” he continues, “that the subject of inquiry is that concerning which Hippocrates of Chios and Antiphon, who carefully investigated it, invented the paralogisms which, I think, are accurately known to those who have examined the History of Geometry by Eudemus and have studied the Ceria of Aristotle.” This is probably a reference, to a passage in the Sophistici Elenchi where Aristotle says that not all erroneous constructions are objects of controversy, either because they are formally correct or because they are concerned with something true, “such as that of Hippocrates or the quadrature by means of lunes.”24 In the passage in Aristotle’s physics on which both Alexander and Simplicius are commenting,25 Aristotle rather more clearly makes the point that it is not the task of the exponent of a subject to refute a fallacy unless it arises from the accepted principles of the subject. 15, porism). It helps to transform specific mathematical questions into more general problems to solve them efficiently. The main source for our detailed knowledge of what he did is a long passage in Simplicius’ commentary on Aristotle’s Physics22 Simplicius acknowledges his debt to Eudemus’ History of Geometry and says that he will set out word for word what Eudemus wrote, adding for the sake of clarity only a few things taken from Euclid’s Elements because of Eudemus’ summary style. Pick a style below, and copy the text for your bibliography. Hippocrates of Chios, the foremost mathematician of the fifth century BC, knew of similarity properties, but there is no evidence that he dealt with the concept of homothecy. He was initially a merchant then a teacher in mathematics, and he was an astronomer also. He explained that they were due to refraction of solar rays by moisture inhaled by a putative planet near the Sun and the Stars. For the mathematical work of Hippocrates generally, the best secondary literature is George Johnston Allman, Greek Geometry From Thales to Euclid (Dublin-London, 1889), pp. 450–ca. Let p and q be two integers, \(\begin{align}\frac{{{p^2}}}{{{q^2}}} = 2,\rm{then}\,{p^2} = 2{q^2} = \end{align}\) even number p is an even number. Indeed, Hippocrates was the author of the irst Elements (Euclid’s Elements were the fourth such work), where geometrical theorems were systematically expounded in a deductive though not yet en- tirely axiomatic way. He then lays down that by continually doubling the number of sides in the inscribed polygon, we shall eventually come to a point where the residual segments of the second circle over S. For this he relies on a lemma, which is in fact the first proposition of Book X: “If two unequal magnitudes be set out, and if from the greater there be subtracted a magnitude greater than its half, and from the remainder a magnitude greater than its half, and so on continually, there will be left some magnitude which is less than the lesser magnitude set out.” On this basis Euclid is able to prove rigorously by reductio ad absurdum that S cannot be less than the second circle. These factors contribute to the Pythagorean traces in his mathematical contributions. 66–67—give only limited help. Worked on the classical problems of squaring the circle and duplicating the cube. B, 3 (1936), 411–418. To find a line such that twice the square on it shall be equal to three times the square on a given line. Proclus, op. (Whether Hippocrates solved this theoretically or empirically is discussed below.). square the circle. The most powerful argument for believing the quadratures to have been contained in a separate work is that of Tannery: that Hippocrates’ argument started with the theorem that similar segments of circles have the same ratio as the squares on their bases. He was teaching mathematics in Athens during the period from 450 B.C to 430 B.C. He was born on the isle of Chios, where he originally was a merchant. 7. Hippocrates himself was also very interested in astronomy, trying to solve the mystery of comets and the Milky Way, both of which he believed to be optical illusions. Hippocrates of Chios (born c. 470–died 410 BC) - first systematically organized Stoicheia - Elements (geometry textbook) Mozi (c. 468 BC–c. 4. II.12). Retrieved March 09, 2021 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/hippocrates-chios. Robbed of his wealth by pirates in the sea. https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/hippocrates-chios, "Hippocrates of Chios After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation, where he became a leading mathematician. Pauk Tannery, La geometrie grecque, p. 108; Maria Timpanaro Cardini, Pitagorici, fasc. In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list. )16 There is no reason to doubt that Hippocrates was the first to effect this reduction; but is does not follow that he, any more than Plato, invented the method. What Proclus says implies that Hippocrates’ book had the shortcomings of a pioneering work, for he tells us that Leon was able to make a collection of the elements in which he was more careful, in respect both of the number and of the utility of the things proved. The “Eudemian summary” of the history of geometry reproduced by Proclus states that Oenopides