Does (or did) "a trouser" or "a scissor" have a meaning?
We say (a pair of) trousers, (a pair of) scissors. For these two particular words, is/was there something like "a trouser" or "a scissor"? Did it use to mean anything?
E.g. in Czech, the word for scissors is also plural but is derived from "knives". So I was wondering if the pair-words like these are derived from some (now forgotten) words with a meaning in singular. Similarly, the Slovak word for trousers is a plural of a Czech word meaning "a single trouser leg". (Czech and Slovak are very close.)
Solution 1:
Scissors apparently derives form the plural of the Latin cīsōrium for cutting tool, as does chisel.
Scissor is used in modern times in the singular as a verb, so "a scissor" is not necessarily (grammatically) wrong.
The excellent answer FumbleFingers pointed to for pants covers that subject fully.
Solution 2:
There are a lot of tools in English that are made of two parts and are plural: shears, scissors, tweezers, pliers, clippers, tongs, bellows, pincers. English uses plurals for these, but that doesn't mean that they come from a singular word that meant just one of the two parts.
Consider tongs. This word was derived from the Old English word tang (plural tangan) which was singular and meant a pair of tongs. The cognates in Danish (tang, meaning tongs or forceps), German (Zange, meaning pliers, pincers, or tongs), Dutch (tang, meaning pliers or tongs) are all singular. The first citation the OED has for a plural form meaning "a pair of tongs" is from 890, and the last for a singular form meaning "a pair of tongs" is from 1480. So somewhere between late Old English and Middle English, it changed its plurality.
The same thing happened with bellows. It (bælg) was singular in Old English, and the last singular use the OED knows about is from the 15th century.
Solution 3:
As you suspected, the OED derives trousers from “trouse” referring to an article of clothing later described as “drawers or knee-breeches”.
Singular “scissor” is uncommon but OED cites several sources where authors have used it in place of the more common plural. A more common use of the singular form is to form compound words as in “scissor-hands”. Both forms seem to be used since being introduced to English by Anglo-Normans. A better fit to your Czech example may be “shears” where the singular form is usually employed as a verb meaning “to cut”.