Marcus Vitruvius Pollio

Born: about 85 BC in possibly Fundi, Campania, Italy
Died: about 20 BC in Italy

Marcus Vitruvius Pollio is known almost exclusively through his famous ten volume work On Architecture. Even his name is in doubt with only Vitruvius being certain. Other than what can be deduced from that work, little is known about his life although he is mentioned in works by Pliny the Elder and Frontinus. Two different towns have been proposed by historians as his birthplace. We have suggested Fundi (now Fondi), which is about midway between Rome and Naples. However the other suggestion is Verona which is in the north of Italy, roughly west of Venice.

It is clear that he must have been born into a prominent Roman family. He trained in architecture and served with the engineering corps in Caesar's army. He travelled widely with the army and we know he served in Gaul, for example he was in the fortress of Larignum in 56 BC and in Marseilles in 48 BC. He was also in Zama in North Africa in 46 BC, the site of the Battle of Zana in 202 BC in which the Romans defeated Hannibal to end the Second Punic War. The Romans were building a city there in Vitruvius's time. After Caesar was assassinated in 44 BC, Vitruvius joined the army of Octavian (later the Emperor Augustus), as a military engineer. By 33 BC we know that he was involved in the construction of aqueducts.

His most famous (and only known) work is the ten volumes of On Architecture which we know was written near the end of Vitruvius's life. The first comment to make about his masterpiece is that it is a little difficult to tell how close to the original is the book which has come down to us today. It is clear that the work has been regarded as an architect's manual from the time it was written up to the middle ages, so has been improved over the years as one does with a manual. The second comment must be that, for Vitruvius, architecture had a much wider scope than we would consider today. For example water clocks, sundials and pumps are all described by Vitruvius, topics which would hardly be considered to be part of the study of architecture today. Next we note Vitruvius's interest in history - this means that we are treated to information about earlier works and scientists which would otherwise have been lost.

The work is dedicated to Augustus whom he thanks in a dedication at the beginning of the book:-

... so with Marcus Aurelius, Publius Minidius, and Gnaeus Cornelius, I was ready to supply and repair ballistae, scorpiones, and other artillery, and I have received rewards for good service with them. After your first bestowal of these upon me, you continued to renew them on the recommendation of your sister. Owing to this favour I need have no fear of want to the end of my life, and being thus laid under obligation I began to write this work for you, because I saw that you have built and are now building extensively, and that in future also you will take care that our public and private buildings shall be worthy to go down to posterity by the side of your splendid achievements. I have drawn up definite rules to enable you, by observing them, to have personal knowledge of the quality both of existing buildings and those which are yet to be constructed.
Vitruvius believes that the architect needs to have studied many disciplines:-
Let him be educated, skilful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens.
Mathematics plays an important role for Vitruvius:-
Geometry is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics, again, the light in buildings can be drawn from fixed quarters of the sky. It is true that it is by arithmetic that the cost of buildings are calculated and measurements are computed, but difficult questions involving symmetry are solved by means of geometrical theories and methods.
Let us briefly describe the ten volumes. The first contains the dedication and the education of an architect from which we have quoted. After giving the fundamentals of architecture, Vitruvius looks at the siting of a city and city walls. He discusses the direction of the streets particularly taking into account the direction of the winds. Volume II looks at the origins of architecture, but is mostly concerned with building materials such as bricks, sand, lime, pozzolan, stone and timber.

Volume III contains a discussion of symmetry in both temples and the human body, then discusses the proportion of columns. It gives the rules for constructing Ionic temples. Volume VI continues to discuss temples, this time Doric and Tuscan temples. In particular temple doors and altars are looked at in detail. Volume V discusses the construction of public buildings such as the forum, the basilica, the theatre and its porticos, the palaestra, the baths and harbours. Harmonics and acoustics of the theatre make interesting reading. Volume VI is on private houses of both Roman and Greek style. He pays attention to climate, symmetry and proportions.

In Volume VII is on interior decoration such as stucco work, fresco painting, and the materials needed to produce natural and artificial colours. Volume VIII concerns water - how to find it, rainwater, aqueducts, wells and cisterns. Astronomy is the first topic of Volume IX, followed by mathematical tools such as a method of doubling a square, a method of constructing a right angled triangle, the mathematical principles of a sundial and of water-clocks. The final volume deals with machines used in engineering, both for military purposes and for buildings. Vitruvius describes machines for lifting and transporting weights using a pulley, he gives the principle of the lever, and describes machines that convert circular to linear motion and vice-versa. Also described are the water-screw, the pump of Ctesibius, the hydraulic organ, the hodometer, and machines with military applications such as catapults, scorpions, balistae, siege engines, tortoises and how to defend against them.

Article by: J J O'Connor and E F Robertson

July 2008
MacTutor History of Mathematics