The Classical Composite Order was developed in Rome and, as its name suggests, is the result of a composition of Ionic and Corinthian Orders. In the Composite column capital there is a combination of Ionic volutes and Corinthian acanthus leaves.

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Composite Order
The Composite order is mixed, the capital is the combination of the Ionic order and the Corinthian order. This order is essentially treated as the former one except for the capital, with no consistent differences to that above or below the capital.
In many versions, there is generally some ornament placed centrally between the volutes. The column is ten diameters high, though as with all the orders these details may be adjusted by the architect for particular buildings.

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The Composite order is not found in ancient Greek architecture and until the Renaissance was not ranked as a separate order. It was considered as an imperial Roman form of the Corinthian order. The Arch of Titus, in the forum in Rome, is sometimes cited as the first prominent surviving example of composite order, that was probably invented before Augustus’s reign and certainly developed before his death.
It was added by Renaissance writers to make five classical orders. Sebastiano Serlio was the first one in his book “I Sette Libri d’Architettura”, to mention it as an own order and not just as an evolution of the Corinthian order as previously.

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Composite Style Features
This style has the following characteristics:
- Tall and slender columns (10 diameters high) that can outline column design or materials;
- Capitals with acanthus leaves with big scrolls; its entablature shows an ostentatiously sculpted frieze and cornice;
- The volutes of the Composite capital were adapted from Phoenician and Egyptian capital designs. They are large and some ornament is generally placed between the volutes;
- Entablatures are the tallest of all the orders (2 diameters high); From the bottom to the top, it presents: the architrave, the frieze and the cornice.
- Composite decoration reflects a sense of triumph; it was used to represent victory, prestige, opulence and success;

Image source: https://en.wikipedia.org/wiki/Arch_of_Titus
Composite Order Later in History
Palazzo Madama in Turin is a large historic building, which owes its name to the resident widows of the 17th century dukes of Savoy. It was also used by the Italian Senate. Today it houses the Museum of Ancient Arts. Despite its name, it is a large collection of paintings, statues and church ornaments.

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Another wonderful example that needs to be considered is the facade of San Carlo alle Quattro Fontane. Borromini received the commission in 1634 from Cardinal Barberini. However the building project suffered various financial difficulties, it is one of at least three churches in Rome dedicated to San Carlo.

Image source: https://en.wikipedia.org/wiki/San_Carlo_alle_Quattro_Fontane
The Lescot Wing in the courtyard of the Louvre palace (Paris, France) is the oldest part of the existing complex. The Wing was executed between by the architect Pierre Lescot. Strongly tinged with Italian Mannerism, it became the Parisian Renaissance style.

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Info source: https://www.classicist.org/articles/classical-comments-the-composite-order-an-overview/