Further information: Mathematics and architecture Vitruvius is the author of De architectura, libri decem, known today as The Ten Books on Architecture,  a treatise written in Latin on architecture, dedicated to the emperor Augustus. In the preface of Book I, Vitruvius dedicates his writings so as to give personal knowledge of the quality of buildings to the emperor. This work is the only surviving major book on architecture from classical antiquity. According to Petri Liukkonen, this text "influenced deeply from the Early Renaissance onwards artists, thinkers, and architects, among them Leon Battista Alberti — , Leonardo da Vinci — , and Michelangelo —
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Further information: Mathematics and architecture Vitruvius is the author of De architectura, libri decem, known today as The Ten Books on Architecture,  a treatise written in Latin on architecture, dedicated to the emperor Augustus. In the preface of Book I, Vitruvius dedicates his writings so as to give personal knowledge of the quality of buildings to the emperor. This work is the only surviving major book on architecture from classical antiquity.
According to Petri Liukkonen, this text "influenced deeply from the Early Renaissance onwards artists, thinkers, and architects, among them Leon Battista Alberti — , Leonardo da Vinci — , and Michelangelo — Vitruvius is famous for asserting in his book De architectura that a structure must exhibit the three qualities of firmitatis, utilitatis, venustatis — that is, stability, utility, beauty. These are sometimes termed the Vitruvian virtues or the Vitruvian Triad. According to Vitruvius, architecture is an imitation of nature.
As birds and bees built their nests, so humans constructed housing from natural materials, that gave them shelter against the elements. When perfecting this art of building, the Greeks invented the architectural orders: Doric , Ionic and Corinthian. It gave them a sense of proportion, culminating in understanding the proportions of the greatest work of art: the human body.
This led Vitruvius in defining his Vitruvian Man , as drawn later by Leonardo da Vinci : the human body inscribed in the circle and the square the fundamental geometric patterns of the cosmic order.
In this book series, Vitruvius, also wrote about climate in relation to housing architecture and how to choose locations for cities.
However, many of the other things he did would not now be considered the realm of architecture Vitruvius is sometimes loosely referred to as the first architect, but it is more accurate to describe him as the first Roman architect to have written surviving records of his field. He himself cites older but less complete works. He was less an original thinker or creative intellect than a codifier of existing architectural practice.
Vitruvius had a much wider scope than modern architects. Roman architects practised a wide variety of disciplines; in modern terms, they could be described as being engineers, architects, landscape architects , surveyors, artists, and craftsmen combined. The first of the Ten Books deals with many subjects which now come within the scope of landscape architecture.
Architecture is a science arising out of many other sciences, and adorned with much and varied learning; by the help of which a judgment is formed of those works which are the result of other arts. Practice and theory are its parents. Practice is the frequent and continued contemplation of the mode of executing any given work, or of the mere operation of the hands, for the conversion of the material in the best and readiest way.
Theory is the result of that reasoning which demonstrates and explains that the material wrought has been so converted as to answer the end proposed. Wherefore the mere practical architect is not able to assign sufficient reasons for the forms he adopts; and the theoretic architect also fails, grasping the shadow instead of the substance. He who is theoretic as well as practical, is therefore doubly armed; able not only to prove the propriety of his design, but equally so to carry it into execution.
In Book I, Chapter 3 The Departments of Architecture , Vitruvius divides architecture into three branches, namely; building; the construction of sundials and water clocks ;  and the design and use of machines in construction and warfare. Public building includes city planning, public security structures such as walls, gates and towers; the convenient placing of public facilities such as theatres, forums and markets, baths, roads and pavings; and the construction and position of shrines and temples for religious use.
Just so the parts of Temples should correspond with each other, and with the whole. The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square.
For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square. The drawing itself is often used as an implied symbol of the essential symmetry of the human body, and by extension, of the universe as a whole.
This is the only location in the work where Vitruvius specifically addresses his personal breadth of knowledge. The topics range across many fields of expertise reflecting that in Roman times as today construction is a diverse field.
Vitruvius is clearly a well-read man. In addition to providing his qualification, Vitruvius summarizes a recurring theme throughout the 10 books, a non-trivial and core contribution of his treatise beyond simply being a construction book. Vitruvius makes the point that the work of some of the most talented are unknown, while many of those of lesser talent but greater political position are famous. Vitruvius illustrates this point by naming what he considers are the most talented individuals in history.
Vitruvius Britannicus: The Classic of Eighteenth-Century British Architecture
Further volumes using the successful title were assembled by Woolfe and Gandon , and published in and In the empirical vein, it was not a treatise but basically a catalogue of design , containing engravings of English buildings by Inigo Jones and Sir Christopher Wren , as well as Campbell himself and other prominent architects of the era. In the introduction that he appended and in the brief descriptions, Campbell belaboured the "excesses" of Baroque style and declared British independence from foreigners while he dedicated the volume to Hanoverian George I. The drawings and designs contained in the book were under way before Campbell was drawn into the speculative scheme. The success of the volumes was instrumental in popularising neo- Palladian Architecture in Great Britain and America during the 18th century. The somewhat promotional volume, with its excellently rendered engravings, came at a propitious moment at the beginning of a boom in country house and villa building among the Whig oligarchy.