of Chios was somewhat younger than Anaxagoras of Clazomenae; and “after them Hippocrates of Chios, who found out how to square the lune, and Theodore of Cyrene beame distinguished in geometry. vertices of the triangle were denoted as A, B, C by Hippocrates. ), Paul Potter, Edward Theodore Withington (1959). It is clear that Hippocrates, like Alcmaeon and Empedocles before him, believed that rays of light proceeded from the eye to the object; and it seems probable that he thought visual rays were refracted in the moisture around the comet toward the sun (the sun then being in a position in which this could happen), and reflected from the sun back to the moisture and the observer’s eye (hence the choice of the neutral word “deflected”). That is, he got two mean proposals x and y. (Berlin, 1900), 45.24–46.24, 68.30–69. To find a line the square on which shall be equal to three times the square on a given line. 460 BCE), Hippocratic Oath" and "The Law of Hippocrates" (Fifth Century B.C. The chief ancient references to Hippocrates are collected in Maria Timpanaro Cardini, Pitagorici, testimonianze e frammenti, fasc. The credit for introducing letters to mark the geometric points and figures in propositions goes to Hippocrates. Timpanaro Cardini, op. The next figure shows the so-called Lunes of Hippocrates, named after Hippocrates of Chios (not the physician!) 187–190, must be studied with it. 287 b.c. 57–77, reproducing a paper which first appeared in Hermathena, 4 , no. Files are available under licenses specified on their description page. (Cambridge, Mass., 1918; 2nd ed., Hildesheim, 1967); and in the following volumes of Commentaria in Aristotelem Graeca: XII, pt. 10. Thomas Heath, A History of Greek Mathematics, I, 201. , having been developed by the Pythagoreans, was well within the capacity of Hippocrates or any other mathematician of his day. 4—"Magnitudes are said to have a ratio one to another if they are capable, when multiplied, of exceeding one another"—and this is used to prove Euclid X.1. 463–467.A new attempt to separate the Eudemian text from Simplicius was made by O. Becker, :Zyr Textgestaktyng des Eudemischen Berichts uber die Quadratur der Möndchen durch Hippocrates von Chios,” in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abt. Alexander, In Aristotelis Meteorologica, Hayduck ed., 38.28–32. Thought previously by astronomers as a single body sun from the earth, a planet of long and irregular orbit, and at a low elevation above the horizon, like planet mercury, which cannot be seen. Proclus, op. He was the enemy of all specialization, and appeared at Olympia gorgeously attired in a costume entirely of his own making down to the ring on his finger. The quadrature of lunes is the subject of papers by Paul Tannery: “Hippocrate de Chio et la quadrature des lunes,” in Memoires de la Societe des sciences physiques et naturelles de Bordeaux, 2nd ser., 2 (1878), 179–184; and “Le fragment d’Eudème sur la quadrature des lunes,” ibid., 5 (1883), 217–237, which may be more conveniently studied as reproduced in Tannery, Memoires scientifiques, I (Paris, 1912), 46–52, 339–370. Proclus explains that in geometry the elements are certain theorems having to those which follow the nature of a leading principle and furnishing proofs of many properties; and in the summary which he has taken over from Eudemus he names Hippocrates, Leon, Theudius of Magnesia, and Hermotimus of Colophon as writers of elements.30 In realizing the distinction between theorems which are merely interesting in themselves and those which lead to something else, Hippocrates made a significant discovery and started a famous tradition; but so complete was Euclid’s success in this field that all the earlier efforts were driven out of circulation. In an isosceles triangle whose vertical angle is double the angle of an equilateral triangle (that is, 120°), the square on the base is equal to three times the square on one of the equal sides. Aristotle does an injustice to Antiphon, whose inscription of polygons with an increasing number of sides in a circle was the germ of a fruitful idea, leading to Euclid’s method of exhaustion; Aristotle no doubt thought it contrary to the principles of geometry to suppose that the side of the polygon could ever coincide with an arc of the circle. Hermann Hankel, Zur Geschichte der Mathematik in Alterthum und Mittelalter, p. 122. 370 B.C. What Euclid does is to say that if the ratio of the squares on the diameters is not equal to the ratio of the circles, let it be equal to the ratio of the first place to be less than the second circle. Therefore S must be equal to the second circle, and the two circles stand in the ratio of the squares on their diameters. 