1. For an overview of the Roman calendar see the discussion of the
"Development of the Modern Calendar" under the entry for Calendar in The
Columbia Encyclopedia, 6th edition, ©2000. Also extremely useful for
converting Roman calendar dates is Otfried Lieberknecht's Calendar Tools
(JavaScript calculator).

2. See also Edward R. Hobbs' playful Compvter Romanvs (Java applet), a true
calculator which accepts Roman numerals in the range 1 - 3,999,999,
validates the input, and performs basic mathematical functions -- addition,
subtraction, multiplication, and division.

3. The smaller number must be a power of ten (I, X or C) and precede a
number no larger than 10 times its own value. The smaller number itself can
be preceded only by a number at least 10 times greater (e.g. LXC is invalid)
and it must also be larger than any numeral that follows the one from which
it is being subtracted (e.g. CMD is invalid).

4. Cappelli indicates that the Romans rarely used the subtraction principle
and that the convention was equally uncommon during the Middle Ages. See his
Dizionario di abbreviature latine ed italiane, 6th ed., Milano, 1967, p.
LIV.

5. Chronograms are sentences, phrases, inscriptions, or other brief texts
that contain dates embedded within them, usually in the form of upper case
Roman numerals. If upper case letters appear on the title page of a book
seemingly at random, the letters may well represent a chronogram for the
date of publication. The intended date can usually be deciphered by making a
simple total of all of the letters' corresponding numerical values without
regard for their order (the order isn't usually meaningful). For example,
the phrase "I MarrIeD LuCy In CInCInnatI" would suggest that its author was
married in 1856.

6. See R.B. McKerrow, Introduction to Bibliography for Literary Students,
Oxford, 1927 (appendix 3) for a brief discussion. Also his fuller treatment
of 16th-century practices in The Library, 3rd Ser., no. 1.

7. Sometimes referred to as a "backwards C", although the term is not
strictly accurate. Like modern-day rubber stamps, type used in making early
books consisted of a raised printing surface (face) cast on a solid body
(shank) with no reverse-side image. Consequently, it wasn't physically
possible to turn type over, or backwards, to create an exact mirror image
such as this:
(image of a backwards C)
Rather, printers would reverse the C by rotating the type 180 degrees to an
upside down position.

This is the classic form of the apostrophic C, used throughout the era of
the handpress and still occasionally found in printed books today. Digital
technology of course makes it a simple matter to produce backwards, or
mirror image letters, as can be seen in the Unicode Consortium's published
standard for the apostrophic C, or ROMAN NUMERAL REVERSED ONE HUNDRED
(Unicode glyph U+2183, v. 4.0 (.pdf)).

8. Bongo's curious work on "the mystery of numbers" (or Numerorum Mysteria,
as it was commonly known), was first published in two parts at Bergamo
(1583-1584) and frequently reissued. The partial table reproduced here
originally appeared in the 1614 edition and was scanned from a text
illustration in David Smith's Rara Arithmetica, Boston, 1908 (see figs.
190-191). Click here to view a reproduction of the title-page of Bongo's
original work (part 2, dated 1584), which bears a Roman numeral imprint date
displaying several of the features under discussion.