Final answer:
Mendeleev's connection is the universal order that governs the natural world, human relations, and the universe, highlighted by his development of the periodic table.
Step-by-step explanation:
The connection Mendeleev is making between nature, human relations, and the universe is one of universal order. This is aligned to his work on the periodic table, where he organized elements based on atomic weights and later by atomic numbers, bringing a sense of order and predictability to the field of chemistry. Mendeleev's insight into the periodic table exemplifies the scientific pursuit to understand the natural world and its intrinsic laws that also govern human social and political realms, indicating a comprehensive order extending throughout all aspects of the universe.