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LEONTINI (mod. Lentini)

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Originally appearing in Volume V16, Page 455 of the 1911 Encyclopedia Britannica.
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LEONTINI (mod. Lentini) , an See also:ancient See also:town in the See also:south-See also:east of See also:Sicily, 22 M. N.N.W. of See also:Syracuse See also:direct, founded by Chalcidians from See also:Naxos in 729 B.C. It is almost the only See also:Greek See also:settlement not on the See also:coast, from which it is 6 m. distant. The site, origin-ally held by the Sicels, was seized by the Greeks owing to its command of the fertile See also:plain on the See also:north. It was reduced to subjection in 498 B.C. by See also:Hippocrates of See also:Gela, and in 476 Hieron of Syracuse established here the inhabitants of Catana and Naxos. Later on Leontini regained its See also:independence, but in its efforts to retain it, the intervention of See also:Athens was more than once invoked. It was mainly the eloquence of See also:Gorgias (q.v.) of Leontini which led to the abortive Athenian expedition of 427. In 422 Syracuse supported the oligarchs against the See also:people and received them as citizens, Leontini itself being forsaken. This led to renewed Athenian intervention, at first mainly See also:diplomatic; but the exiles of Leontini joined the envoys of See also:Segesta, in persuading Athens to undertake the See also:great expedition of 415. After its failure, Leontini became subject to Syracuse once more (see See also:Strabo vi. 272).

Its independence was guaranteed by the treaty of 405 between See also:

Dionysius and the Carthaginians, but it very soon lost it again. It was finally stormed by M. See also:Claudius See also:Marcellus in 214 B.C. In See also:Roman times it seems to have been of small importance. It was destroyed by the See also:Saracens A.D. 848, and almost totally ruined by the See also:earthquake of 1698. The ancient See also:city is described by See also:Polybius (vii. 6) as lying in a bottom between two hills, and facing north. On the western See also:side of this bottom ran a See also:river with a See also:row of houses on its western See also:bank under the See also:hill. At each end was a See also:gate, the See also:northern leading to the plain, the See also:southern, at the upper end, to Syracuse. There was an See also:acropolis on each side of the valley, which lies between precipitous hills with See also:flat tops, over which buildings had extended. The eastern hill' still has considerable remains of a strongly fortified See also:medieval See also:castle, in which some writers are inclined(though wrongly) to recognize portions of Greek See also:masonry.

See G. M. See also:

Columba, in Archeologia di Leontinoi (See also:Palermo, 1891), reprinted from Archivio Storico Siciliano, xi.; P. Orsi in Romische Mitteilungen (1900), 61 seq. Excavations were made in 1899 in one of the ravines in a Sicel See also:necropolis of the third See also:period; explorations in the various Greek cemeteries resulted in the See also:discovery of some See also:fine bronzes, notably a fine See also:bronze lebes, now in the See also:Berlin museum. (T. As.) i As a fact there are two flat valleys, up both of which the See also:modern Lentini extends; and hence there is difficulty in fitting Polybius's See also:account to the site. requires readers already acquainted with See also:Euclid's planimetry, who are able to follow rigorous demonstrations and feel the See also:necessity for them. Among the contents of this See also:book we simply mention a trigonometrical See also:chapter, in which the words sinus versus arcus occur, the approximate extraction of See also:cube roots shown more at large than in the See also:Liber abaci, and a very curious problem, which nobody would See also:search for in a geometrical See also:work, viz.—To find a square number remaining so after the addition of 5. This problem evidently suggested the first question, viz.—To find a square number which remains a square after the addition and subtraction of 5, put to our mathematician in presence of the See also:emperor by See also:John of Palermo, who, perhaps, was quite enough Leonardo's friend to set him such problems only as he had himself asked for. Leonardo gave as See also:solution the See also:numbers 1114'4, 16,9474 and 61414, the squares of 3A, 4,11 and 2,72; and the method of finding them is given in the Liber quadratorurn. We observe, however, that this See also:kind of problem was not new.

Arabian authors already had found three square numbers of equal difference, but the difference itself had not been assigned in proposing the question. Leonardo's method, therefore, when the difference was a fixed See also:

condition of the problem, was necessarily very different from the Arabian, and, in all See also:probability, was his own discovery. The Flos of Leonardo turns on the second question set by John of Palermo, which required the solution of the cubic See also:equation x'+2x2+IOx=2o. Leonardo, making use of fractions of the sexagesimal See also:scale, gives X=10 22' 7" 42'" 33" 4° 40°", after having demonstrated, by a discussion founded on the loth book of Euclid, that a solution by square roots is impossible. It is much to be deplored that Leonardo does not give the least intimation how he found his approximative value, outrunning by this result more than three centuries. Genocchi believes Leonardo to have been in See also:possession of a certain method called See also:regula aurea by H. See also:Cardan in the 16th See also:century, but this is a See also:mere See also:hypothesis without solid See also:foundation. In the Flos equations with negative values of the unknown quantity are also to be met with, and Leonardo perfectly understands the meaning of these negative solutions. In the See also:Letter to Magister See also:Theodore indeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a See also:general method any problem of this kind not exceeding the first degree. As for the See also:influence he exercised on posterity, it is enough to say that Luca Pacioli, about 1500, in his celebrated Summa, leans so exclusively to Leonardo's See also:works (at that See also:time known in See also:manuscript only) that he frankly acknowledges his dependence on them, and states that wherever no other author is quoted all belongs to Leonardus Pisanus. Fibonacci's See also:series is a sequence of numbers such that any See also:term is the sum of the two preceding terms; also known as Lame's series. (M.

End of Article: LEONTINI (mod. Lentini)

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