Ancient *slash* → new *back-slash* → disambiguating retronym *forward slash*
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It's all about ancient coinage
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The *slash* character came first, with a different formal name *solidus*. This name comes from Latin and was associated with coinage - hence (I guess) it's use in writing down prices in older currencies: `10/6` was quite a common notation for prices in British currency pre-decimalisation. The solidus mark probably indicates the first number is units of solidus, the second of denarius. Or in the British case: shillings and pence. Note common first letter abbreviations s and d were used in Britain (also £ is L for Latin libra).

The slash (or solidus) was around for a very very long time before the reversed version was invented. The reversed version therefore acquired the more informal name back-slash to indicate a reversed form of slash.

The name "forward slash" has probably evolved since the general public started to use computer keyboards incorporating two characters that look like a slash.  There was a need to disambiguate *slash* for people who didn't learn about computers in a formal teaching context.



American Standard Code for Information Interchange (ASCII) 1963
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[American Standards Association (ASA) X3.4 subcommittee](http://worldpowersystems.com/J/codes/X3.4-1963/)


    /   slant
    ...
    \   reverse slant


[Unicode consortium](http://www.unicode.org/charts/PDF/U0000.pdf) 1991
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    002F   /     SOLIDUS
                 = slash, virgule

    005C   \     REVERSE SOLIDUS
                 = backslash.
    

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So it is clear that the name backslash was introduced to indicate a novel character that was the reversed version of a long established character.

The name forward slash therefore subsequently became needed to disambiguate the name for the earlier character.