Francisco Martínez Mindeguía

In all probability, we cannot speak about axonometric projections as such, referring to drawings before the 18th century, since that is when it is conceived and defined scientifically as a way of representation. It was Gaspar Monge who described it in his book Géométrie descriptive, in 1798, which culminated the previous works by Amédée-François Frézier (La théorie et la pratique de la coupe des pierres et des bois... ou traité de stéréotomie..., in 1737) and by Gérard Desargues (published by Abraham Bosse, Manière universale de M. Desargues pour practiquer la prospettive par petit-pied, comme le géométral, in 1648). However, this type of drawing did exist before, probably before conic perspective. This is the reason why that kind of drawing prior to Monge, which has pseudo-axonometric features, is called parallel projection or oblique parallel projection. It is not called axonometric since it may seem an incongruity.
The fact is that this kind of drawing did exist before; however, it did not have the same consideration as perspective projection, neither did it interest Renaissance intellectuals and artists in the same way. The undeniable prominence of perspective projection may lead to the belief that axonometric is an invention of the 18th century, but this is not certain. At the end of the 15th Century, Alberti and Piero della Francesca had already set the theoretical and practical basis for perspective projection, initially at least. A similar basis related to projects was set in the second half of the 16th century. However, intellectuals such as Luca Paccioli were already using it in 1509, to illustrate the geometrical demonstrations in the Divina Proportione (Venice, 1509).   The same happens with Niccolò Tartaglia in Quesiti et inventioni diverse, (Venice, 1546).   

Its use was not always linked to the difficulty of conic perspective, but to the convenience of this kind of representation. The drawing adjoined, a work by Leonardo da Vinci from the Codex Atlanticus, 1493, explains how it works and what parts integrate the capstan, a tool used to lift heavy weights. Leonardo could have used perspective, but instead he uses a kind of representation which allows him to show the frontal axis and the pieces slightly turned around. Reading the drawing from left to right, it starts with the image of a machine, and then follows its decomposition into different parts. The drawing could be used as a direction for anyone to construct a machine of this sort, and a perspective projection might have not improved its understanding.
  A key factor for such understanding is that Leonardo keeps the image of the capstan already set, next to the individual components. Without that image, it would be hard to imagine how it would look like. To appreciate it better, it might be necessary to see some de-compositions that do not take this into account, as the following drawing by Luis M. Mansilla and Emilio Tuñón, at the Provincial Museum in Zamora. The authors show the precedence of every part, as well as the displacements and turns that they go through, but it is impossible to “visualize” the image of the initial state. It is fair to suppose that such representation is now considered a standard procedure, well known by professionals.

In this drawing by Richard Fernau and Laura Hartman, the body of the building dismembers but portrays the mark of the eliminated volume. Somehow, this allows a certain reconstruction of the cluster.

Another drawing of this kind is Jones Partners’, in which it is difficult to imagine the previous state prior to dismemberment.

The previous drawing by Leonardo, as well as other drawings from the Codex, proves that the reason why this kind of projection is used was not so much the need to represent the object in space, as perspective projections do, but, rather, representing the space surrounding the object or its volume. A system was needed that prioritized the 3D geometrical features of the object.  Next is another drawing of the same kind by Leonardo.

In the second half of the Cinquecento, some military architecture treatises appeared, generally portraying fortifications, inexpugnable in theory.  These drawings require clarity and accuracy. As Diego Gonzales De Medina Barba (Examen de fortificación..., Madrid, 1599, page 5), a subject of Philip III of Spain said: the imperfection of a line wrongly interpreted may be responsible for the loss of strength.


In 1564, Girolamo Maggi and Giacomo Castriotto’s book, Della fortificazione delle Città, is published in Venice. In this book, axonometric and perspective projections are opposed for the first time. This is one of the drawings in the book.
Girolamo Maggi and Giacomo Castriotto were military engineers. In the book, Castriotto says: no one should expect to find any perspective projection rules in this work of mine, firstly because since it is not a soldier’s duty, I would not be able to do them. Secondly, because due to the foreshortenings that would result, they would be seen better if they were drawn on the plant, and the essence of this work will be in those plants and sections, which will be called military perspective (“perspectiva soldadesca”, in Second book, chapter III, page 40).

