Przełom w trygonometrii połowy XV wieku Kopernik jako spadkobierca i jako kontynuator tego przełomu

Rosińska, G.

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Tytuł artykułu

Przełom w trygonometrii połowy XV wieku Kopernik jako spadkobierca i jako kontynuator tego przełomu

Autorzy

Rosińska G.

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http://www.ejournals.eu/KHNT/

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Warianty tytułu

The breakthrough in trigonometry in the middle of the 15th century Copernicus as successor and continuator of that breakthrough

Języki publikacji

Abstrakty

The article points out the transformations in trigonometry (tables of trigonometric functions) initiated around the middle of the 15th century. Up until then, trigonometry, described in Latin culture as a „science of lines in a circle” that was subordinate to astronomy, had been known in the form transmitted in the first book of Ptolemy’s Almagest (ca. 150 AD). Insignificant improvements made in the 14th century at Oxford and Paris under the influence of Islamic mathematics and mathematical astronomy mainly concerned recalculating Ptolemy’s table of chords into a table of sines and attempts to replace the Menelaus theorem of the ratios of six quantities, the use of which made astronomical calculations extremely difficult, by a theorem of the ratio of four quantities, derived from Geber (Jabir ibn Afflah). In the section of the paper dealing with 15u'-century trigonometry, the achievements of Bianchini and of Regiomontanus are considered in relation to the Renaissance mathematics: these were marked by the evolution of the computational techniques, on the one hand, and by the extension of the concept of number, on the other. As a consequence of this evolution, the first tables of the decimal trigonometric functions were calculated about 1440 by Bianchini, the author of the exposition on the arithmetic of the decimal positional fractions (more than one hundred years before Simon Stevin’s De Thiende). Copernicus continued the work of the earlier 1 S^-century mathematicians: he calculated tables of the decimal trigonometric functions, and was interested in functions other then the sine (in fact, he is the author of the decimal table of secants). He began modestly, by copying down a simple sexagesimal table of sines, embedded in the tradition of John of Lineriis’s sine table based on Ptolemy’s table of chords. Copernicus’s own table of sines, included in the De revolutionibus, which follows the pattern of Bianchini’s trigonometric tables (the decimal radius and steps of 10'), is discussed in relation to Regiomontanus’s tables of sines, known in Cracow by the end of the 15th century, included the table calculated on the R=107 and one minute intervals. As for Copernicus’s table of secants, calculated in the 16th century and not used explicitly in his works, it was not influenced by Bianchini’s table of cosecants, calculated about the mid of the 15th century, and known in Cracow a little later. The paper concludes with a hypothesis concerning the existence of a table of sinescosines that was originally appended to Copernicus’s De lateribus (1542), and subsequently substituted by the Table of Regiomontanus, calculated on the R=107. In fact, Copernicus refers himself in the De lateribus to a table of sines calculated on the R=106 (and not on the R=107), it could therefore be assumed that s uch a table would be found in the appendix. Apparently, the remnants of a such table can be found in the table appended eventually to the De lateribus (for instance, the value of the sin 90° equal to 106 instead of 107).

Słowa kluczowe

trygonometria Kopernik Mikołaj astronomia

trigonometry Copernicus Nicolaus astronomy

Wydawca

Instytut Historii Nauki im. L. i A. Birkenmajerów Polskiej Akademii Nauk

Czasopismo

Kwartalnik Historii Nauki i Techniki

Rocznik

2002

Tom

R. 47, nr 4

Strony

7--32

Opis fizyczny

Bibliogr. 52 poz.

Twórcy

autor

Rosińska G.

Instytut Historii Nauki PAN Warszawa

Bibliografia

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Typ dokumentu

Bibliografia

Identyfikator YADDA

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