THALES OF MILETUS (640-546 B.C.), son of Examyus and Cleobuline, is universally recognized as the founder of Greek geometry, astronomy, and philosophy. He is said by Herodotus and others to have been of Phoenician extraction, but the more common account (see Diogenes Laertius) is that he was a native Milesian of noble birth. Zeller thinks that his ancestors belonged to the Cadmean tribe in Bceotia, who were intermingled with the Ionians of Asia Minor, and thus reconciles the con-flicting statements. The nationality of Thales is certainly Greek and not Phoenician. The high estimation in which he was held by his contemporaries is shown by the place he occupied as chief of the seven " wise men " of Greece; and in later times amongst the ancients his fame was quite remarkable. It is well known that this name (o"o<^>os) was given on account of practical ability; and in accordance with this we find that Thales had been occupied with civil affairs, and indeed several instances of his political sagacity have been handed down. Of these the most remarkable is the advice, praised by Herodotus, which he gave to his fellow-countrymen " before Ionia was ruined,"—" that the Ionians should constitute one general council in Teos, as the most central of the twelve cities, and that the remaining cities should nevertheless be governed as independent states" (Herod., i. 170). It is probable, however, that in the case of Thales the appellation " wise man," which was given to him and to the other six in the archonship of Damasius (586 B.C.),1 was conferred on him not only on account of his political sagacity, but also for his scientific eminence (Plut., Solon, c. 3). To about the same time must be referred his celebrated prediction of the eclipse of the sun, which took place on May 28, 585 B.C. This event, which was of the highest importance, has given rise to much discussion. The account of it as given by Herodotus (i. 74) contains two statements :—(1) the fact that the eclipse did actually take place during a battle between the Medes and the Lydians, that it was a total eclipse (Herodotus calls it a " night battle "), that it caused a cessation of hostilities and led to a lasting peace between the contending nations; (2) that Thales had foretold the eclipse to the Ionians, and fixed the year in which it actually did take place. Various dates—ranging from 625 B.C. to 583 B.C.—have been assigned by different chrono-logists to this eclipse; but, since the investigations of Airy,2 Hind,3 and Zech,4 the date determined by them (May 28, 585 B.C.) has been generally accepted. This date agrees nearly with that given by Pliny (H. N.. ii. 12). The second part of the statement of Herodotus—the reality of the prediction by Thales—has been frequently called in question, chiefly on the ground that, in order to predict a solar eclipse with any chance of success, one should have the command of certain astronomical facts which were not known until the 3d century B.C., and then merely approximately, and only employed with that object in the following century by Hipparchus. The question, however, is not whether Thales could predict the eclipse of the sun with any chance of success—much less whether he could state beforehand at what places the eclipse would be visible, as some have erroneously supposed, and which of course would have been quite impossible for him to do, but simply whether he foretold that there would be a solar eclipse in that year, as stated by Herodotus. Now as to this there is quite a remarkable unanimity in the testi-mony of the ancients, and the evidence is of the strongest kind, ascending to Herodotus, and, according to the account of Diogenes Laertius, even to Xenophanes, who was an Ionian, and not much later than Thales. Further, we know that in the 8th century B.C. there were observatories in most of the large cities in the valley of the Euphrates, and that professional astronomers regularly took observations of the heavens, copies of which were sent to the king of Assyria; and from a cuneiform inscrip-tion found in the palace of Sennacherib at Nineveh, the text of which is given by George Smith, we learn that at that time the epochs of eclipses of both sun and moon were predicted as possible—probably by means of the cycle of 223 lunations or Chaldeean Saros—and that observations were made accordingly.
The wonderful fame of Thales amongst the ancients must have been in great part due to this achievement, which seems, moreover, to have been one of the chief causes that excited amongst the Hellenes the love of science which ever afterwards characterized them. Thales seems not to have left any writings behind him, though as to this there appears to be some doubt (see Diog. Laer., i. 23). Many anecdotes, amusing rather than instructive, are related of him, which have been handed down by Diogenes Laertius and other writers. From some of them it would appear that he was engaged in trade, which is indeed expressly stated by Plutarch {Solon, c. 2). It is probable that in the pursuit of commerce he was led to visit Egypt. Of the fact that Thales visited Egypt, and there became acquainted with geometry, there is abun-dant evidence. Hieronymus of Rhodes (ap. Diog. Laer., i. 27) says, " he never had any teacher except during the time when he went to Egypt and associated with the priests."
