Livonians and force them to pay the contribution and fulfil all the conditions of the previous treaty. The initial success gave the tsar hope of conquering all Livonia, but here his interests clashed with the interests of Poland- Lithuania and Sweden, and thus a local conflict grew into a long and exhaustive war between the greatest powers of the Baltic region.
As the war progressed, Ivan IV changed allies and enemies; the scene of operations also changed. So, in the course of the war one can distinguish four different periods: 1) from 1558 to 1561, the period of initial Russian success in Livonia; 2) the 1560s, the period of confrontation with Lithuania and peaceful relations with Sweden; 3) from 1570 to 1577, the last efforts of Ivan IV in Livonia; and 4) from 1578 to 1582, when severe blows from Poland-Lithuania and Sweden forced Ivan IV to give up all his acquisitions in Livonia and start peace negotiations.
During the campaign of 1558, Russian armies, encountering no serious resistance, took the important harbor of Narva (May 11) and the city of Dorpat (July 19). After a long pause (an armistice from March through November 1559), in 1560 Russian troops undertook a new offensive in Livonia. On August 2 the main forces of the Order were defeated near Ermes (now Ergeme); on August 30 an army led by prince Andrei Kurbsky captured the castle of Fellin (now Vilyandy).
As the collapse of the enfeebled Livonian Order became evident, the knighthood and cities of Livonia began to seek the protection of Baltic powers: Lithuania, Sweden, and Denmark. In 1561 the country was divided: The last master of the Order, Gottard Kettler, became vassal of Sigismund II Augustus, the king of Poland and grand duke of Lithuania, and acknowledged sovereignty of the latter over the territory of the abolished Order; simultaneously the northern part of Livonia, including Reval (now Tallinn), was occupied by the Swedish troops.
Regarding Sigismund II as his principal rival in Livonia and trying to ally with Erik XIV of Sweden, Ivan IV declared war on Lithuania in 1562. A large Russian army, led by the tsar himself, besieged the city of Polotsk on the eastern frontier of the Lithuanian duchy and seized it on February 15, 1563. In the following years Lithuanians managed to avenge this failure, winning two battles in 1564 and capturing two minor fortresses in 1568, but no decisive success was achieved.
By the beginning of the 1570s the international situation had changed again: A coup d’?tat in Sweden (Erik XIV was dethroned by his brother John III) put an end to the Russian-Swedish alliance; Poland and Lithuania (in 1569 the two states united into one, Rzecz Pospolita), on the contrary, adhered to a peaceful policy during the sickness of King Sigismund II Augustus (d. 1572) and periods of interregnum (1572-1573, 1574-1575). Under these circumstances Ivan IV tried to drive Swedish forces out of northern Livonia: Russian troops and the tsar’s vassal, Danish duke Magnus (brother of Frederick II of Denmark), besieged Revel for thirty weeks (August 21, 1570-March 16, 1571), but in vain. The alliance with the Danish king proved its inefficiency, and the raids of Crimean Tartars (for instance, the burning of Moscow by Khan Devlet- Girey on May 24, 1571) made the tsar postpone further actions in Livonia for several years.
In 1577 Ivan IV made his last effort to conquer Livonia; his troops occupied almost the entire country (except for Reval and Riga). Next year the war entered its final phase, fatal to the Russian cause in Livonia.
LOBACHEVSKY, NIKOLAI IVANOVICH
In 1578 Russian troops in Livonia were defeated by combined Polish-Lithuanian and Swedish forces near the fortress Venden (now Tsesis), and the tsar’s vassal, duke Magnus, joined the Polish side. In 1579 the Polish king, Stephen Bathory, a talented general, recaptured Polotsk; the following year, he invaded Russia and devastated the Pskov region, having taken the fortresses of Velizh and Usvyat and having burned Velikiye Luky. During his third Russian campaign in August 1581, Bathory besieged Pskov; the garrison led by prince Ivan Shuisky repulsed thirty- one assaults. At the same time the Swedish troops seized Narva. Without allies, Ivan IV sought peace. On January 15, 1582, the treaty concluded in Yam Zapolsky put an end to the war with Rzecz Pospolita: Ivan IV gave up Livonia, Polotsk, and Velizh (Velikiye Luky was returned to Russia). In 1583 the armistice with Sweden was concluded, yielding Russian towns Yam, Koporye, and Ivangorod to the Swedish side.
