# Jost B\"urgi's Method for Calculating Sines

@article{Folkerts2015JostBM, title={Jost B\"urgi's Method for Calculating Sines}, author={Menso Folkerts and Dieter Launert and Andreas Berthold Thom}, journal={arXiv: History and Overview}, year={2015} }

For a long time it has been known that in the 16th century the Swiss mathematician Jost B\"urgi found a new method for calculating sines, but no information about the details has been available. Recently a manuscript written by B\"urgi himself has come to light in which he explains his algorithm. It is totally different from the traditional procedure which was used until the 17th century. In the first part of the article the standard method is explained which was rooted in Greek antiquity with… Expand

#### 10 Citations

Jost Bürgi’s methods of calculating sines, and possible transmission from India

- Philosophy
- Archive for History of Exact Sciences
- 2019

AbstractA few years ago, a manuscript by Jost Bürgi (1552–1632) was brought to scholarly attention, which included an ingenious sine calculation method. The purpose of this paper is to discuss two… Expand

Some remarks on Bürgi’s interpolations

- Mathematics
- 2016

Jost Burgi (1552-1632) was one of the first ones to have used the calculus of differences in order to construct a table of sines. His table of sines at 2'' intervals is lost, but in these notes, we… Expand

How Bürgi computed the sines of all integer angles simultaneously in 1586

- Mathematics
- 2018

We present an algorithm discovered by Jost Bürgi around 1586, lost until 2013, and proven in 2015. Bürgi’s method needs only sums of integers and divisions by $$2$$2 to compute simultaneously and… Expand

A preliminary note on Bürgi's computation of the sine of the first minute

- Mathematics
- 2016

A recently rediscovered manuscript by Jost Burgi from around 1590 contains novel approaches to the computation of sines. In this note, we examine a specific point in Burgi's analysis of the sine of… Expand

The star catalogue of Wilhelm IV, Landgraf von Hessen-Kassel

- Mathematics, Physics
- Astronomy & Astrophysics
- 2021

We analyse a manuscript star catalogue by Wilhem IV, Landgraf von Hessen-Kassel from 1586. From measurements of altitudes and of angles between stars, given in the catalogue, we find that the… Expand

Jost Bürgi's skillful computation of sines

- Mathematics
- 2015

This brief note suggests an explanation for Burgi's simple method for the computation of sines to any accuracy, devised in the 1580s.

A reconstruction of Bürgi’s sine table at 1' intervals (ca. 1587)

- Mathematics
- 2016

This document gives a reconstruction of Burgi’s sine table at 1' intervals. This table is found in a manuscript recently rediscovered by Menso Folkerts. This reconstruction helps assess the accuracy… Expand

A note on the complexity of Bürgi's algorithm for the computation of sines

- Mathematics
- 2016

This note studies the accuracy and complexity of Burgi's novel algorithm for the computation of sines.

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