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LOGOCYCLIC CURVE, STROPHOID or FOLIATE, a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line. The polar equation is r cos θ = a(1 ± sinθ), the upper sign referring to the case when the vector is increased, the lower when it is diminished. Both branches are included in the Cartesian equation (x2 + y2)(2a − x) = a2x, where a is the distance of the line from the origin. If we take for axes the fixed line and the perpendicular through the initial point, the equation takes the form y √(a − x) = x √(a + x). The curve resembles the folium of Descartes, and has a node between x = 0, x = a, and two branches asymptotic to the line x = 2a.
LOGOGRAPHI (λόγος, γράφω, writers of prose histories or
tales), the name given by modern scholars to the Greek historiographers
before Herodotus.[1] Thucydides, however, applies
the term to all his own predecessors, and it is therefore usual
to make a distinction between the older and the younger logographers.
Their representatives, with one exception, came from
Ionia and its islands, which from their position were most favourably
situated for the acquisition of knowledge concerning the
distant countries of East and West. They wrote in the Ionic
dialect, in what was called the unperiodic style, and preserved
the poetic character of their epic model. Their criticism amounts
to nothing more than a crude attempt to rationalize the current
legends and traditions connected with the founding of cities,
the genealogies of ruling families, and the manners and customs
of individual peoples. Of scientific criticism there is no trace
whatever. The first of these historians was probably Cadmus
of Miletus (who lived, if at all, in the early part of the 6th century),
the earliest writer of prose, author of a work on the founding
of his native city and the colonization of Ionia (so Suïdas);
Pherecydes of Leros, who died about 400, is generally considered
the last. Mention may also be made of the following: Hecataeus
of Miletus (550–476); Acusilaus of Argos,[2] who paraphrased
in prose (correcting the tradition where it seemed necessary)
the genealogical works of Hesiod in the Ionic dialect; he confined
his attention to the prehistoric period, and made no attempt
at a real history; Charon of Lampsacus (c. 450), author of
histories of Persia, Libya, and Ethiopia, of annals (ὧροι) of
his native town with lists of the prytaneis and archons, and of
the chronicles of Lacedaemonian kings; Xanthus of Sardis in
Lydia (c. 450), author of a history of Lydia, one of the chief
authorities used by Nicolaus of Damascus (fl. during the time of
Augustus); Hellanicus of Mytilene; Stesimbrotus of Thasos,
opponent of Pericles and reputed author of a political pamphlet
on Themistocles, Thucydides and Pericles; Hippys and Glaucus,
both of Rhegium, the first the author of histories of Italy and
Sicily, the second of a treatise on ancient poets and musicians,
used by Harpocration and Plutarch; Damastes of Sigeum,
pupil of Hellanicus, author of genealogies of the combatants
before Troy (an ethnographic and statistical list), of short
treatises on poets, sophists, and geographical subjects.
On the early Greek historians, see G. Busolt, Griechische Geschichte (1893), i. 147-153; C. Wachsmuth, Einleitung in das Studium der alten Geschichte (1895); A. Schäfer, Abriss der Quellenkunde der griechischen und römischen Geschichte (ed. H. Nissen, 1889); J. B. Bury, Ancient Greek Historians (1909), lecture i.; histories of Greek literature by Müller-Donaldson (ch. 18) and W. Mure (bk. iv. ch. 3), where the little that is known concerning the life and writings of the logographers is exhaustively discussed. The fragments will be found, with Latin notes, translation, prolegomena, and copious indexes, in C. W. Müller’s Fragmenta historicorum Graecorum (1841–1870).
See also Greece: History, Ancient (section, “Authorities”).
LOGOS (λόγος), a common term in ancient philosophy and
theology. It expresses the idea of an immanent reason in the
world, and, under various modifications, is met with in Indian,
Egyptian and Persian systems of thought. But the idea was
developed mainly in Hellenic and Hebrew philosophy, and we
may distinguish the following stages:
1. The Hellenic Logos.—To the Greek mind, which saw in the world a κόσμος (ordered whole), it was natural to regard the world as the product of reason, and reason as the ruling principle in the world. So we find a Logos doctrine more or less prominent from the dawn of Hellenic thought to its eclipse. It rises in the realm of physical speculation, passes over into the territory of ethics and theology, and makes its way through at least three well-defined stages. These are marked off by the names of Heraclitus of Ephesus, the Stoics and Philo.
It acquires its first importance in the theories of Heraclitus (6th century B.C.), who, trying to account for the aesthetic order of the visible universe, broke away to some extent from the purely physical conceptions of his predecessors and discerned at work in the cosmic process a λόγος analogous to the reasoning power in man. On the one hand the Logos is identified with γνώμη and connected with δίκη, which latter seems to have the function of correcting deviations from the eternal law that rules in things. On the other hand it is not positively distinguished either from the ethereal fire, or from the εἱμαρμένη and the ἀνάγκη according to which all things occur. Heraclitus holds that nothing material can be thought of without this Logos, but he does not conceive the Logos itself to be immaterial. Whether it is regarded as in any sense possessed of intelligence and consciousness is a question variously answered. But there is most to say for the negative. This Logos is not one above the world or prior to it, but in the world and inseparable from it. Man’s soul is a part of it. It is relation, therefore, as Schleiermacher expresses it, or reason, not speech or word. And it is objective, not subjective, reason. Like a law of nature, objective in the world, it gives order and regularity to the movement of things, and makes the system rational.[3]
The failure of Heraclitus to free himself entirely from the physical hypotheses of earlier times prevented his speculation from influencing his successors. With Anaxagoras a conception entered which gradually triumphed over that of Heraclitus, namely, the conception of a supreme, intellectual principle, not identified with the world but independent of it. This, however, was νοῦς, not Logos. In the Platonic and Aristotelian systems, too, the theory of ideas involved an absolute separation between the material world and the world of higher reality, and though the term Logos is found the conception is vague and undeveloped. With Plato the term selected for the expression of the principle to which the order visible in the universe is due is νοῦς or σοφία, not λόγος. It is in the pseudo-Platonic Epinomis that λόγος appears as a synonym for νοῦς. In Aristotle, again, the principle which sets all nature under the rule of thought, and directs it towards a rational end, is νοῦς, or the divine spirit itself; while λόγος is a term with many senses, used as more or less identical with a number of phrases, οὖ ἕνεκα, ἐνέργια, ἐντελέχεια, οὐσία, εἶδος, μορφή, &c.
In the reaction from Platonic dualism, however, the Logos doctrine reappears in great breadth. It is a capital element in the system of the Stoics. With their teleological views of the world they naturally predicated an active principle pervading it and determining it. This operative principle is called both Logos and God. It is conceived of as material, and is described in terms used equally of nature and of God. There is at the same time the special doctrine of the λόγος σπερματικός, the seminal Logos, or the law of generation in the world, the principle of the active reason working in dead matter. This parts into λόγοι σπερματικοί, which are akin, not to the Platonic ideas, but rather to the λόγοι ἔνυλοι of Aristotle. In man, too, there is a Logos which is his characteristic possession, and which is ἐνδιάθετος, as long as it is a thought resident within his breast,
- ↑ The word is also used of the writers of speeches for the use of the contending parties in the law courts, who were forbidden to employ advocates.
- ↑ There is some doubt as to whether this Acusilaus was of Peloponnesian or Boeotian Argos. Possibly there were two of the name. For an example of the method of Acusilaus see Bury, op. cit. p. 19.
- ↑ Cf. Schleiermacher’s Herakleitos der Dunkle; art. Heraclitus and authorities there quoted.
