Isaac Newton's $De$ $Analysi$ (The study of the history of mathematics 2017)

"The study of the history of mathematics 2017". September 19-22, 2017. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.Isaac Newton gives three rules for quadrature in his De Analysi per aequationes numero terminorum infinitas (1669). First we read Nicolaus Mercator's Logarithmotechnia (1668) which gives Newton a chance to write De Analysi, and we compare Mercator's study on computation of logarithms with that by Newton. Next we consider the three rules in De Analysi. In particular, we compare operations in decimal numbers with those in literals (general variables). Moreover we also clarify the meanings of "p and x separately are of least dimension" and "x and y either separately or multiplied together are of the most and equal dimensions everywhere" in the literal resolution of affected equations