This is what we refer to as (orthographic?) cabinet projection, a drawing in which, by keeping the plan unaltered (that is, without deforming its angles), the lateral planes are represented as well, and contours not converging in vanishing points.
  Many of the drawings are done with projections in which the lateral plane is not seen. The lay-out may seem unclear, but it has the advantage that the elevation is portrayed with the angles not being deformed.
  In this case, the drawing allows showing the effective control of flanks that the city wall had to guarantee.

There are obvious construction errors in these drawings. There were also architects and painters who did similar mistakes. However, it is evident that it is easier to do this kind of drawings since they are not as complex as conic perspective projections.


From this moment on, studies are more frequent. A singular example of this use is Androuet du Cerceau’s drawing.

Du Cerceau (1515-1585) was an architect, but he is mainly known for his books. Perhaps, the most known ones are the Livre d'architecture, published in 1559 and Les Plus Excellents Bastiments de France, 1576. He was contemporary to Michelangelo and Du Pérac and a very renowned architect in France. He wrote a perspective projection treatise, too.
Palace of Fontainebleau,

Depending on each case, Du Cerceau uses perspective projection, elevations or axonometric, even using unclear projections, to show some of the side planes. This latter image belongs to the Livre des edifices antiques, (1549-1584).  The two previous ones belong to Livre d'architecture, 1582.
  In 1597, the engineer Buonaiuto Lorini, who wrote a book about fortresses, states that this is the prospettiva più comune (the most common kind of perspective), and describes the procedure for doing it (Delle fortificazione... libri cinque, Venece, 1597 and 1609).

The theme of city defense is important and mobilizes a large part of intellectuals, architects, and engineers (Francesco di Giorgio Martini, Miguel Ángel, Sangallo il Giovane...).

In 1598, Giovanni Battista Belici, author of Nuova inventione di fabricar fortezze (Venece, 1598) says that perspective (referring to the military one) is useful in practice…because we have the need to see things in a complete, clear, and dimensional way, and he opposes it to the perspective projection, which in warfare will not work since we have the need to see everything, not just a view.

In 1601, the military architect Jaques Perret de Chamberry (~1540-~1619), author of Des Fortifications et artifices de architecture et perspective (Paris, 1601), states that any measurement of the drawing can be taken with a simple compass. The following are some images of his book.

In this use of parallel projection, cabinet perspective should be differentiated from the cavalier one, which is more used by painters as a pseudo-perspective, a kind of drawing used long before by the Romans.

This is the copy of a painting in one house from Pompeii done by the German architect Georg Friedrich Ziebland (1800-1873), in 1828.

Some other examples are Giotto di Bondone’s paintings (1266-1337). The following are two images at the Scrovegni Chapel, in Padua (1305-1306).

The scientific codification of axonometric is done by the French mathematician and engineer Gérard Desargues (1591-1662), who did not actually publish his work, but who was known thanks to his disciple Abraham Bosse (1602-1676) divulgation, in his book Manière universale de M. Desargues pour practiquer la prospettive par petit-pied, comme le géométral, 1648. Also important are the studies by Amédée François Frézier, Traté de Stéréromie à l'usage de l'Architecture, in 1737, and finally the definitive treatise Géométrie descriptive by Gaspard Monge, in 1798.

’s treatise Traité théorique et practique de l'art de bâtir (1802 -1803). Rondelet was an architect and advised Gaspar Monge in the creation of the École Polytechnique, in which he was a professor, as well as in the École de Beaux-Arts, from 1799 to 1828.

And another engineer from the École des Ponts et Chaussées, Auguste Choisy (1841-1909), was the one who applied the system in the formal description of historic architecture.

Recommended bibliography:
Yve-Alain Bois, "Metamorphosis of Axonometry", Daidalos, 1, 1981, pp. 41-58
Massimo Scolari, "Elementi per una storia dell'axonometria", Casabella, 500, March 1984, pp. 42-49
- "La perspectiva gesuitica in China", Casabella, nº 507, November 1984, pp. 48-51
- "Elements for a History of Axonometry", Architectural Design, 55, 1985, pp. 73-78

© of the texts Francisco Martínez Mindeguía

© by Ruth Costa Alonso, Francisco Martínez Mindeguía, and Antonio Millán: English translation


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