But the characteristic feature of the work of Thales was that to the knowledge thus acquired he added the capital creation of the geometry of lines, which was essentially abstract in its character. The only geometry known to the Egyptian priests was that of surfaces, together with a sketch of that of solids, a geometry consisting of some simple quadratures and elementary cubatures, which they had obtained empirically. Thales, on the other hand, intro-duced abstract geometry, the object of which is to establish precise relations between the different parts of a figure, so that some of them could be found by means of others in a manner strictly rigorous. This was a phenomenon quite new in the world, and due, in fact, to the abstract spirit of the Greeks.
The following discoveries in geometry are attributed to Thales :—o (1) the circle is bisected by its diameter (Procl., op. ext., p. 157) ; (2) the angles at the base of an isosceles triangle are equal (Id., p. 250) ; (3) when two straight lines cut each other the vertically opposite angles are equal (Id., p. 299) ; (4) the angle in a semicircle is a right angle ; (5) the theorem Euclid i. 26 is referred to Thales by Eudemus (Procl., op. cit., p. 352). Two applications of geometry to the solution of practical problems are also attributed to him :—_ (1) the determination of the distance of a ship at sea, for which he made use of the last theorem ; (2) the determination of the height of a pyramid by means of the length of its shadow : according to Hieronymus of Rhodes (Diog. Laert., i. 27) and Pliny (iV. H., xxxvi. 12), the shadow was measured at the hour of the day when a man's shadow is the same length as himself. Plutarch, however, states the method in a form requiring the knowledge of Euclid vi. 4, but without the restriction as to the hour of the day (Sept. Sap. Conviv., 2). Further, we learn from Diogenes Laertius (i. 25) that he perfected the things relating to the scalene triangle and the theory of lines. Proclus, too, in his summary of the history of geometry before Euclid, which he probably derived from Eudemus of Rhodes, says that Thales, having visited Egypt, first brought the knowledge of geometry into Greece, that he discovered many things himself, and communicated the beginnings of many to his successors, some of which he attempted in a more abstract manner (KadoAiKaripoy) and some in a more intuitional or sensible manner (alo-6-nTiK<!>T¤pov) (op. cit., p. 65).
From these indications it is no doubt difficult to determine what Thales brought from Egypt and what was due to his own inven-tion. This difficulty has, however, been lessened since the transla-tion and publication of the papyrus Rhind by Eisenlohr ; and it is now generally admitted that, in the distinction made in the last passage quoted above from Proclus, reference is made to the two forms of his work,—alaBrtriKÛrepov pointing to what he derived from Egypt or arrived at in an Egyptian manner, while KaOoKiKtirepov indicates the discoveries which he made in accordance with the Greek spirit. To the former belong the theorems (1), (2), and (3), and to the latter especially the theorem (4), and also, probably, his solution of the two practical problems. We infer, then, [1] that Thales must have known the theorem that the sum of the three angles of a triangle are equal to two right angles. This inference is made from (4) taken along with (2). No doubt we are informed by Proclus, on the authority of Eudemus, that the theorem Euclid i. 32 was first proved in a general way by the Pytha-goreans (see PYTHAGORAS, vol. xx. p. 140) ; but, on the other hand, we learn from Geminus that the ancient geometers observed the equality to two right angles in each kind of triangle—in the equilateral first, then in the isosceles, and lastly in the scalene ( Apoll., Conica, ed. Halleius, p. 9), and it is plain that the geometers older than the Pythagoreans can be no other than Thales and his school. The theorem, then, seems to have been arrived at by induc-tion, and may have been suggested by the contemplation of floors or wails covered with tiles of the form of equilateral triangles, or squares, or hexagons. [2] We see also in the theorem (4) the first trace of the important conception of geometrical loci, which we, therefore, attribute to Thales. It is worth noticing that it was in this manner that this remarkable property of the circle, with which, ill fact, abstract geometry was inaugurated, presented itself to the imagination of Dante :—
" 0 se del mezzo cerchio far si puote Triangol si, eh"un retto non avesse.",—Par., c. xiii. 101.
[3] Thales discovered the theorem that the sides of equiangular triangles are proportional. The knowledge of this theorem is dis-tinctly attributed to Thales by Plutarch, and it was probably made use of also in his determination of the distance of a ship at sea. Let us now consider the importance of the work of Thales.
I. In a scientific point of view : (a) we see, in the first place, that
by his two theorems he founded the geometry of lines, which has
ever since remained the principal part of geometry ; (b) he may,
in the second place, be fairly considered to have laid the founda-
tion of algebra, for his first theorem establishes an equation in the
true sense of the word, while the second institutes a proportion.
