Unless you are an astronomer, this might not sound like much. However, an example included with this translation, taken from Tycho's logs, should convince you that “reducing” (extracting information from) just one observation could take you a long time even with a calculator. Back in the late sixteenth century, there were no calculators; there were not even any mathematical equations! Consequently, showing someone how to do a typical calculation was far from trivial. To make matters worse, these math problems were almost always in spherical trigonometry which is as hard as it sounds. So Tycho's chief assistants (his postdocs, as it were) took it upon themselves to produce a tutorial. The article linked below is a translation of this tutorial along with some additional, explanatory description.
It is not easy reading; there are difficulties of a different sort. For instance, one of the simplest algorithms, in English, instructs the student to proceed as follows:
|*** Planar Algorithm 2 ***|
|Multiply the side adjacent to the right angle by the whole and divide by the side subtending the right angle to give the sine of the angle subtended by that side. The third angle is given by the complement of 90 of this arc. If you multiply the sine of this by the side subtending the right angle and divide by the whole, it gives the other side adjacent to the right angle that was sought.|
Perfectly clear, yes? No?
It will be apparent, from the text, that another thing scientists did not have in those days was peer reviewers. There were a lot of typos and other errors that have been corrected here as much as possible.
This article is a PDF file (40 pages) available at the following link: