Kepler's answer to the second objection was to publish a proof of how logarithms worked, based on an impeccably respectable source: Euclid 's Elements Book 5. Kepler calculated tables of eight-figure logarithms, which were published with the Rudolphine Tables (Ulm, 1628).
Kepler's kasagutan sa ikalawang pagtutol ay na-publish ng isang patunay ng kung paano logarithms nagtrabaho, batay sa isang impeccably kagalang-galang source: Euclid 's Sangkap ng Book 5. Kepler ikinakalkula mga talahanayan ng walong-figure logarithms, na kung saan ay nai-publish sa Rudolphine Table (Ulm, 1628).