II. In a philosophic point of view : we see that in these two-
theorems of Thales the first type of a natural law, i.e., the ex-
pression of a fixed dependence between different quantities, or, in
another form, the disentanglement of constancy in the midst of
variety—has decisively arisen. III. Lastly, in a practical point
of view : Thales furnished the first example of an application of
theoretical geometry to practice, and laid the foundation of an
important branch of the same—the measurement of heights and
distances. For the further progress of geometry see PYTHAGORAS.
4 Ein mathematisches Ilandbuch der alten Aegypter, Leipsic, 1877.
5 Auguste Comte, Système de Politique Positive, iii. pp. 297, 300.
9 This is the received interpretation of the passage in Diogenes Laertius, i. 24 (see Wolf, Gesch. der Astron., p. 169), where <reAr]vaiov is probably a scribe's error for ÇcpSiaKov. Cf. Apuleius, Florida, iv. 18, who attributes to Thales, then old, the discovery : " quotiens sol mag-nitudine sua cireulum quern permeat metiatur."
As to the astronomical knowledge of Thales we have the follow-ing notices :—(1) besides the prediction of the solar eclipse, Eu-demus attributes to him the discovery that the circuit of the sun between the solstices is not always uniform ; (2) he called the last day of the month the thirtieth (Diog. Laert,, i. 24); (3) he divided the year into 365 days (Id., i. 27); (4) he determined the dia-meter of the sun to be the 720th part of the zodiac ;s (5) he appears to have pointed out the constellation of the Lesser Bear to his countrymen, and instructed them to steer by it [as nearer the pole] instead of the Great Bear (Calliniachus ap. Diog. Laert, i. 23 ; cf. Aratus, Phwnomena, v. 36 sq.). Other discoveries in astronomy are attributed to Thales, but on authorities which are not trustworthy. He did not know, for example, that " the earth is spher-ical," as is erroneously stated by Plutarch (Placita, iii. 10); on the contrary, he conceived it to be a flat disk, and in this supposition he was followed by most of his successors in the Ionian schools, including Anaxagoras. The doctrine of the sphericity of the earth, for which the researches of Anaximander had prepared the way,1 was in fact one of the great discoveries of Pythagoras, was taught by Parmenides, who was connected with the Pythagoreans, and remained for a long time the exclusive property of the Italian schools.2
"Whilst in virtue of his political sagacity and intellectual eminence Thales held a place in the traditional list of the wise men, on the strength of the disinterested love of knowledge which appeared in his physical speculations he was accounted a philosopher " (<pi\6-<ro<pos). His "philosophy" is usually summed up in the dogma " water is the principle, or the element, of things"; but, as the technical terms " principle " (apx^l) and " element " (aroix^o") hacl not yet come into use, it may be conjectured that the phrase " all things are water " (iravra v$up icri) more exactly represents his teaching. Writings which bore his name were extant in antiquity; but, as Aristotle, when he speaks of Thales's doctrine, always depends upon tradition, there can be little doubt that they were forgeries.
From Aristotle we learn (1) that Thales found in water the origin of things ; (2) that he conceived the earth to float upon a sea of the elemental fluid ; (3) that he supposed all things to be full of gods ; {i) that in virtue of the attraction exercised by the magnet he attributed to it a soul. Here our information ends. Aristotle's suggestion that Thales was led to his fundamental dogma by observation of the part which moisture plays in the pro-duction and the maintenance of life, and Simplicius's, that the impressibility and the binding power of water were perhaps also in his thoughts, are by admission purely conjectural. Simplicius's further suggestion that Thales conceived the element to be modi-fied by thinning and thickening is plainly inconsistent with the statement of Theophrastus that the hypothesis in question was peculiar to Anaximenes. The assertion preserved by Stobreus that Thales recognized, together with the material element "water," " mind," which penetrates it and sets it in motion, is refuted by the precise testimony of Aristotle, who declares that the early physicists did not distinguish the moving cause from the material cause, and that before Hermotimus and Anaxagoras no one postulated a creative intelligence.
It would seem, then, that Thales sought amid the variety of things a single material cause ; that he found such a cause in one of the forms of matter most familiar to him, namely, water, and accordingly regarded earth and all that it contains as water vari-ously metamorphosed ; and that, asking himself no questions about the manner of its transformation, he was content to see in the forces of nature present deities " (Zeller).
