© Museum of the History of Science, Oxford

These weights were made in Nuremberg in Germany in the 17th century and were probably used in Hanover. They might have been used to help weigh out food or some other sort of everyday item.
When we think about maths and mathematicians now we usually imagine someone sitting alone at a desk in a study doing lots of equations. But mathematics is all around us every day. Almost every aspect of our daily lives involves practical jobs that need some sort of maths. The same was true at the time when these weights were made: people called 'practical mathematicians' were very closely connected to people who did practical things which needed maths, such as shopkeepers and other traders, and architects and surveyors. Like measuring, weighing is an important way that maths can be used to do useful things.
Today we mostly use electronic scales to do weighing. But before computers and electronic scales were invented most weighing was done on a balance or a set of scales. A balance is just a rod which is pivoted in the middle and which has a tray hanging from each end. In one of the trays you put the thing that you want to weigh and in the other you put something that you already know the weight of. If the rod balances then you know that the thing you want to know the weight of weighs the same as the thing you already know the weight of.
Obviously, when you are weighing it is useful to have a set of different weights that you already know the weight of very accurately. These are called 'standard weights'. In the past standard weights came in lots of different shapes, like cubes, discs and even human and animal shapes. The most popular type of weights was cup weights, like these. Cup weights were popular because they could all be packedup inside each other and therefore took up very little space.
This set of cup weights contains eight separate cup weights going from a very small and quite light one at the centre to a large heavy one on the outside. When they are all put together they weigh a total of 16 pounds which is about seven kilograms. All the cup weights fit inside each other and are made of brass. They are actually calibrated in 'loth' which was an old German unit of weight. Thirty two loth equalled one pound, or about half a kilogram.
Nuremberg was a very important place for mathematics and for trading in Germany in the 17th century. This was because it was at the centre of Europe and acted like a crossroads between important cities like Prague, Vienna, Hamburg and Brussels.
Weights do something very simple but still very important. The fact that these weights would have been important to their owner and would have been looked after carefully is shown by the fact that the case they are in is nicely decorated. The hinge for the lid has been made to look like three dogs and the catch looks like two imaginary horses, one of which has a fish's tail.