 A method of determining by mere inspection the derivatives from two equations of any degree

Paper 9 by James Joseph Sylvester, reprinted on pp. 54–57 in The Collected Mathematical Papers of James Joseph Sylvester, Volume I. The reprint identifies the original publication as Philosophical Magazine XVI (1840), 132–135. Henry Frederick Baker edited the collection; he is not credited as author of this paper.

Inspected collection OCR: archive.org/stream/collectedmathem01sylvrich/collectedmathem01sylvrich_djvu.txt

Cited passages: paper 9, printed pp. 54–55, rules 1–4, shifted coefficient rows and the permutation sign sum. The historical word derivatives in the title is not used here to mean differentiation in calculus. The title page and prefatory note establish the separate 1904 collection date.