Set squares were around long before they were used in mathematics. From at least as long ago as Babylonian times, several thousands of years ago, carpenters and masons used wooden and metal set squares to mark square edges and corners. The pyramids could never have been built without this most basic tool.
We know from instruments that have been dug up in archaeological investigations that the Romans used set squares and that their set squares were sometimes quite elegantly designed. In the Renaissance, set squares started to be covered with very beautiful decoration. Obviously a set square doesn't have to have any decoration on it in order to be able to work properly. The fact that set squares became highly decorated shows that maths and the mathematicians who used them were considered important at the time and that set squares themselves were highly valued.
© Museum of the History of Science, Oxford
This set square is an example of one that is quite nicely decorated. It comes from 18th century Germany and has leafy scroll shapes at each end. It has a hinge at the corner so it can be folded up. This was probably so it could fit better into a case with other mathematical drawing instruments. It is made of quite heavy brass and opens up to exactly 90 degrees.
As well as being a set square it is also a protractor. So, as well as being used to draw right angles it could also be used to draw angles at other degrees. It is actually quite hard to use it as a protractor because it has quite complicated scales on it. To use these scales you also need a pair of dividers. For this reason it was probably used by someone who did technical drawings, like engineering drawings or architectural drawings, rather than by someone working on a building site such as a working carpenter or in a workshop such as a metal worker.
Like dividers, set squares have been an important symbol of maths and mathematicians from the Middle Ages onwards.