Gothic architecture appeared in the Île-de-France region during the 12th century. The style was originally called Francigenum Opus, meaning "French art". It quickly spread throughout Europe, until the beginning of the Renaissance.

Gothic art is characterized by a system of vaults known as ribbed vaults. As can be seen in the drawing, it is based on two diagonal ribs, the ogives, which form the framework and support the thin panel-filling partitions, the voûtains.

The advantage of this framework is that it allows the vault elements to remain independent and free to play. It is thus capable of resisting structural movements in the building.

In the Gothic system, forces follow the line of the ribs and weigh directly on the vertical of the pillars (red arrows), with the remainder of the tangential forces being transmitted, via the buttresses, to the massive outer buttresses.

The main purpose of these Gothic-style buttresses is to push out the heavy buttresses that had previously kept the building in darkness. The side walls were also relieved of thrust by the use of segmental arches, allowing stained glass to replace stone. The stone book is transformed into a glass book.

The combined use of pointed arches, ribs and buttresses means that proportions and lighting can be freely modulated. From a structural point of view, each part, each element is self-sufficient and can exist autonomously.

However, the fact remains that the master plan proposes, and the strength of the materials disposes. The builders were in possession of a principle, a program, which was developed in successive stages. In those days, it was impossible to model or predict the statics of a monument; you had to experiment to find out. And yet, despite the evolution of techniques, the vaults only evolved in terms of details. Their principles are fixed from the outset, and only the shape of the arches changes with the times.
In fact, the only major structural transformation in French Gothic is the replacement of the square plan by the barlong plan, which means longer on one side than the other. We've gone from a square to a rectangle.

A brief explanation is in order: originally, Gothic architects tried their hand at Romanesque buildings. They placed ribbed vaults where groin vaults and cupolas had drawn square structures. To achieve this, they developed a system known as sexpartite vaulting. Formed by the crossing of three ogives, this vault is divided into six parts, or vaûtains. Figure 2 illustrates this principle. The diagonal ogives rest on four large piers called "strong piers" (A), while the secondary doubleau, the transverse ogive used to take up the remaining thrust, rests on two smaller piers (B).
Note that each bay in the central nave corresponds to two bays in the aisles. This arrangement has the disadvantage of distributing thrust unevenly between strong pillars (A) and weak pillars (B). In the field, this can be seen in the alternating size of the supports.

Fig. 2 - Sexpartite vault

Fig. 3 - Barrel vaulting

Fig. 2b - Senlis vaults

Fig. 3b - Chartres vaults

It didn't take long for architects to realize the absolute flexibility of their system and its ability to cover complex plans. From then on, they emancipated themselves from the square plan, and exchanged the sexpartite vault for a quadripartite structure, known as the barlong vault (fig. 3 & 3b).
The result of Gothic thinking, this process combines logic and aesthetics, reducing the opening of diagonal arches and thus the intrinsic height of large vaults. Naturally, the alternation of strong and weak pillars disappears, and the number of bays between the naves is balanced.

In what art historians refer to as "transitional Gothic", it is important to avoid confusing the development of an innovative concept with the improvement of an old principle, for while processes may sometimes change in form, they remain invariable in principle. In this sense, the revolutionary aspect of the Gothic style is indisputable.

But what is the origin of the Gothic idea? From a purely architectural point of view, asking this question comes down to determining the origin of the elements that are supposed to define the style: the pointed arch, the ribbed vault and the flying buttress.

The pointed arch is found in certain Cluniac buildings, particularly in Burgundy, not to mention Norman architecture. Yet this design is as much a part of human history as the discovery of the wall or fire. Outside the Middle East, India and other Asian countries can boast of having used it.
However, no people in history will ever suspect its promise. It was left to the Gothic genius to fuse this arch with the rib, giving rise to the ribbed vault and expressing it in a new architectural, structural and visual concept.

The origin of the flying buttress remains undisputed. This system is nothing more than an evolution of the half-beam used in certain Romanesque buildings to counterbalance the thrust of the vaults.

In conclusion, the combined use of these processes is the expression of rational and logical thinking, of a spirit of analysis of which Descartes' homeland can be justly proud, for the cradle of Gothic architecture is undoubtedly the Île-de-France region.

Of course, all this didn't happen overnight, and techniques evolve from year to year. In this respect, it is remarkable how quickly errors are corrected and solutions disseminated to all building sites. This sharing of information enabled the Gothic style to reach full maturity in just a few decades.