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## Über dieses Buch

This book is one of the finest I have ever read. To write a foreword for it is an honor, difficult to accept. Everyone knows that architects and master masons, long before there were mathematical theories, erected structures of astonishing originality, strength, and beauty. Many of these still stand. Were it not for our now acid atmosphere, we could expect them to stand for centuries more. We admire early architects' visible success in the distribution and balance of thrusts, and we presume that master masons had rules, perhaps held secret, that enabled them to turn architects' bold designs into reality. Everyone knows that rational theories of strength and elasticity, created centuries later, were influenced by the wondrous buildings that men of the sixteenth, seventeenth, and eighteenth centuries saw daily. Theorists know that when, at last, theories began to appear, architects distrusted them, partly because they often disregarded details of importance in actual construction, partly because nobody but a mathematician could understand the aim and func­ tion of a mathematical theory designed to represent an aspect of nature. This book is the first to show how statics, strength of materials, and elasticity grew alongside existing architecture with its millenial traditions, its host of successes, its ever-renewing styles, and its numerous problems of maintenance and repair. In connection with studies toward repair of the dome of St. Peter's by Poleni in 1743, on p.

## Inhaltsverzeichnis

### 1. Methodological Preliminaries

Abstract
The history of many branches of science follows the same generalized pattern: knowledge grows by the expansion of experimental techniques and the refinement of mathematical (or non-mathematical) formalization. Someone asks a question, which leads to the development of the techniques needed to approach the question. We harvest the data and come up with a rule, a relation, a law, a generalization. Then we get on with the next question. This pattern allows historians to work neatly from the earliest confused and incomplete discoveries to the later, better defined ones, finally reaching the present day when the old premisses have found their conclusions and the new questions have been stated.
Edoardo Benvenuto

### 2. The Law of the Lever

Abstract
Archimedes (287–212 BC), in his works on statics, first attempted to give the science of equilibrium an axiomatic, deductive structure similar to Euclid’s for geometry. In our discussion of his work, we shall confine our attention to a few passages in his treatise On the Equilibrium of Planes (Περί’Επιπέδων ’Ισορροπι$$\tilde \omega$$ν). While Aristotle relates mechanics to a physical theory, aiming for a universal synthesis, Archimedes thinks of statics as a rational and autonomous science, founded on almost self-evident postulates and built upon rigorous mathematical demonstrations. Both his intention and the source of his empirical data are also different. He is interested not in motion, but in equilibrium; not in the causes of velocity, but in the effects of a weight suspended at the end of a balance arm, that is, at a distance from a fixed point.
Edoardo Benvenuto

### 3. The Principle of Virtual Velocities

Abstract
Of the two propositions—the equation of virtual velocities and the rule of the composition of forces—the former is clearly richer in tradition and well-known references. It seems to promise more to the advancement of knowledge and to the solution of the eternal “why?”
Edoardo Benvenuto

### 4. The Parallelogram of Forces

Abstract
In his splendid (if disputable) introduction to Principes fondamentaux de l’équilibre et du mouvement, Carnot states that “there are two ways to envisage mechanics in its principles. The first views it as a theory of forces, that is, of causes that provoke movements. The second considers it as a theory of movements in themselves.”1 We know that Carnot unquestionably preferred the second, because the first “has the disadvantage of being based on a metaphysical and obscure notion, that is, force” —a cause which cannot be measured except by its effects. If the first way can be differentiated from the second, the distinction must be an essential one, for the first way is alien to the language of mathematics. “Frankly,” Carnot adds,
all the demonstrations in which the word force is employed bring about an absolutely inevitable character of obscurity: that is why, in this sense, in my opinion, there cannot be any exact demonstration of the parallelogram of forces; the existence alone of the word force in the enunciation of the proposition makes this demonstration impossible because of the nature of things itself.2
Edoardo Benvenuto

### 5. Galileo and His “Problem”

Abstract
In 1684 Leibniz published a fundamental essay on the resistance of solids in the Acta eruditorum of Leipzig. The work begins, “Mechanical science seems to have two parts: the first one concerns the power of acting or moving, the other the power of reacting or resisting, that is, the strength of bodies.”1 According to Leibniz, therefore, the resistance of bodies is not merely one chapter of the many which make up mechanics; it is half of the entire discipline. Usually, such dichotomies are hardly probatory: they belong to a metaphysical way of thinking, according to which reality is two-faced, since every concept is linked with its opposite.
Edoardo Benvenuto

### 6. First Studies on the Causes of Resistance

Abstract
Who was first to develop the themes of the First and Second Days of the Discorsi? According to Fr. Guido Grandi, a monk of Camaldoli, it was Vincenzo Viviani, Galileo’s favorite pupil. As we shall see, the matter is not quite so simple, and Grandi cannot be considered impartial. In fact, Viviani had published nothing before the discussion on the resistance of solids exploded, with considerable eclat, in Italy and France. All the same, Grandi’s reasons for this claim are significant, and they may provide a good introduction to the debate that arose as early as the 1640s about the physical (or even metaphysical) causes of resistance.
Edoardo Benvenuto

### 7. The Initial Growth of Galileo’s Problem

Abstract
In the preceding pages, we have tried to describe the development of the First Day of the Discorsi as a journey—albeit a digressive one—from a definite beginning to a less definite end. But the ideas presented in the Second Day had a less clear-cut fate. Their history is characterized by fragmentation; instead of a highway, we have dozens of footpaths, weaving all over the terrain, sometimes parallel, sometimes intersecting, never straightforward.
Edoardo Benvenuto

### 8. Early Theories of the Strength of Materials

Abstract
The contributions of Fabri and Pardies have led us towards new points of view. Fabri’s “intermediate force” opens up questions on the deformation of a beam, and points towards an explanation of resistance itself. Pardies’s study of the equilibrium of ropes, and his peculiar model for a beam, a “string carrying beads,” change the context in which Galileo’s problem must be placed. For the first time, the concept of lengthening and shortening longitudinal fibers (the cords in the model) is connected to resistance.
Edoardo Benvenuto

### Backmatter

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