M chapter.indd - Charles Babbage Institute

830
Erwin Tomash Library
Magini, Giovanni Antonio Magini, Giovanni Antonio
Year: 1592
Place: Venice
Publisher: Batistam Ciottum
Edition: 1st
Language: Latin
Binding: later patterned boards
Pagination: ff. [4], 36 (misnumbered 34 as 62 and 36 as 64)
Collation: a 4 A–I 4
Size: 194x146 mm
Giovanni Magini earned a degree in philosophy from the
University of Bologna in 1579. In 1588, he was chosen
over the younger Galileo to occupy one of the two chairs
of mathematics in Bologna. Modern comparisons with
Galileo have often been to Magini’s detriment, but he
was regarded highly during his lifetime. He proved to
be a reasonable scholar, corresponded with Brahe and
Galileo on astronomical matters, published the first
detailed atlas of Italy and made a number of original
astronomical observations. It has been noted that he
sided with others against Galileo, but such actions were
not unusual at the time and were often conducted with a
bitterness that seems entirely out of place today.
Even before the invention of logarithms, a number of
shortcuts were available for the performance of complex
arithmetic calculations. Perhaps the best known of
these was the method of prosthaphaeresis (see entry
for Clavius, Christoph; Astrolabium, Rome, 1593).
Other approaches involved finding the squares and
square roots of quantities. The large amount of work
involved in applying these methods often obviated
their use. However, they indeed proved to be useful if a
table of squares could be consulted to quickly obtain an
approximate value.
M 17
Magini calculated this table of squares for precisely such
use. It lists the squares of each integer from 1 to 10,100.
His examples (as were Napier’s a few years later when
he invented logarithms) are oriented towards arithmetic
involving sines because these were heavily used in
astronomy, astrology and navigation. Magini shows that
given x, one can find its square root by looking in the
table for two perfect squares that bracket x, and then
it is simply a matter of subtraction to find a very close
approximation to its square root. In modern notation:
x = a 2 + y, x = (a+1) 2 – z,
√x = a + y/z
These tables are a separate issue of the tables that are
part of Magini’s work De planis triangulis that appeared
in the same year. The same setting of type was used as
can be seen from the last page of the tables where the
catchword Tavola appears in the lower corner because
in De planis triangulis a table titled Tabula Sinuum
followed the table of squares. This volume is dedicated
to Tycho Brahe, but that dedication is not part of the
larger work.
Illustrations available:
Title page
Last table page
M 18
Magini, Giovanni Antonio (1555–1617)
Primum mobile duodecim libris contentum, in quibus
habentur trigonometria sphæricorum, et astronomica,
gnomonica, geographicaque problemata, ac præterea
magnus trigonometrius canon emendatus, et auctus,
ac magna primi mobilis tabula ad decades primorum
scrupulorum per utrumque latus supputata.
b/w: Magini, Giovanni Antonio; Tabulæ generales
ad primum mobile spectantes, et primo quidem
sequitur magnus canon mathematicus, 1609.
b/w: Magini, Giovanni Antonio; Tabula proportionalis
ad usum generalis primi mobilis, 1609.
Year: 1609
Place: Bologna
Publisher: For the author by Jo. Bapt. Bellagambam
Edition: 1st
Language: Latin
Figures: engraved title page
Binding: contemporary half-vellum over boards; raised bands
Pagination: ff. [9], 104, [1], 106 – 290 (misnumbered 4 as 7,
110 as 109, 141 as 241, 142 as 242, 146 as 246, 233 as
236, 250 as 248, 251 as 249)
Collation: π 3 b 4 c 2 A–4B 4 4C 6
Size: 355x238 mm
Reference: DSB IX, pp. 12–13