9. Hippocrates’ tutor Oenopides had previously traveled to Egypt and studied both geometry and astronomy under the Egyptian priests. p & q have common factor of 2 here and  \(\begin{align}\frac{p}{q}\end{align}\) is not an irreducible fraction. Let K be the center of two circles such that the square on the diameter of the outer is six times the square on the diameter of the inner. ... (New Astronomy) of 1609. If the great semicircle on the hypotenuse is folded up, Hippocrates is the earliest of those who are recorded as having written Elements.”5 Since Anaxgoras was born about 500 b.c. 21–22, much earlier (1754) had given the correct interpretation: “Hippocrate ne vouloit point proposer un moyen qu’il jugeoit propre à conduire quelque jour à la quardrature du cercle?". Complete Dictionary of Scientific Biography. ." (Basel, 1969), 59.28–66.6. Hippocrates is said by Proclus to have been the first to effect the geometrical reduction of problems difficult of solution.11 By reduction (άπαγωγή) Proclus explains that he means"a transition from one problem or theorem to another, which being known or solved, that which is propounded is also manifest.”12 It has sometimes been supposed, on the strength of a passage int he Republic, that Plato was the inventor of this method; and this view has been supported by passages from Proclus and Diogenes Laertius.13 But Plato is writing of philosophical analysis, and what Proclus and Diogenes Laertius say is that Plato “communicated” or “explained” to Leodamas of Thasos the method of analysis (άναλύσις)—the context makes clear that this is geometrical analysis—which takes the thing sought up to an acknowledged first principle. There is a full essay on this subject in T. L. Heath, The Works of Archimedes, pp. 23.Archimedis opera omnia, Heiberg ed., 2nd ed., III, 228.11–19. window.__mirage2 = {petok:"b71fc62fcae90ae9741502fd42a5148448c99d85-1615378359-86400"}; 19. ; Proclus, op. The documentation of Hippocrates’ life is not concrete, and there may be some inaccurate and incomplete information. Aristotle proceeds to give five fairly cogent objections to these theories.42, After recounting the views of two schools of Pythagoreans, and of Anaxagoras and Democritus on the Milky Way, Aristotle adds that there is a third theory, for “some say that the galaxay is a deflection of our sight toward the sun as is the case with the comet.” He does not identify the third school with Hippocrates; but the commentators Olympiodorus and Alexander have no hesitation in so doing, the former noting that the deflection is caused by the stars and not by moisture.43, 1. Let C be the midpoint of KB and let CD bisect BK at right angles. He knew how to solve the following problems: (1) about a given triangle to describe a circle (IV.5); (2) about the trapezium drawn as in problem 9, above, to describe a circle; (3) on a given straight line to describe a segment of a circle similar to a given one (cf.III.33). There would not appear to be any difference in meaning between “reduction” and “analysis,” and there is no claim that Plato invented the method. Then and the area of the lune is 1/2 r2 (k sin 2ϕ-r2 sin2θ). The geometer Hippocrates of Chios is sometimes confused with a contemporary of his, the famous physician Hippocrates of Cos, for whom the Hippocratic Oath is named.Not much is known about him past what is read here. He was a genius mathematician but believed to have little common sense. The geometer Hippocrates of Chios is sometimes confused with a contemporary of his, the famous physician Hippocrates of Cos, for whom the Hippocratic Oath is named.Not much is known about the geometer Hippocrates past … mathematics, mechanics. Two medieval versions of Hippocrates’ quadratures are given in Marshall Clagett, “The Quadratura circuli per lunulas,” Appendix II, Archimedes in the Middle Ages, I (Madison, Wis., 1964), pp. A merchant and wealthy in his early days. Aristotle, Meteorologica, A6, 343a21–343b8, Fobes ed., 2nd ed. He thought that they were optical illusions. The ancient commentators are probably right in identifying the quadrature of a circle by means of segments with Hippocrates’ quadrature of lunes; mathematical terms were still fluid in Aristotle’s time, and Aristotle may well have thought there was some fallacy in it. The name by which Hippocrates the mathematician is distinguished from the contemporary physician of Cos1 implies that he was born in the Greek island of Chios; but he spent his most productive years in Athens and helped to make it, until the foundation of Alexandria, the leading center of Greek mathematical research. According to Aristotle, 38 certain Italians called Pythagoreans said that the comet—it was apparently believed that there was only one—was a planet which appeared only at long intervals because of its low elevation above the horizon, as was the case with Mercury.39 The circle of Hippocrates and his pupil Aeschylus40 expressed themselves in a similar way save in thinking that the comet’s tail did not have a real existence of its own; rather, the comet, in its wandering through space, occasionally assumed the appearance of a tail through the deflection of our sight toward the sun by the moisture drawn up by the comet when in the neighborhood of the sun.41 A second reason for the rare appearance of the comet, in the view of Hippocrates, was that it retrogressedc so slowly in relation to the sun, and therefore took a long time to get clear of the sun. Alexander goes on to say that if the rectilinear figure equal to the three lunes is subtracted (“for a rectilinear figure was proved equal to a lune”), the circle will be squared. He attended lectures and became so proficient in geometry that he tried to square the circle. Hippocrates of Chios was an ancient Greek mathematician, (geometer), and astronomer, who lived c. 470 – c. 410 BCE. 27. 