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#1751
Eons ago when I was a young lad, I was introduced to the art of printing. No keyboards and computers with masses of fonts in those days. Metal movable type was stored in flat trays called cases. Each tray was divided into compartments and these contained the individual letters of a particular typeface. There were two trays to each font. Bear in mind that you had a different set of type for each font, then for each point size then for normal, bold, italic and bold italic for each typeface that you needed. This meant that if you used Times Roman which most small jobbing printers did then you would have at least four sizes, in at least two weights (regular and bold) in normal, and italic so 16 cases in all. But full fonts would need a case for small letters and puntuation marks and a case for capital and symbols or more often small capitals. These cases were kept in cabinets and when you were "Setting" the type you would have a sloping top to the cabinet where the case with small letters was put at the front and the one with capitals was placed above the other. Hence one was the "upper case" and the other the "lower case".
The term "Sentence case" now to be found in MS Word is used as an instruction to capitalise a sentence but has no relevance to the old term of upper and lower case.
Here's two images of upper and lower cases
In additions to the above explanation
The way that movable type was set is also responsible for another, (British?), saying...
"Mind your P's and Q's" -meaning to watch what you're saying ...
This comes from the fact that as type was set reversed and upside-down extra care had to be taken with the lowercase P and q
Someone else here who worked with fonts before computers
Oh and the word font is derived from the French word form "fondre" - melt, so also owes it's origin to the print with metal type