Divide a right angle in as many parts as you want and construct herefrom the sine table. (Einen rechten Winckell in also viel theile theilenn alß man… - Jost Bürgi

[D]ue to a lack of languages, the door to... authors has not always been open to me, as... to others, I have had to follow my own thoughts a little more than the learned and well-read, and seek new paths.
(Und weil mir auß mangel der sprachen die thür zu den authoribus nit alzeitt offen gestanden, wie andern, hab jch etwas mehr, als etwa die glehrte vnd belesene meinen eigenen gedanckhen nachhengen vnd newe wege suechen müessen.)

In such a way, with much trouble and labor, the whole Canon has been established. For many hundreds of years, up to now, our ancestors have been using this method because they were not able to invent a better one. However, this method is uncertain and dilapidated as well as cumbersome and laborious. Therefore we want to perform this in a different, better, more correct, easier and more cheerful way. And we want to point out now how all sines can be found without the troublesome inscription [of polygons], namely by dividing a right angle into as many parts as one desires.