29. He was the first to compose an Elements of Geometry in the manner of Euclid’s famous work. Although Hippocrates is not named, it would, as Allman points out, accord with the accounts of Aristotle and Philoponus if he were the Pythagorean in question.9 The belief that Hippocrates stood in the Pythagorean tradition is supported by what is known of his astronomical theories, which have affinities with those of Pythagoras and his followers. According to the Aristotelian commentator John Philoponus, he was a mercahnt who lost all his property through being captured by pirates.2 Going to Athens to prosecute them, he ws obliged to stay a long time. This last quadrature, rather than that recorded by Alexander, may be the source of the belief that Hippocrates had squared the circle, for the deduction is not so obviously fallacious. Tannery, op. He wrote the first textbook in geometry, named as ‘Elements’. ." It appears to be the case that the Cos writers sought to create general biomedical \"laws\" that for the most part would give the explanation for … In the second quadrature AB is the diameter of a semicircle; and on CD, equal to twice AB, a semicircle. Hippocrates was evidently familiar with the geometry of the circle; and since the Pythagoreans made only a limited incursion into this field, he may himself have discovered many of the theorems contained in the third book of Euclid’s Elements and solved many of the problems posed in the fourth book. 36. cit., p. 91, inclines to the same view; but Timpanaro Cardini, op. Hippocrates of Chios 470 BC – 410 BC Hippocrates was a teacher of geometry in Athens. 2021 . xxiii-xxxi, is an appendix Hippocratea by H. Usener, “De supplendis Hipporcratis quas omisit Eudemus constructionibus.”. ; d. Syracuse, 212 b.c.) Hippocrates of Chios Introduction to the mathematics of lunules Analysis of the quadrature of lunules as reported by Alexander 5. Proclus gives as an example of the method the reduction of the problem of doubling the cube to the problem of finding two mean proportionals between two straight lines, after which the problem was pursued exclusively in that form.14 He does not in so many words attribute this reduction to Hippocrates; but a letter purporting to be from Eratosthenes tp Ptolemy Euergetes, which is preserved by Eutocius, does specifically attribute the discovery to him.15 In modern notation, if a:x = x:y = y:b, then a3:x3 =a:b; and if b = 2 a, it follows that a cube of side x is double a cube of side a. adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A He generalized this concept, though unaware of numbers then, later Elucid has proved there is one mean proposal between two square numbers and two between two cube numbers. To construct a square equal to a given rectilinear figure (II.14). 22. The ancient references to Hippocrates’ speculations on comets and the galaxy are in Aristotle, Meteorologicorum libri quattuor A6, 342a30–343a20 and A8, 345b9, Fobes ed. Hippocrates was born about 410 BC in Chios, Greece and died about 410 BC. 270–271; and Thomas Heath, Mathematics in Aristotle, pp. It influenced the attempts to duplicate cubes and proportional problems. Proclus, the last famous Greek philosopher, had also confirmed that. Hippocrates was a Greek geometer and astronomer whose works are known only through references by later authors. cit., fasc. Complete Dictionary of Scientific Biography. In the first, AB is the diameter of a semicircle, AC, CB are sides of a square inscribed in the circle, and AEC is a semicircle inscribed on AC. In support, it is pointed out that Hippocrates first places EF without producing it to B and only later joins BF.31 But it has to be admitted that the complete theoretical solution of the equation Hippocrates was originally a merchant. cit., Stuve ed., 45.29–30, notes that where as Pythagoras maintained that both the comet and the tail were made of the fifth substance, Hippocrates held that the comet was made of the fifth substance but the tail out of the sublunary space. 24. Duplication of the Cube. Hippocrates was a Greek geometer and astronomer whose works are known only through references by later authors. cit., 66.4–6, in fact mentions the squaring of the lune as a means of identifying Hippocrates. at Chios, in Greece. He proved that the area of the shaded portion i.e., lune = the area of the triangle ABC. Plutarch, Vita Solonis 2. Cuemath, a student-friendly mathematics platform, conducts regular Online Live Classes for academics and skill-development and their Mental Math App, on both iOS and Android, is a one-stop solution for kids to develop multiple skills. The method involves dividing the circle into several crescent-shaped parts (Lunes) and calculating the areas of all crescents which gives the area of the whole circle. 2. (fl. Greek Physician, Hippocrates and the Hippocratic Corpus (b. Simplicius of Cilicia was a 5th century neo Platonist philosopher. In astronomy he propounded theories to account for comets and the galaxy. 