Periodic table (detailed cells)
Although precursors to this table exist, its invention is generally credited to Russian chemist Dmitri Mendeleev in 1869. Mendeleev invented the table to illustrate recurring ("periodic") trends in the properties of the elements. The layout of the table has been refined and extended over time, as new elements have been discovered, and new theoretical models have been developed to explain chemical behavior.
Numerology
The discovery of atomic triads, an early attempt to sort the elements into some logical order by their physical properties, was once considered a form of numerology, and yet ultimately led to the construction of the periodic table. Here the atomic weight of the lightest element and the heaviest are summed, and averaged, and the average is found to be very close to that of the intermediate weight element. This didn't work with every triplet in the same group, but worked often enough to allow later workers to create generalizations.