**Universality**

The principles evoking beauty are universal – universal in time and universal in space. This means, they do not depend on the taste and fancies of an epoch or a culture. They are incontrovertible, immutable, indisputable. What the principles are based in is mathematics. This is the basic idea underlying François Blondel’s Cours d’architecture.

In his Cours, Blondel describes how to apply the mathematical principles for designing different architectural elements – columns, pedestals, architrave, frieze and cornice as parts of the entablature, pilasters, pediments, arches, niches, doors, windows as well as colonnades, intercolumniation, superimposed orders, arcades, porticoes, peristyles, and triumphal arches. He starts from elaborating the appropriate dimensions of the five orders.

According to Blondel’s idea, mathematics is the foundation of beauty in architecture as well as in music. In the fifth part of his Cours, he states that there are harmonic numbers – one, two, three, four. These numbers correspond to the relation of two tones, i.e. two sound wave frequencies: unison (1:1) , octave (2:1), or quint (3:2), for instance. The architects make common use of these numbers.

Blondel was educated in mathematics. In the Cours, he cites Pythagoras: *La nature est toujours la même en toutes choses.* The term universality refers to something generally valid, however, the validity is related to our universe. This signifies that the principles affirmed by Blondel do have boundaries which are determined by our context of perception. And even within this context, from today’s perspective, Blondel’s position might be debatable, thinking of Arnold Schöneberg’s twelve-tone technique as representation of free atonality or Indian classical music, dividing an octave not only into twelve half tones but even breaking it down to quarter tones. Analogous breakouts are conceivable for architectural design.

Why does Blondel advocate such idea? It might be important to think about Blondel’s relation to and ambitions towards power. The appointing of universal principles might have been a possibility of implicitly escaping the omnipotence of the king, to whom he dedicates his book, because it was given that he would do so. Blondel could have detached himself from the idea of the imperative reigning of a principal by stipulating formulas that are uncontradictable because he constitutes them as independent from power. With this, he might have intended to breach authority. Beauty is not defined by a person, but it is universal. By propagating this concept, despite his external dedication to the crown, he might have deviated from the zeitgeist of being entirely committed to the king.

*Keywords*: mathematics, principles, beauty