The failure of the Livonian war spelled disaster for Ivan IV’s foreign policy; it weakened the position of Russia towards its neighbors in the west and north, and the war was calamitous for the northwestern regions of the country. See also: IVAN IV
BIBLIOGRAPHY
Esper, Thomas. (1966). “Russia and the Baltic, 1494-1558.” Slavic Review 25:458-474. Kirchner, Walter. (1954). The Rise of Baltic Question. Newark: University of Delaware Press.
(1792-1856), mathematician; creator of the first non-Euclidean geometry.
Nikolai Lobachevsky was born in Nizhny Novgorod to the family of a minor government official. In 1809 he enrolled in Kazan University, selecting mathematics as his major field. From Martin Bartels and Franz Bronner, German immigrant professors, he learned the fundamentals of trigonometry, analytical geometry, celestial mechanics, differential calculus, the history of mathematics, and astronomy. Bronner also introduced him to the current controversies in the philosophy of science. In 1811 Lobachevsky was granted a magisterial degree, and three years later he was appointed instructor in mathematics at Kazan University. His first teaching assignment was trigonometry and number theory as advanced by Carl Friedrich Gauss. In 1816 he was promoted to the rank of associate professor. In 1823 he published a gymnasium textbook in geometry and, in 1824, a textbook in algebra.
Lobachevsky’s strong interest in geometry was first manifested in 1817 when, in one of his teaching courses, he dwelt in detail on his effort to adduce proofs for Euclid’s fifth (parallel) postulate. In 1826, at a faculty meeting, he presented a paper that showed that he had abandoned the idea of searching for proofs for the fifth postulate; in contrast to Euclid’s claim, he stated that more than one parallel could be drawn through a point outside a line. On the basis of his postulate, Lobachevsky constructed a new geometry including, in some opinions, Euclid’s creation as a special case. Although the text of Lobachevsky’s report was not preserved, it can be safely assumed that its contents were repeated in his “Elements of Geometry,” published in the Kazan Herald in 1829-1830. In the meantime, Lobachevsky was elected the rector of the university, a position he held until 1846.
In order to inform Western scientists about his new ideas, in 1837 Lobachevsky published an article in French (“Geometrie imaginaire”) and in 1840 a small book in German (Geometrische Unter-suchungen zur Theorie der Parallellinien). His article “Pangeometry” appeared in Russian in 1855 and in French in 1856, the year of his death. At no time did Lobachevsky try to invalidate Euclid’s geometry; he only wanted to show that there was room and necessity for more than one geometry. After becoming familiar with the new geometry, Carl Friedrich Gauss was instrumental in Lobachevsky’s election as an honorary member of the Gottingen Scientific Society.
After the mid-nineteenth century, Lobachevsky’s revolutionary ideas in geometry began to attract serious attention in the West. Eugenio Beltrami in Italy, Henri Poincare in France, and Felix Klein in Germany contributed to the integration of non-Euclidean geometry into the mainstream of modern mathematics. The English mathematician William Kingdon Clifford attributed Copernican significance to Lobachevsky’s ideas.
On the initiative of Alexander Vasiliev, professor of mathematics, in 1893 Kazan University
LOCAL GOVERNMENT AND ADMINISTRATION
celebrated the centennial of Lobechevsky’s birth. On this occasion, Vasiliev presented a lengthy paper explaining not only the scientific and philosophical messages of the first non-Euclidean geometry but also their growing acceptance in the West. At this time, Kazan University established the Lobachevsky Prize, to be given annually to a selected mathematician whose work was related to the Lobachevsky legacy. Among the early recipients of the prize were Sophus Lie and Henri Poincar?.
In 1926 Kazan University celebrated the centennial of Lobachevsky’s non-Euclidean geometry. All speakers placed emphasis on Lobachevsky’s influence on modern scientific thought. Alexander Kotelnikov advanced important arguments in favor of close relations of Lobachevsky’s geometrical propositions to Einstein’s general theory of relativity. Lobachevsky also received credit for a major contribution to modern axiomatics and for proving that entire sciences could be created by logical deductions from assumed propositions. See also: ACADEMY OF SCIENCES
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