# Early Methods For Finding Tangents

The first person to formulate explicitly the ideas of limits and derivatives was Sir Isaac Newton in the 1660s. But Newton acknowledged that “If I have seen further than other men, it is because I have stood on the shoulders of giants.” Two of those giants were Pierre Fermat (1601–1665) and Newton’s mentor at Cambridge, Isaac Barrow (1630–1677). Newton was familiar with the methods that these men used to find tangent lines, and their methods played a role in Newton’s eventual formulation of the calculus.
The following references contain explanations of these methods. Read one or more of the references and write a report comparing the methods of either Fermat or Barrow to modern methods. In particular, use the method of Section 2.1 to find an equation of the tangent line to the curve y = x3 + 2x at the point (1, 3) and show how either Fermat or Barrow would have solved the same problem(Use Equation Editor in the word!). Although you used derivatives and they did not, point out similarities between the methods.
1. Carl Boyer and Uta Merzbach, A History of Mathematics (New York: Wiley, 1989), pp. 389, 432.
2. C. H. Edwards, The Historical Development of the Calculus (New York: Springer-Verlag, 1979), pp. 124, 132.
3. Howard Eves, An Introduction to the History of Mathematics, 6th ed. (New York: Saunders, 1990), pp. 391, 395.
4. Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), pp. 344, 346.

MATH BOOK: Calculus By Stewart James Pg. 114

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