After an abbreviation.
This was 50 years ago (i.e.1860 A.D.) 2.

At the end of an independent sentence lying entirely within the parenthesis.
Lincoln was at the height of his powers in 1860 (He was elected to the presidency at this time.) When a sentence ends with a quotation, the period always goes inside the quotation marks.
I have just read DeVinne's "Practice of Typography." The same rule applies to the use of the other low marks, comma, semicolon, and colon, in connection with quotation marks.

Unlike most rules of grammar and punctuation, this rule does not rest on a logical basis.

It rests on purely typographic considerations, as the arrangement of points indicated by the rule gives a better looking line than can be secured by any other arrangement.
_Other Uses of the Period_ 1.

The period is used as a decimal point.
2.