Briggs (1624) first instance of binomial theorem for a fractional exponent:
![\[(1+x)^{1/2}=1+\fr{2}x-\frac{1\cdot 1}{2\cdot 4}x^2+\frac{1\cdot 1\cdot 3}{2\cdot 4\cdot 6}x^3-\frac{1\cdot 1\cdot 3\cdot 5}{2\cdot 4\cdot 6\cdot 8}x^4+\dots\]](https://www.adamponting.com/wp-content/ql-cache/quicklatex.com-5585b9613bfef6b097c25a29616fa55f_l3.png "Rendered by QuickLaTeX.com")
Mercator (1668) integrated:
![\[\fr{1+x}=1-x+x^2-x^3+\dots\]](https://www.adamponting.com/wp-content/ql-cache/quicklatex.com-983620268b2bc2a90f41643991f84793_l3.png "Rendered by QuickLaTeX.com")
to get:
![\[log(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\dots\]](https://www.adamponting.com/wp-content/ql-cache/quicklatex.com-276abed1f0d1ecf521fa208f2f4aa61d_l3.png "Rendered by QuickLaTeX.com")
Stillwell – Mathematics and its History
Briggs (1624) first instance of binomial theorem for a fractional exponent:
Mercator (1668) integrated:
to get:
Stillwell – Mathematics and its History