In 1553 Italian architect, engineer and mathematician Camillo Agrippa published his "Trattato Di Scientia d' Arme, con un Dialogo di Filosofia" ("Treatise on the Science of Arms, with a Philosophical Dialogue"). In it, he applies geometrical principles to analysing the fight between two fencers. On that basis, he poses that thrusts, following a straight line, are faster, and therefore more effective, than cuts. In addition, his is the first published treatise describing how the reach of an attack can be increased by increasing the distance between the feet after stretching the arm, i.e. describing a precursor to the stoccada, or lunge. He also proposes the use of only four guards: Prima, Secunda, Tertia and Quarta, that are quite similar to the four hand positions used in later rapier fencing. Because of this, Camillo Agrippa is considered as an important founder of the art of rapier fencing.
Two important rapier fencing schools derived from Agrippa's work. In Italy, a dynamic and athletic method of fencing developed that, though it was still based on geometrical and mathematical principles, did not strongly focus on those aspects. The thrust became the most important attack as it was faster than the cut. Movement between the fencers mainly took place along a straight line. Furthermore, in Italian rapier fencing four hand positions were used, that were based on the positions described by Agrippa. Important Italian Masters were for instance Salvator Fabris (1544-1618) whose "Lo Schermo, overo Scienza d'Arme" was first published in 1606, Nicoletto Giganti, author of the "Scola, overo, Teatro", which was also published in 1606, Ridolfo Capo Ferro, author of "Gran Simularcro dell'Arte Eddelluso della Scherma" (published in 1610), and Francesco Ferdinando Alfieri. The Italian rapier fencing art quickly spread across all of Western Europe, and also became an important self-defense art in for instance Germany, where Fabris and his students had a strong influence.
In Spain, a method of fencing with the name "La Verdadera Destreza" evolved. Within the Destreza, geometry and mathematics were of much greater importance in the analysis and treatment of the duel. The fencers did not move along a straight line, but approached each other along a circle in order to attack from an angle. The only hand position used in the Destreza is comparable to the Italian Tertia, but the arm was always held extended parallel to the ground. Important Masters of the Destreza included Jerónimo Sánchez de Carranza, author of the "De la Filosofía de las Armas y de su Destreza y la Aggression y Defensa Cristiana" published in 1582, and Luis Pacheco de Narváez (1570-1640). The method of rapier fencing described by Girard Thibault of Antwerp (1574-1629), who trained with Narváez in Spain, was strongly influenced by the Destreza.
Rapier fencing remained an important self-defense art in Western Europe until around the end of the 17th century. During this period both the hilt and the blade of the rapier continuously evolved. Likewise, the manner of fencing also evolved, and the use of dui-tempi counters (parry-riposte) increased somewhat relative to the stresso-tempo counter. The evolution of the hilt was usually aimed at increasing the protection of the sword hand, by adding extra rings, metal plates, or even a metal cup. However, the length of the blade and the size of the rapier hilt where considered impractical in social situations. Especially in France, this lead to the development of a sword with a shorter blade and a considerably smaller hilt, something that, to a certain degree, Thibault was already a proponent of. This smallsword (or court sword, epée de cour in French) was not only shorter, but also lighter than a rapier, and therefore it was used differently. As the weapon became faster relative to the fencer the parry-riposte (dui-tempi counter), rather than the stresso-tempo or contra-tempo counter, became the main reaction to an attack. In addition, the fencing style that developed for the smallsword was more formal and elegant, and the official duel became a more important aspect of the art.
Also in France, around the same time, the foil was developed as a practice and competition variant of the smallsword. Modern foil fencing is derived directly from the competitions held with that weapon. Modern épée fencing is derived from the later duelling style that evolved from fencing with the smallsword.
The main difference between 17th century rapier fencing and modern (Olympic) fencing lies in the intention of the art. In the 17th century, rapier fencing was the main self-defense art for the upper layers of society, intended both for self-defense against a sudden attack on the street, as for the (friendly or unfriendly) duel. The main intention is to efficiently defend yourself against the attacks of an adversary. In addition to that, you try to take out this adversary, using whatever means necessary. Rapier fencing thus is an effective martial art. Modern fencing on the other hand, is a (self-defense) sport with a strong competition element, in which scoring a point, by touching the opponent on the designated target area before he hits you, is the main goal. As a sport, modern fencing is bound to strict rules considering, for instance, the target area, the use of the left hand, and the allowed techniques. Rapier fencing, as practised by the School for Historical Fencing Arts, does not have a strong competition element, and has (almost) no rules. Techniques such as left hand parries, disarms and throws are allowed. In addition, because of the larger mass of the rapier compared to modern fencing weapons, the focus in defense lies more on direct counter attacks with one action providing both defense and offense, in stead of the parry-riposte in two actions known in for instance foil fencing.
Of course, rapier fencing is not a directly applicable self-defense art in modern society, as carrying a rapier is no longer permitted or socially accepted. Studying and training the art of rapier fencing, however, is not a useless exercise, but an excellent way to keep both body and mind active and nimble. In addition, training a martial art is a very good way to become more conscious of your own body.
References and interesting reading material
Fencing: A Renaissance Treatise by Camilla Agrippa, translated by Ken Mondschein, Italica Press, New York, 2009
The Art of Dueling - Salvator Fabris' rapier fencing treatise of 1606, translated by Tommaso Leoni, The Chivalry Bookshelf, Highland Village, 2005
Venetian Rapier - The School, or Salle - Nicoletto Giganti's 1606 Rapier Fencing Curriculum - translated by Tom Leoni, Freelance Academy Press, Wheaton, 2010
Rapier the Art and Use of Fencing - Great Simulation of the Art and Use of Fencing by Ridolfo Capo Ferro, translated by Nick S. Thomas, Sword Works, U.K., 2007
Academy of the Sword, Girard Thibault d'Anvers, translated by John Michael Greer, The Chivalry Bookshelf, Highland Village, 2006
And, of course, wikipedia.