What’s with the vertical alignment of old written numbers?

I’m trying to find out why old numbers, both handwritten, printed from a printing press, and typewritten, sometimes drop down and swing upwards. They show a bit of vertical offset. 1, 2, and 0 seem to be equal in height, while 3, 4, 5, 7, and 9 have their long part swing downwards. 6 and 8 swing upwards.

It’s not so in all cases, too. On the continental note attached, you can see handwritten “61530” in the top right that doesn’t follow this, but the printed date, “September 26th, 1778”, and “50 DOLLARS” does. The Declaration of Independence has these oddly positioned numbers, too. The modern Georgia font uses numbers like this as well.

Do History.org shows an example from The American Young Man’s Best Companion Containing Spelling, Reading, Writing, and Arithmetick by Fisher, George (1786). Here is a link to the pages it uses as a guide for how to read old printed typeface. Notice the page numbers. Unfortunately, this page doesn’t go over why numbers are written vertically offset. I can’t find much documentation or discussion about this at all, in fact, so I’m hoping somebody has some insight.

See the numbers in "September 26th, 1778. 50 DOLLARS"
Notice the date in upper right, "July 4, 1776"
A perfect showing of what I'm talking about

Answer

Just as there are uppercase and lowercase letters, there are “uppercase” (or titling) and “lowercase” (or text) figures.

Most fonts contain only one or the other version of figures, but there are fonts that contain both. The following example, found in the German Wikipedia articles on titling and text figures, shows letters and figures in both upper and lower case from the font Linux Libertine.

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