By Horwood F.J.
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In Dictionary of Scientific Biography, vol. 9, edited by Charles C. Gillispie, 609–613. New York: Scribner, 1972. Encyclopedic biography including a detailed description of the basis for his logarithms. Boyer, Carl, and Uta Merzbach. A History of Mathematics. 2nd ed. New York: Wiley, 1991. Chapter 16 relates Napier’s work to that of his contemporaries. Hodges, Jeremy. “Significant Scots: John Napier,” Electric Scotland. com. Available online. htm. Accessed April 18, 2005. Online reprint of Hodges’s extensive July 8, 2000, article from the Daily Mail.
In fulfillment of his responsibilities as tutor for their daughter Catherine, he wrote a collection of essays on various scientific subjects. A compilation of several of these works published in 1637 under the title Principes de cosmographie, tirés d’un manuscrit de Viette, et traduits en français (Principles of cosmography, drawn from a manuscript of Viète and translated into French) included essays on the sphere, geography, and astronomy. During his three-year stint with the family, he also researched and wrote several private manuscripts, including “Mémoires de la vie de Jean de Parthenay Larchevêque” (Memoirs on the life of Jean de Parthenay Larchevêque) and “Généalogie de la maison de Parthenay” (Genealogy of the House of Parthenay).
This work explained his techniques for finding the highest and lowest points on a curve, the points that in modern terminology are known as local extrema or local maximums and minimums. Borrowing the technique “adequality” from the third-century Greek mathematician Diophantus of Alexandria, he analyzed a given curve by assuming that the curve took its extreme value at two points A and A + E. After creating an equation that related these two roots to one of the coefficients in the equation of the curve, he set the two roots equal to each other.