(mathematics) The trumpet-shaped plane curve whose points in polar coordinates (r, θ) satisfy the equation r2 = a/θ.
A Roman brass instrument consisting of a long tube turning in upon itself at the end, in the shape of a ‘J’. It was used for military and ceremonial, especially funereal, occasions. Bach used the term for a type of horn in Cantata no.118, a funeral motet.

The word lituus originally meant a curved augural staff (cp. "crozier") or a curved war-trumpet in the ancient Latin language. In English it is used with several meanings.
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The lituus was a crooked wand (similar in shape to the top part of a crosier) used as a cult instrument in ancient Roman religion by augurs to mark out a ritual space in the sky (a templum). The passage of birds through this templum indicated divine favor or disfavor for a given undertaking.
The lituus was also used as a symbol of office for the college of the augurs to mark them out as a priestly group.
The ancient lituus was an old Etruscan high-pitched brass instrument, which was bent at the end, similar to the Gallic carnyx. It was later used by the Romans, especially for processional music and as a signalling horn in the army.[1] In 17th century Germany a variant of the bent ancient lituus was still used as a signalling horn by nightwatchmen.
The mediaeval lituus was a different brass instrument than the ancient Etruscan instrument, described by Kürzinger (1763) as a variant of the early trumpet or horn, i.e. a later development of the ancient Roman tuba. One of the last compositions orchestrated for the mediaeval lituus was Bach's motet O Jesu Christ, meins Lebens Licht (BWV 118). Scientists from Edinburgh University tried to recreate the lituus in May 2009, when the instrument had been out of use for 300 years.[2][3]
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