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Mathematical Treasures - Johann Scheubel's De Numeris

Frank J. Swetz and Victor J. Katz

Title page of Scheubel's De Numeris


This is the title page of the De Numeris et Diversis Rationibus (1545) of Johann Scheubel (1494-1570).  Scheubel was a German cossist, who wrote textbooks in arithmetic, algebra, and geometry. In general, his works were written in Latin and were theoretical rather than practical.  Thus, they appealed to the academically-minded rather than the merchants for whom other cossists were writing.



Pascal Triangle in Scheubel


On this page (sig. b, f. 2, r), Scheubel displayed his version of the Pascal triangle. Note the typographical errors toward the bottom. Scheubel noted that the triangle would aid in finding roots of numbers.  He spent many pages in the text working through the procedures using the triangle that would enable one to extract higher roots.