# Page:Popular Science Monthly Volume 44.djvu/114

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THE POPULAR SCIENCE MONTHLY.

 MATHEMATICAL CURIOSITIES OF THE SIXTEENTH CENTURY.
By M. V. BRANDICOURT.

IN the great intellectual revival of the sixteenth century, mathematics as well as letters and the arts were recuperated first from the pure sources of antiquity. Casting away poor Latin translations, second-hand versions through the Arabic, on which the Middle Ages had fed, geometricians emulated one another in zeal for learning the Greek language, in order that they might read in the original text the works of Euclid, Archimedes, Ptolemy, and Diophantus. Most of the works published at this epoch were only translations from Grecian authors. "The great thought of that time," says Montucla, "was simply to refine the minds of students and cause them to taste of a learning almost unknown till then. This could not be done all at once, and the human mind, like a weak stomach which too solid food would tire out, had to be brought by degrees to considerations of a higher order."

One of the earliest translations of Euclid is found in the Margarita philosophica of G. Riesch, prior of La Chartreuse at Friborg—a Latin book printed in Gothic characters at Heidelberg in 1496. It is a sort of encyclopædia of the science of the beginning of the sixteenth century, and certifies to the very extensive knowledge of the author. Each of the scientific treatises contained within it is adorned with very curious engravings of a naïve character.

Memmius, a noble of Venice, made a translation of the works of Apollonius in 1537, which was published after his death by one of his sons.

The mathematical sciences were then cultivated with most success in Italy; and when Francis I, of France, sent across the Alps for architects, painters, and sculptors to construct and adorn the magnificent châteaux of Chambord and Chenonceaux, he was thus also able to ask for his colleges algebraists who were certainly the first mathematicians in Europe. Algebra was not then what it has since become, a science employing only letters, signs, and symbols, having a well-defined significance and serving as the characters of a very clear and very precise language, which the initiated could understand as well as they could their mother tongue. The unknown quantity was then called "the thing" (res, coser; from which algebra was for some time named the art of the thing), and it was often represented by R. The square of the unknown quantity was called census (2). The signs ${\displaystyle \times }$ and ${\displaystyle =}$ were not known, but the initials of the words for which they stand