Good question. In short, Dmitri Mendeleev noticed that certain properties of the elements repeated, i.e., were periodic. This allowed him to create an initial framework for the elements that had rather intriguing empty spaces. In this way, he predicted as yet undiscovered elements. A periodic table. Eventually these discoveries happened.
A longer version of how the Periodic Table came to be and what it all means, one that I very highly recommend, is the book The Periodic Kingdom: A Journey Into The Land Of The Chemical Elements.
In between, you can watch this recently produced video:
Chemestry? or Chemistry?
Best book on the historic origins of the periodic table is Eric R. Sherri’s The Periodic Table: Its Story and Its Significance https://www.amazon.com/Periodic-Table-Its-Story-Significance/dp/0195305736/ref=sr_1_1?s=books&ie=UTF8&qid=1517379886&sr=1-1&keywords=eric+scerri
Scerri not Sherri! I hate autocorrect!
Thanks Tony.
Quite a good video I thought.
One small problem, the implication that only Mendeleev recognized chemical periodicity. Another, the notion that Lecoq De Boisbaudran somehow ‘beat’ Mendeleev. Actually Mendeleev won the bout if anybody did since Mendeleev was able to correct the Frenchman’s data without even performing any experiments.
For the full story see my book that Thony kindly referred to.
Eric Scerri
UCLA, Department of Chemistry
http://www.ericscerri.com