I would consider it incorrect to mix old style and lining numbers on the same page, let alone the same date. I will be interested to see what others say.

Yes, the mix is very disconcerting. This thread which addresses similar issues might be of interest.

I disagree with Don about not having the two on one page: old style and lining just have different goals. For instance, you can use one for the main text and the other for page numbers...
But I agree that mixing the two in the same line makes the text look odd.

@s0me0ne: I find your image disturbing but I personally don't mind using lining and non lining figures on the same line when the semantics is clearly distinct (lining figures in formulas, and "old style" figures in the text):

I have been known to use lining and oldstyle figures together in a single text for different purposes. It can be done. I think of it as analogous to knowing when to use capitals vs. lowercase.

In your example, however, you are being inconsistent, without any semantic logic.

Also, in most style guides the use of the ordinals in "21st" would be incorrect. Even if one would read it as "21st," in formal writing the date should be set as simply "September 21, 1794."

Lorem

I once agreed that having lining page numbers and OS within text made sense. After all, if the rationale for OS numbers is provide smooth typographic color within the text stream, then why should they be used outside the textstream, in the running heads (particularly if the heads were in full caps).

I could never get an editor to agree with me, and gradually realized that they might be right. Having two different sets of numbers _may_ inadvertently confuse a reader, and that is a cardinal sin in good typography, in my opinion.

Yeah, but then practically anything might confuse a reader, sadly, in my experience. :¬/

I'd still advocate keeping OS numerals well away from superscript note cues and most mathematical content even if used for the rest of the running text...

> practically anything might confuse a reader

True, but you aim to minimize the possibilities.

Although I did think of a place where I _might_ use lining numbers with OS. In a scholarly text I would have used footnote references lining, even if the text elsewhere on the page is OS. This was because with 10pt text, footnotes were set at 7 point, baseline shifted, and the light weight of the reduced OS numbers would make them too weak.

I'd have to do a lot of testing (well some) first if I was still doing books, because many fonts have true superior figures that could be used without the weaking of using a reduced font. OS footnote refs might be acceptable in that case.

I'd agree with Kent, your example has no rationale. Consider the following:

"In 1933, Whosis developed the equation (put equation here)."

I have set texts where dates & non-mathematical number usage used old-style figures, but equations used lining figures.

As to confusing a reader, one should always have some sense of who a reader might be. I once set a book where the designer specified the chapter opening epigraphs to be set in italic. The run-in source had the author's name also in italic, with the title in roman. Usual practice in such a situation. An editor objected; it might comfuse the reader. You know, they might think of that wonderful novel Ernest Hemingway by The Old Man and the Sea. I'd add that most anyone without at least a high school education wouldn't have understood the text of the book, filled as it was with academic jargon . . .