[146] _Logik_ (1873, 1889), Eng. trans. ii. 17. [147] _Op. cit._ ii. 289. [148] _Introd. to Logic._, trans. Abbott, p. 10. [149] _Ueber Annahmen_ (1902, &c.) [150] _Logik_ (1880, and in later editions). [151] Yet see _Studies in Logic_, by John Dewey and others (1903). 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[theta] = a(1 ± sin[theta]), 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 [root](a - x) = x [root](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. [Illustration.] LOGOGRAPHI ([Greek: logos], [Greek: graphô], 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 ([Greek: hôroi]) of his native town with lists of the prytaneis and archons, and of the chronicles of Lacedaemonian kings; Xanthus of Sardis in Lydia (c.