A lettrine or drop cap is a large initial letter (usually with some illustration) at the start of a chapter in a book.
In the English language, which is preferable: "lettrine" or "drop cap"? Incidentally, is it correct to indent a lettrine?
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Non-hanging drop caps are indeed indented in the sense that they don't hang outside of the paragraph: the left side of the initial letter or letters does align with the left edge of the rest of the paragraph.
Modern Drop Cap
Hanging drop caps hang out to the left of the paragraph and are less common in print; I suspect the rarity is primarily due to the fact that they're more difficult to create than indented drop caps when using modern page layout software. Conversely, hanging drop caps are (generally) easier than non-hanging ones on web pages and so may be seen there more often.
Hanging Drop Cap
Just in case: if you're asking if the drop cap should be indented farther to the right than required to make the left edge of the paragraph line up with the rest of the paragraph -- the way regular paragraphs are commonly indented in books and periodicals -- the answer is no, that is rarely appropriate.
Indented Drop Cap (uncommon)
Home > drop cap drop cap
In desktop publishing, the first letter of a paragraph that is enlarged to "drop" down two or more lines, as in the next paragraph. Drop caps are often seen at the beginning of novels, where the top of the first letter of the first word lines up with the top of the first sentence and drops down to the four or fifth sentence.
So, even in modern times, drop caps would look like this
To give an image to see what I mean by lining up with the top of the first sentence, take a look at this:
See how the drop cap lines up with the top of the next sentence, so that the drop cap is not indented, but lined up.