34–35. Aristotle, Physics A 2, 185a14, Ross ed. He came to Athens to prosecute the pirates and, staying a long time in Athens by reason of the indictment, consorted with philosophers, and reached such proficiency in geometry that he tried to affect the quadrature of the circle. Then, copy and paste the text into your bibliography or works cited list. Antiphon was the first native Athenian to be class…, square / skwe(ə)r/ • n. 1. a plane figure with four equal straight sides and four right angles. Hippocrates’ research into lunes shows that he was aware of the following theorems: 1. T. Clausen gave the solution of the last four cases in 1840, when it was not known that Hippocrates had solved more than the first. 33.Archimedis opera omnia, Heiberg ed., 2nd ed., II, 264.1–22. It is not clear how Aristltle thought the appearance to be caused, and the commentators and translators—Thomas Heath, Aristarchus of Samos, p. 243; E. W. Webster, The Works of Aristotle, III, Meteorologica, loc. "Hippocrates of Chios cit., Stuve ed., 68.30–35; he reckons it a “fourth opinion,” presumably counting the two Pythagorean 3. This and references by Aristotle to οί περί ‘Ιπποκράτην imply that Hippocrates had a school. This is anachronistic. It is a systematically organized writing on basics for building mathematical blocks. Hippias is chiefly memorable for his efforts in the direction of universality. 40–43; Timpanaro Cardini, op. 21–66.7. Hippocrates, "the father of medicine," may have lived from c. 460-377 B.C., a period covering the Age of Pericles and the Persian War. 5. The suggestion was made by Bretschneider, and has been developed by Loria and Timpanaro Cardini,17 that since the problem of doubling a square could be reduced to that of finding one mean proportional between two lines,18 Hipporcrates conceived that the doubling of a cube might require the finding of two mean proportionals. Alexander shows that the lune AEC is equal to the triangle ACD. Hippocrates’ three solutions correspond to the values 2, 3, 3/2 for k.29. It is speculated that Hippocrates studied astronomy during his life in Chios. Hippocrates was born on the island of Chios, off the west coast of what is now Turkey, and spent most of his adult life in Athens, where he journeyed to prosecute pirates who had stolen his property. Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. c-cxxii. In A question that has been debated is whether Hippocrates’ quadrature of lunes was contained in his Elements or was a separate work. 9 Mar. This method was found not correct by mathematician Ferdinand von Lindamann in 1829. I chose to write about Hipprocates because the little-known people who contribute to the … The fallacy, of course, is that the lune which is squared along with the circle is not one of the lunes previously squared by Hippocrates; and although Hippocrates squared lunes having outer circumferences equal to, greater than, and less than a semicircle, he did not square all such lunes but only one in each class. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites: http://www.chicagomanualofstyle.org/tools_citationguide.html. Quadrature of Lunes. Hippocrates of Chios Born: about 470 BC in Chios (now Khios), Greece Died: about 410 BC Summary: Greek mathematician. Encyclopedia.com. Another stylistic test is the earlier form which Eudemus would have used, δυνάμει εί̂ναι (“to be equal to when square”), for the form δύνασθαι, which Simplicius would have used more naturally. For example, this can be used to prove that there is no smallest rational number. It was shown by M. J. Wallenius in 1766 that the lune can be squared by plane methods when x = 5 or 5/3 (Max Simon, Geschichte der Mathematik im Altertum, p. 174). The task of separating what Simplicius added has been attempted by many writers from Allman to van der Waerden. In the same volume, pp. have contented himself with an empirical solution, marking on a ruler a length equal to KA in Figure 5 and moving the ruler about until the points marked lay on the circumference and on CD, respectively, while the edge of the ruler also passed through B. Encyclopedia.com. More strictly “the lemma of Archimedes” is equivalent to Euclid V, def. He was, in Timpanaro Cardini’s phrase, a para-Pythagorean, or, as we might say, a fellow traveler.10. Paul Tannery, who is followed by Maria Timpanaro Cardini, ventures to doubt that Hippocrates needed to learn his mathematics at Athens.7 He thinks it more likely that Hippocrates taught in Athens what he had already learned in Chios, where the fame of Oenopides suggests that there was already a flourishing school of mathematics. Hippocrates of Chios flourished c. 440 BC Long summary: Greek geometer. 18. and Plato went to Cyrene to hear Theodore after the death of Socrates in 399 b.c., the active life of Hippocrates may be placed in the second half of the fifth century b.c. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation. He was born in 470 B.C. Plutarchi vitae parallelae, Sintenis ed., I, 156.17–20. John Phioloponus, In Aristotelis Physica, Vitelli ed., 31.3–9. 13. But this is only suggestion, not proof, for the ancient Greeks never worked out a rigorous procedure for taking the limits.
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