B chapter.indd - Charles Babbage Institute - University of Minnesota

Francesco Barozzi (also known as Franciscus Barocius
or Barociusi) was a native of Crete who was a member of
a patrician Venetian family. He studied at Padua and also
lectured there c.1559. He published works on astronomy
and mathematics and is known to have produced a
number of translations of Greek and Latin mathematical
texts, among them Proclus’ commentary on the first
book of Euclid. In 1587, he was charged with sorcery
and brought before the Inquisition.
This volume is essentially a translation of Claude de
Boissière’s description of the number ratio game known
as Rithmomachia from the Greek rhythmos (number)
and machia (combat). In the title, the game is attributed
to Pythagoras; however, the attribution is suspect as no
known reference predates the eleventh century.
As Smith (History of Mathematics) notes, the game is
difficult to describe. It is based on the Greek number
philosophy of Nicomachus and played on an elongated
chess board with 8x16 squares. It uses variously shaped
counters to represent numerical ratios. The object was
to move the counters so as to get four numbers in a row
that were related to arithmetic, geometric and harmonic
progressions—there are apparently only six winning
combinations of pieces.
An introduction to the game can be found in Smith, D.
E. and C. C. Eaton; “Rithmomachia, the great medieval
number game,” The American Mathematical Monthly,
April 1911, pp. 73–80. For a more complete historical
and bibliographical discussion, see Folkerts, Menso;
Essays on medieval mathematics, Aldershot, Ashgate
108
Erwin Tomash Library
Barozzi, Francesco Barreme, François Bertrand de
B 95
Variorum, 2003. Chapter XI is titled Rithmomachia, a
mathematical game from the middle ages.
Folkerts points out that Rhythmos means not number
but numerical relationship and that accordingly,
Rithmomachia is a game that deals not with numbers but
with the ratios of numbers.
Illustrations available:
Title page
Game board
Rithmomachia game board, B 95
B 96
Barreme, François Bertrand de (1640–1704)
La geometrie servant a l’arpentage. Ouvrage si
facile & si commode que par la seule addition on
peut mesurer toute sorte de terres, bois, & batimens;
et generalement toute figures & superficies pour
irregulieres qu’elles puissent estre.
Year: 1672
Place: Paris
Publisher: Barreme
Edition: 1st
Language: French
Figures: engraved title page; 1 engraved plate
Binding: contemporary calf; gilt spine
Pagination: pp. [17], 5, [1], 7–17 (misnumbered 7 as 6, 8 as 6,
9 as 7, 10 as 7, 11 as 8, 12 as 8, 13 as 8, 14 as 8, 15 as
10, 16 as 11, 17 as 12), [2], ff. 13-30, pp. [72], [36], [36]
Collation: a 6 * 12 C–E 6 * 6 R–X 6 g–3g 6 *-3* 6
Size: 142x82 mm
François Barreme was a native of Lyons who founded a
private commercial mathematics school in Paris. He was