Mathematical Treasure: Collected Works of Johann Bernoulli

Johann Bernoulli (1667–1748) was one of the most eminent mathematicians of the Enlightenment. He was a teacher of Leonhard Euler and of the Marquis de l’Hospital. Shown above is the title page of the first volume of his collected works, covering the period 1690-1713 and published in 1742. The contents of this volume testify to the genius and versatility of this mathematician.

At the top of page 46 of the Collected Works, above, Bernoulli discussed the conception of the conic sections as cuts in a right cone. Illustrations for this discussion were given in Plate No. II on the adjacent page. Note that at this time mathematical diagrams were still drawn separately, printed separately, and then attached to mathematical texts. Larger versions of the two individual pages are provided below.

A dedication page (directly above, left) was included to honor Bernoulli’s royal patron, Charles Frederick, King of the Prussians. This was Charles Wilhelm Frederick I who reigned from 1713 to 1740. On the adjacent page we find some illustrations of previous problems discussed by Bernoulli. The reader can speculate on the meanings of the various figures.

At the top of page 132, shown above, is a listing of the topics to be considered in the article that followed:

• “An observation about the preceding solution by the illustrious Marques Hospital.” L’Hospital and Bernoulli became acquainted in 1691 and began a correspondence that would last for many years and result in an historical mathematical controversy.
• “A demonstration of the identity of the curve of equilibrium with the cycloid described by a wheel revolving on a wheel of equal size.” Bernoulli was noted for his research on the cycloid and, in particular, for his solution of the brachistochrone problem.
• “The general consideration of the same curve, accomplished by geometry.”
• “The solution of a companion problem posed in October of 1694.”

Acknowledgments

Assistance with the Latin translation was kindly provided by Barnabas Hughes.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in Mathematical Treasures. In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.