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

Erwin Tomash Library
Borghi, Pietro Borghi, Pietro
B 208
The first and last folios contain poems headed by the
initials SDSU (some read it as SHSU), about which there
has been much speculation. Smith seems to think that the
letters S H S U which appear twice are thought to stand
for J H S U, Jesus, possibly changed on account of some
conjectured pronunciation.
This work is more elaborate than the Treviso arithmetic
and had far greater influence on education. More than
any other book, it set a standard for the arithmetics of the
succeeding century. Borghi first treats notation, carrying
his numbers as high as 1 numero de million de million de
million and making no mention whatever of the Roman
numerals. In the same spirit, he eliminates all of the
medieval theory of numbers, asserting that he does this
because he is preparing a practical book for the use of
merchants.
The sequence of material is unusual because
multiplication is the first operation Borda considers.
This is followed by division, despite the fact that both
of these use addition and subtraction. The multiplication
table (see illustration) gives the products of all pairs of
numbers from 1 – 10 but also includes the products of
12, 16, 20, 24, 32, 36 because they were useful factors
for the currency then in use. The author gives the method
of checking by casting out 7s and 9s. Multiplication per
colonna (i.e., by reference to the columns of the table)
follows, with its checks by 7 and 9, and per crocetta
(cross multiplication), showing that these methods
were in common use in Venice of the day. Division is
then explained by the galley form; our present method,
then known as the method of giving, a danda, was
not mentioned. Then follow addition, subtraction,
denominate numbers, common fractions (also beginning
with multiplication), rule of three, partnership, barter,
alligation and false position. The examples are generally
practical, and they reveal much information concerning
business customs at the close of the fifteenth century.
Illustrations available:
First folio with “SDSU” poem
First page
Multiplication table
Galley division
Last folio with “SDSU” poem and colophon
Division examples, B 208
Multiplication table, B 208
177