http://www.sam.math.ethz.ch/sam_reports/

there is a (pdf) report 2012-43 which explains his method and analyses the accuracy of the resulting tables.

]]>I’ll get back to you on the question of Archimedes and the logarithms he definitely knew about the parallelism of geometric and arithmetic series, the basis of logarithms but I can’t say, without looking it up where this is to be found in his work.

]]>The method of prosthaphaeresis is largely unknown because it was only used for a very short period of time starting around 1580. It had almost totally disappeared by the time Henry Briggs published his base ten logarithms in 1624. Although I studied both mathematics and the history of mathematics I only stumbled across prosthaphaeresis because of my interest in Renaissance astronomy.

]]>First, one caption mentions a quartz clock. I presume this is not referring to the timing mechanism! The dome is quartz, perhaps? Why quartz instead of glass?

Second, you say that Archimedes had the basic idea on which logarithms are based. Are you referring to The Sand Reckoner?

]]>For those interested in the mechanics of prosthaphaeresis, there is a decent article with examples at Wikipedia here http://en.wikipedia.org/wiki/Prosthaphaeresis ]]>