Mendeleev formulated the periodic law, which stated that the properties of the chemical elements vary periodically when the elements are arranged according to atomic weight. This principle became the foundation for his periodic system of 1869.
The law allowed Mendeleev to organize elements with similar chemical behavior into recurring groups. More importantly, it led him to leave blank spaces for elements that had not yet been discovered and to predict their approximate properties. Germanium, gallium, and scandium later filled those gaps with notable accuracy.
The original law referred to atomic weight because atomic number and the internal structure of atoms were not yet understood. After the discovery of atomic number in the early 20th century, the modern formulation became that elemental properties are periodic functions of atomic number.
“Law of octaves” is a different proposal associated with John Newlands, while the “law of triads” was developed by Johann Döbereiner. Neither is the name of Mendeleev’s principle.