How did the Colosseum influence the facade of Palazzo Rucellai?

The facade of the Palazzo Rucellai, designed by Leon Battista Alberti, was significantly influenced by the Colosseum in Rome.12

Alberti drew inspiration from the Colosseum’s exterior to organize the palace's elevation through the application of the three classical orders. By superimposing pilasters of different orders across the three stories—ranging from the short, robust Tuscan order on the ground floor to the tall, decorative Corinthian order at the top—Alberti established a logical, harmonious relationship between the differentiated levels. This approach mirrored the canonical arrangement of the classical orders found on the Colosseum, which similarly utilizes arcades framed by half-columns of varying orders to indicate upward progression.123