English Translation of Roger Cotes's Logometria with Commentary

Three years ago (almost exactly) I wrote an answer on History of Science and Mathematics StackExchange trying to explain how Roger Cotes came up with the logarithm form of the Euler's formula. It was quite challenging to work through this problem, and it stuck with me for some time afterwards. A few months ago I was let go from my job, and suddenly found myself with enough free time to revisit this problem. The result was a new translation and commentary on the Logometria of Roger Cotes. While there already exists a published translation by Ronald Gowing (Gowing, Roger Cotes - Natural Philosopher, Cambridge University Press. 1983.), this book is unfortunately a bit difficult to get a hold of, and the commentary is less comprehensive in covering the background to Cotes's work. So drawing on several original sources, I've written what I believe is quite an accurate reflection of the background matter, as well as improved explanations of just what exactly Cotes was talking about. When doing this translation, I avoided Gowing's own translation to avoid "cross-contamination." In fact, as of publication, I still have not seen it; I've only reviewed when was available in a preview. 

And so, this is my translation from Latin into English of Roger Cotes, Logometria, as it appeared in the posthumous collection Harmonia Mensurarum (1722). This is what Gowing refers to as the Logometria "Part 1"; I did not translate the additional examples from Cotes's tables of integrals. Included in this part of the Logometria are six propositions relating to the application of logarithms to geometry, and a wide range of additional geometric solutions given mostly without proof in a large General Scholium. 

It was important to me that I publish today, as tomorrow I start a new job, and my free time and energy will be more limited. 

Please comment any criticisms, errors/corrections, and recommendations, or email me at sjgallagher2@gmail.com.


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