The definite article is used before ordinal numbers and superlative adjectives:
This is the first time I've ridden a horse.
The 20th century has seen the bloodiest wars in the history of humankind.
Jill is the most intelligent girl in the class.
The to-infinitive is often used in non-finite defining relative clauses after ordinal numbers (the first, the second etc.), superlatives (the best, the most beautiful etc.) and after next, last and only:
A to-infinitive clause can replace a defining relative clause after ordinal numbers (the first, the second etc.), after superlatives (the best, the most beautiful etc.) and after next, last and only: