1. I HAVE observed, Emperor, that many in their treatises and volumes of commentaries on architecture have not presented the subject with well-ordered completeness, but have merely made a beginning and left, as it were, only desultory fragments. I have therefore thought that it would be a worthy and very useful thing to reduce the whole of this great art to a complete and orderly form of presentation, and then in different books to lay down and explain the required characteristics of different departments. Hence, Caesar, in my first book I have set forth to you the function of the architect and the things in which he ought to be trained. In the second I have discussed the supplies of material of which buildings are constructed. In the third, which deals with the arrangements of temples and their variety of form, I showed the nature and number of their classes, with the adjustments proper to each form according to the usage of the Ionic order, one of the three which exhibit the greatest delicacy of proportion in their symmetrical measurements. In the present book I shall speak of the established rules for the Doric and Corinthian orders, and shall explain their differences and peculiarities.