The Collected Works of John Wallis (1616-1703) were published from 1693 to 1699.
![Title page from 1695 first volume of John Wallis's collected works.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v1_titlepageA.png)
The frontispiece for this Collection was a portrait of Wallis.
![Frontispiece from John Wallis's collected works (volume 1, 1695).](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v1_frontispieceA.png)
Within this Collection is a complete copy of Wallis’s Algebra, first published in 1685.
![Title page from John Wallis's Treatise on Algebra (1685) in his collected works.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v2_titlepageB.png)
The frontispiece for the Algebra is also a portrait of the author but in a more formal pose.
![Frontispiece from John Wallis, Treatise on Algebra (1685).](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v3_frontispiece.png)
On page 105 of his Algebra, Wallis gave a table explaining his algebraic notation, where: quadratum, symbolized by “q”, indicates ‘raised to the second power’ and cubus, “c”, means ‘raised to the third power’. Thus, for a modern reader: \({\rm{Xq}}=x^2,\) \({\rm{Xc}}=x^3,\) \({\rm{Xqq}}=x^4,\) \({\rm{Xqc}}=x^5\dots.\)
![Page 105 of John Wallis, Treatise on Algebra (1685).](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v2_body0105.png)
Wallis’s concern for the cycloid is contained in a contribution beginning on page 499 of the Collection.
![Page 499 of John Wallis's collected works (1712).](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/U-Penn-Libs/FolioQA_33_W25_1695v1_body0499.png)
The images above are presented courtesy of the University of Pennsylvania Libraries.
Index to Mathematical Treasures