How did recurring properties lead Dmitri Mendeleev to the periodic law?

Dmitri Mendeleev’s discovery of the periodic law emerged from his systematic effort to organize the chemical elements while writing his textbook, The Principles of Chemistry.1

While composing a chapter on halogens, Mendeleev compared their properties to those of alkali metals. He observed similarities in the progression of atomic weights across these groups and hypothesized that such patterns might exist among other elements. By analyzing these recurring properties alongside atomic weights and valency—the number of single bonds an element can form—he established that atomic weights could be used to arrange both individual elements and entire groups.123

This correlation led him to propose the periodic law in 1869, stating that elements arranged by their atomic weights exhibit a clear periodicity of properties. His deep confidence in this law allowed him to correct existing atomic weight values and accurately predict the existence and properties of then-unknown elements, such as scandium, gallium, and germanium, which ultimately secured the scientific community's acceptance of his periodic table.132