Three rod

Triquetrum (three rod) by Claudius Ptolemy

The three-bar , also known as the triquetrum or parallactic ruler , is an old astronomical goniometer for measuring the zenith distances of the stars and the parallax of the moon .

description

From the principle of the similarity of triangles, which two sides and an angle have in common, the obvious idea derives of constructing measuring devices whose function is based on this geometric law from three rulers (rules). The triquetrum was already described by Claudius Ptolemy in the fifth book of the Almagest .

It was one of the most popular astronomical instruments until the invention of the telescope . It could measure angles with greater accuracy than the astrolabe . Numerous scholars have studied the triquetrum after Ptolemy; B. the Arabs al-Battani and Jabir ibn Aflah . Also Regiomontanus grappled with the question of the possible use. He dedicated a small pamphlet to the Hungarian king Matthias Corvinus , in which he restricted himself to measuring heights in the field. In the years from 1515 to 1525 the triquetrum was used by Nicolaus Copernicus to determine the zenith distances of the moon and the fixed star Spica . He describes its use in the fourth book of De revolutionibus orbium coelestium under the heading Instrumenti parallactici constructio . The instrument was also described, illustrated and used by Tycho Brahe .

Nicolaus Copernicus' three-rod
(description in text)

The picture on the left shows the instrument of Copernicus. It consists of three rulers that form an isosceles triangle. One of the same legs is vertical, the other can be rotated around the upper end point of the first, has sights and is aligned with the star to be observed; The length of the unequal side is measured on the third ruler BD with a graduation, and thereby the angle at A and thus the zenith distance of the stars is determined: ${\displaystyle {\overline {AB}}}$ ${\displaystyle {\overline {AC}}}$ ${\displaystyle {\overline {BC}}}$ ${\displaystyle z}$

${\displaystyle z=\arcsin {\frac {\overline {BC}}{{\overline {AB}}+{\overline {AC}}}}}$

See also

• Jacob's staff
• quadrant
• Torquetum

Web links

Commons : Triquetrum  - collection of images, videos and audio files

Individual evidence

1. ^ Ernst Zinner : German and Dutch astronomical instruments of the 11th - 18th centuries. , CH Beck'sche Verlagsbuchhandlung, Munich 1956, pp. 199f
2. ^ Translation by Karl Manitius : The Claudius Ptolemy Manual of Astronomy as a digitized version on the Internet Archive: Fifth Book, Twelfth Chapter, p. 296
3. ^ Franz Adrian Dreier: Winkelmessinstrumenten , Kunstgewerbemuseum Berlin 1979, p. 38f
4. ^ Biblioteka Jagiellońska: De Revolutionibus, Revolutionum Liber Quartus, Cap. XV: Instrumenti parallactici constructio
5. ^ Zeno: Old astronomical instruments in Meyers Großes Konversations-Lexikon 6th edition 1905–1909