Repeating circle

[1] He invented it while an assistant of Jean-Charles de Borda, who later improved the instrument.

It was notable as being the equal of the great theodolite created by the renowned instrument maker, Jesse Ramsden.

The repeating circle is made of two telescopes mounted on a shared axis with scales to measure the angle between the two.

Repeating the procedure causes the instrument to show 4× the angle of interest, with further iterations increasing it to 6×, 8×, and so on.

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12-inch repeating circle. [ clarification needed ]
Borda reflecting circle, on display at Conservatoire national des arts et métiers .
Mode of operation:
(1) The instrument is aligned so its plane includes the two points to be measured, and each telescope is aimed at a point;
(2) Keeping the angle between the telescopes locked, the left (black) telescope is rotated clockwise to aim at the right point;
(3) the right (gray) telescope's position is noted, and it is rotated back to the left point.