Fig. 3: Generation of the Pentagon by means of the Golden Section. The three diagrams show geometric systems based on extreme and mean ratio. The “Ad Triangulum” system belongs especially to the guild of medieval stonemasons and denotes the simplicity and beauty with which the geometer masons of the 12th century and later drew this divine proportion © Josep Gonzàlez With the fracture of the medieval guild corporations, the advent of the Renaissance and the consequent progressive dissolution of Lodges, Cayennes and Bauhütte, there followed the diaspora of masters and companions skilled in the art of geometry and construction. They spread out, making public their professional skills and knowledge, entering fully into the imposing constructive and artistic heritage of the “age of humanism” . Masters of tradition such as M. Roriczer published their knowledge of geometry and construction, disregarding their Landmarks, already well into the 15th century, and thereby breaking the Lodge secret. His “Geometria Deutsch” of 1488 contains the description of the proportional system used to calculate and draw Gothic pinnacles. This system, which uses the generation of the “Ad Quadratum”, that is, of the square and the proportional variants generated by it, corresponds to the experience of his building activity in Ulm, Ingolstadt, Regensburg and Eichstätt. Likewise, H. Schmuttermayer, Lorenz Lacher and others did the same, causing the German Bauhütte to progressively lose their hermetic character and their artisanal and productive control of public and religious construction. But this new humanism, an extension of the one that produced the extraordinary cathedrals, gathers up the classical heritage and, through the main city-states of the Italian peninsula, creates centers that propagate classical knowledge and philosophy. The Academies, such as Ficino’s, in which Piero della Francesca, Botticelli, Brunelleschi, Leon B. Alberti and Leonardo, among others, shared knowledge and work, emulate the one in which Plato left his motto: “Do not enter if you are not a Geometer.” And it is from that Christic fusion of Kabbalah and Hermeticism that the revolution of the world of ideas arises, leading that Neoplatonism, a mestizaje of new worlds that smooths the paths of the soul so as to release that new universal knowledge. In this medley Luca Pacioli wrote his “De Divina Proportione” and, helped by Leonardo da Vinci, included in his treatise the polyhedral figures, hollow and solid, that the latter drew for him, showing the very ample range of unique qualities that make the golden number a divine resource. He describes its nature following Euclid and, surely, Leonardo himself, who drew for him the well-known “Vitruvian Man” (Fig. 4), also called in hermetic circles “L’Huomo di Trezzo”, that is, “drawn”. In it are summed up the anthropomorphic proportions of the human being according to the classical description that the Roman architect Vitruvius bequeathed to us: “The navel is the natural central point of the human body. Indeed, if a man is placed face up, with his hands and feet outstretched, and the center of a compass is set on his navel and a circle is drawn, it will touch the tips of both hands and the toes. The circular figure drawn over the human body also makes it possible to obtain a square: if one measures from the soles of the feet to the crown of the head, the resulting measure will be the same as that between the tips of the fingers with the arms extended; its width measures exactly the same as its height, like the squares we draw with the set square. Therefore, if nature has formed the human body so that its members keep an exact proportion with respect to the whole body, the ancients also established this relation in the complete execution of their works, where each of their parts keeps an exact and precise proportion with respect to the total form of the work.” (Vitruvio Op. cit., Book Three, ChapterI.)