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I'm not sure if this is a question that has been posted before, and I'm also not sure if the answer is really mnemonic. If that's the case, I'd like to understand why we assigned $b$ to latitude anyways, so my brain can remember it more easily.

Thanks!

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Länge und Breite are the German words for longitude and latitude. Thus 'b' seems like a natural choice for latitude and 'l' for longitude. A century ago when traditional choice of variable names were chosen by vote of feet, a reasonable amount of research papers were still published in German or people with some form of fluency in German. At the same time it's distinct enough from the variable names used in other coordinate systems which also have longitude and latitude (like the terrestrial where $\lambda$ and $\theta$ are commonly used), so the cause for confusion is reduced - even when you don't know German.

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    $\begingroup$ Etymologically also very close to length and breadth, so even English speakers can relate. $\endgroup$
    – Pierre Paquette
    Commented Mar 18, 2021 at 0:35
  • $\begingroup$ @PierrePaquette Interesting that the word for breadth is used for latitude, when it's normally shown as up/down, so the word for height would seem more natural. $\endgroup$
    – Barmar
    Commented Mar 18, 2021 at 16:19
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    $\begingroup$ Height would be the most inconvenient one to indicate positions on a 2D map as it's the 3rd missing coordinate for a point in 3D. Think of a parchment, a map. Especially on a scroll. The scroll has a length (longtidude), and a width (breadth). A map's rectangle has a width and a length when placed on a table. $\endgroup$
    – planetmaker
    Commented Mar 18, 2021 at 16:33

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