The doctrine of Thales was interpreted and developed in the course of three succeeding generations. First, Anaximander chose for what he called his " principle " (a.px'h), not water, but a cor-poreal element intermediate between fire and air on the one hand and water and earth on the other. Next, Anaximenes, prefer-ring air, resolved its transformations into processes of thinning and thickening. Lastly, Heraclitus asserted the claims of fire, which he conceived to modify itself, not occasionally, but per-petually. Thus Thales recognized change, but was not careful to explain it ; Anaximander attributed to change two directions ; Anaximenes conceived the two sorts of change as rarefaction and condensation ; Heraclitus, perceiving that, if, as his predecessors hat? tacitly assumed, change was occasional, the interference of a moving cause was necessary, made change perpetual. But all four agreed in tracing the variety of things to a single material cause, corporeal, endowed with qualities, and capable of self-transforma-tion. A now departure was taken by the Eleatic Parmenides (see vol. xviii. p. 315), who, expressly noting that, when Thales and his successors attributed to the supposed element changing qualities, they were untrue to the principle of monism, required that the superficial plurality of nature should be strictly distin-guished from its fundamental unity. Hence, whereas Thales and his successors had confounded the One, the element, and the Many, its modifications, the One and the Not-One or Many became with Parmenides matters for separate investigation. In this way two lines of inquiry originated. On the one hand Empedocles and Anaxagoras, abandoning the pursuit of the One, gave themselves to the scientific study of the Many; on the other Zeno, abandoning the pursuit of the Many, gave himself to the dialectical study of the One. Both successions were doomed to failure; and the result was a scepticism from which the thought of Greece did not emerge until Plato, retui-ning to Parmenides, declared the study of the One and the Many, jointly regarded, to be the true office of philosophy. Thus, meagre and futile as the doctrine of Thales was, all the Greek schools, with the solitary exception of that of Pythagoras, took their origin from it. Not in name only, but also in fact, Thales, the first of the Ionian physicists, was the founder of the philosophy of Greece.
1 In likening the earth to a cylinder Anaximander recognized its circular figure in one direction.
2 See G. V. Schiaparelli, / Precursori di Copernico nelV Antichità, p. 2, Milan, 1873.
Bibliography.—(A) GEOMETRICAL AND ASTRONOMICAI..—C. A. Bretschneider. Die Geometrie u. die Geometer vor Euklides, Leipsic, 1870 ; H. Hankel, Zur Geschichte der Mathematik, Leipsic, 1874 ; G. J. Allman, " Greek Geometry from Thales to Euclid," llermathena, No. v., Dublin, 1877 ; M. Cantor, Vorlesungen über Geschichte der Mathematik, Leipsic, 1880 ; P. Tannery, " Thales de Milet ce qu'il a emprunté à l'Egypte," Revue Philosophique, March 18S0 ; " La Tradition touchant Pythagore, Œnopide, et Thaïes," Bull, des Sc. Math., May 1886 ; R. Wolf, Geschichte der Astronomie, Munich, 1877. (B) PHILOSOPHICAL.—E. Zeller, Die Philosophie d. Griechen, i. 168-183, Leipsic, 1876 (Presocratic Philosophy, i. 211-227, Lond., 1881); F. Uebenveg, Grundriss d. Gesch. d. Philosophie, § 12, Berlin, 1871 (Hist, of Philosophy, Lond., 1880) ; T. Decker, De Thalete Milesio, Halle. 1865 ; A. B. Krische, Forschungen, pp. 84-42, Göttingen, 1840. (G. J. A.—H. JA.)


Footnotes

1 Bretschneider (Die Geom. vor Euklides, p. 40), without stating his authority, gives "between 585 and 583 B.C." as the date of the archonship of Damasius. In this lie is followed by some other recent writers, who infer thence that the name "wise" was conferred on Thales on account of the success of his prediction. The date 586 B.C., given above, which is taken from Clinton, is adopted by Zeller.
2 " On the Eclipses of Agathocles, Thales, and Xerxes," Phil. Trans., vol. cxliii. p. 179 sq., 1853. 3 Atltenieum, p. 919, 1852.
4 Aslronomische Untersuchungen der wichligeren Finsternisse, &c8 p. 57, 1853.


Assyrian Discoveries, p. 409.
Of. Pamphila and the spurious letter from Thales to Pherecydes, ap. Diog. Laer. ; Proclus, In primum Euclidis Elementorum Librum Commentarii, ed. Friedlein, p. 65 ; Pliny, H. N., xxxvi. 12 ; 1am-blichus, In Vit. Pythag., 12 ; Plutarch, Sept. Sap. Conviv., 2, De Iside, 10, and Plac., i. 3, 1.
This is unquestionably the meaning of the statement of Pamphila
(temp. Nero), ap. Diog. Laert., i. 24, that he was the first person to
describe a right-angled triangle in a circle.
P. Laffitte, Les Grands Types de l'Humanité, vol. ii. p. 292.
Ibid., p. 294.
Theonis Smyrnœi Platonici Liber de Astronomia, ed. Th. H. Mar-tin, p. 324, Paris, 1849. Cf. Diog. Laert., i. 24.