VEGA, Jurij (1754-1802)
Georg Vega's, ... Logarithmisch-trigonometrische Tafeln : nebst
andern zum Gebrauch der Mathematik eingerichteten Tafeln und
Formeln. - Zweyte, verbesserte, vermehrte und gänzlich
umgearbeitete Auflage. - Leipzig : in der Weidmannischen
Buchhandlung, 1797 (Leipzig : gedruckt bey Christian Friedrich
Solbrig). - 2 vol. (LXXXIV, 409 p., [1] leaf of plates (errata);
LXXIX, [1], 371 p., [1] leaf of plates (errata) : tables ; 4° (23
cm
Jurij Vega’s name is particularly familiar in mathematics, astronomy, and in
other technical sciences for his logarithm tables. New editions of the tables were
published in many languages around the world without the name of their author,
and few people know that their author is Jurij Vega, the son of a crofter who was
made a baron because of this scientific and military achievements. Vega indeed
was not just a mathematician, he also tried to use the knowledge he had acquired
for very practical purposes, especially in ballistics.
As a teacher of mathematics at an artillery school, Vega soon found out that the
students were taught without suitable literature or a real system, and he then
started to write textbooks for his own subject. He published the first volume of
his lectures on mathematics, entitled Vorlesungen uber die Mathemetik, in
Vienna in 1782. It discusses the basic calculation operations for special numbers
and algebra without strict mathematical proof or concise deduction. Because of
the well-chosen matter and methodical clarity (clear structure, easily
understandable explanations and lucid system), the book was soon used in other
schools too.
Before long, Vega’s occupation made him recognise the shortcomings of the
then existing logarithm tables, and he largely dedicated himself to calculating
logarithms in the second half of his life. He continued to work on them even in
wartime. He published his seven-place logarithm tables under the title
Logaritmische, trigonometrische und andere zum Gebrauche der Mathematik
eingerichtete Tafeln und Formeln in Vienna in 1783. The book is divided into
24 chapters and worth mentioning are the formulas of spherical trigonometry,
which Vega presented in logarithmic form.
Vega’ s principal achievement was that improved the calculation of logarithms.
To increase the clarity of the tables, he introduced several novelties. The
accuracy and versatility of his logarithm tables far surpassed all similar tables of
the period and this did not escape his contemporary critics.
In 1784, he published the second volume of his Lectures on Mathematics,
bearing mainly on geometry and, in addition, on the theory of practical
surveying and infinitesimal calculation. The work did not bring any major
novelties, but it was new in the way the author had revised individual sections.
The book highly improved the development of artillery mathematics, because
Vega introduced algebraic analysis and higher mathematics to artillery. The
book was reprinted many times.
The third volume of his Lectures on Mathematics was published in 1788. A
special chapter is dedicated to the parabola theory and its use in throwing
bombs. The book also contains a draft solution for the elaboration of auxiliary
tables for throwing bombs. This volume too was reprinted many times.
Vega’s practical writings on artillery were so successful that individual sections
of his Lectures on Mathematics were published separately with minor additions
and corrections.
In 1792, Vega started to become engaged intensively in mathematics. He set
himself the task to further improve the logarithm tables. He elaborated an
extensive work schedule which envisaged three different logarithm tables: a
short handbook of logarithm tables for students of mathematics, extensive,
completed tables for mathematicians, astronomers and seafarers, and a special,
completed edition of the logarithm tables published in 1783 for teachers of
mathematics. This vast schedule required an enormous amount of work and
perseverance, but he managed to finish all three works in spite of having to join
the front lines in war-time. In this period, Vega achieved his greatest successes
and received the recognition he deserved.
The handbook of logarithm tables with seven decimal places was published in a
bilingual edition (German and Latin) under the title Logaritmisch-
trigonometrisches Handbuch..., and contains two chapters: Briggs’s logarithms
of the natural numbers from 1 to 101 000 and the logarithm tables for
trigonometric functions. Vega published a revised version in 1800. In the second
half of the 19th century, these tables were translated into eight languages. From
their first edition, the work was considered to be the prototype of logarithm and
trigonometry books.
Vega’s most complete and famous work are his ten-place logarithm tables
published under the title Thesaurus logarithmorum completus. In spite of the
fact that Gauss’s remarks on their (lack of) accuracy caused many
mathematicians to doubt the accuracy of Vega’s calculations, the book’s high
degree of precision nevertheless survived quite long. In spite of its errors, the
Thesaurus as a whole is invaluable and until recently it was one of the rare
mathematical aids for accurate calculations. It served as a model, for comparison
and for testing nearly all logarithm tables derived from it. The book was
reprinted many times. Judging from the letter to the Emperor, in which he asked
permission to dedicate the Thesaurus to his majesty, Vega himself considered
the Thesaurus to be the culmination of his scientific work.
In 1800 Vega published the fourth volume of his Lectures on Mathematics. In
addition to the above mentioned works, Vega also wrote eight shorter, but
important treatises and writings, addressing issues of mathematics, astronomy
and physics. He received many awards for his work and had the honour to be
accepted as a member of numerous scientific academies around Europe.