60 3. MATHEMATICAL CULTURES II
physical bodies from various points of view, formulated the Merton rule of uniformly
accelerated motion (named for Merton College, Oxford), and for the first time in
history explicitly used one line to represent time, a line perpendicular to it to
represent velocity, and the area under the graph (as we would call it) to represent
distance.
Regiomontanus. The work of translating the Greek and Arabic mathematical works
went on for several centuries. One of the last to work on this project was Johann
Miiller of Konigsberg (1436-1476), better known by his Latin name of Regiomon-
tanus, a translation of Konigsberg (King's Mountain). Although he died young,
Regiomontanus made valuable contributions to astronomy, mathematics, and the
construction of scientific measuring instruments. In all this he bears a strong re-
semblance to al-Tusi, mentioned above. He studied in Leipzig while a teenager,
then spent a decade in Vienna and the decade following in Italy and Hungary. The
last five years of his life were spent in Nurnberg. He is said to have died of an
epidemic while in Rome as a consultant to the Pope on the reform of the calendar.
Regiomontanus checked the data in copies of Ptolemy's Almagest and made
new observations with his own instruments. He laid down a challenge to astron-
omy, remarking that further improvement in theoretical astronomy, especially the
theory of planetary motion, would require more accurate measuring instruments.
He established his own printing press in Nurnberg so that he could publish his
works. These works included several treatises on pure mathematics. He established
trigonometry as an independent branch of mathematics rather than a tool in as-
tronomy. The main results we now know as plane and spherical trigonometry are
in his book De triangulis omnimodis, although not exactly in the language we now
use.
Chuquet. The French Bibliotheque Nationale is in possession of the original man-
uscript of a comprehensive mathematical treatise written at Lyons in 1484 by one
Nicolas Chuquet. Little is known about the author, except that he describes himself
as a Parisian and a man possessing the degree of Bachelor of Medicine. The treatise
consists of four parts: a treatise on arithmetic and algebra called Triparty en la
science des nombres, a book of problems to illustrate and accompany the principles
of the Triparty, a book on geometrical mensuration, and a book of commercial
arithmetic. The last two are applications of the principles in the first book.
Luca Pacioli. Written at almost the same time as Chuquet's Triparty was a work
called the Summa de arithmetica, geometrica, proportioni et proportionalite by
Luca Pacioli (or Paciuolo) (1445-1517). Since Chuquet's work was not printed until
the nineteenth century, Pacioli's work is believed to be the first Western printed
work on algebra. In comparison with the Triparty, however, the Summa seems
less original. Pacioli has only a few abbreviations, such as co for cosa, meaning
thing (the unknown), ce for censo (the square of the unknown), and <E for <Equitur
(equals). Despite its inferiority to the Triparty, the Summa was much the more
influential of the two books, because it was published. It is referred to by the Italian
algebraists of the early sixteenth century as a basic source.
Leon Battista Alberti. In art the fifteenth century was a period of innovation. In an
effort to give the illusion of depth in two-dimensional representations some artists
looked at geometry from a new point of view, studying the projection of two- and
three-dimensional shapes in two dimensions to see what properties were preserved
