History of Mechanism and Machine Science

History of Mechanism and Machine Science Volume 34 Series editor Marco Ceccarelli LARM: Laboratory of Robotics and Mechatronics DICeM; University of Cassino and South Latium Via Di Biasio 43, 03043 Cassino (Fr), Italy ceccarelli@unicas.it

Aims and Scope of the Series This book series aims to establish a well defined forum for Monographs and Proceedings on the History of Mechanism and Machine Science (MMS). The series publishes works that give an overview of the historical developments, from the earliest times up to and including the recent past, of MMS in all its technical aspects. This technical approach is an essential characteristic of the series. By discussing technical details and formulations and even reformulating those in terms of modern formalisms the possibility is created not only to track the historical technical developments but also to use past experiences in technical teaching and research today. In order to do so, the emphasis must be on technical aspects rather than a purely historical focus, although the latter has its place too. Furthermore, the series will consider the republication of out-of-print older works with English translation and comments. The book series is intended to collect technical views on historical developments of the broad field of MMS in a unique frame that can be seen in its totality as an Encyclopaedia of the History of MMS but with the additional purpose of archiving and teaching the History of MMS. Therefore the book series is intended not only for researchers of the History of Engineering but also for professionals and students who are interested in obtaining a clear perspective of the past for their future technical works. The books will be written in general by engineers but not only for engineers. Prospective authors and editors can contact the series editor, Professor M. Ceccarelli, about future publications within the series at: LARM: Laboratory of Robotics and Mechatronics DICeM; University of Cassino and South Latium Via Di Biasio 43, 03043 Cassino (Fr) Italy email: ceccarelli@unicas.it More information about this series at http://www.springer.com/series/7481

Danilo Capecchi The Path to Post-Galilean Epistemology Reinterpreting the Birth of Modern Science 123

Danilo Capecchi Ingegneria Strutturale e Geotecnica Sapienza University of Rome Rome Italy ISSN 1875-3442 ISSN 1875-3426 (electronic) History of Mechanism and Machine Science ISBN 978-3-319-58309-9 ISBN 978-3-319-58310-5 (ebook) DOI 10.1007/978-3-319-58310-5 Library of Congress Control Number: 2017941055 Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface The birth of early modern mechanics was often said to mark the beginning of modern science and the scientific revolution of the seventeenth century. This process has been rooted equally in the ingenuity of a few scholars, Galileo in primis, in the rediscovery of ancient mathematics and mechanics, in the establishment of a new philosophy of nature and eventually in the new position assumed by empiric experience. This view has now been radically revised, but that has not yet altered how the general public, even a well-educated public, views the history of science. Criticisms of the traditional point of view date back to at least the nineteenth century. Duhem, for example, denied the existence of a scientific revolution. Moreover: 1. Most historians are no longer interested in whether the changes that transpired in the seventeenth century constitute a scientific revolution, but only to establish how these changes actually occurred. 2. The development of science is no longer identified with that of mechanics only and it is recognized that other disciplines such as medicine and chemistry, for instance, played a key role. Kuhn and others, for example, distinguish between mathematical physical sciences and experiment-based sciences, referred to as Baconian sciences. For this latter, the traditional image of science is certainly not applicable. 3. Even the experimental approach is not regarded as a novelty, miraculously introduced by Galileo Galilei. Here two traditions are identified. The philosophical/theoretical tradition in the Aristotelian mould, and expressed in Renaissance enhanced writings such as Meteorologica compared with others of a metaphysical nature Physica and De caelo, to name but two. And the tradition, of a mathematical/applicative nature, motivated by an experimental mindset that was given scope in the implementation and use of simple machines, having precedence in the activity of Hellenistic mathematicians. 4. The development of science is not primarily attributed to the work of isolated geniuses such as Tartaglia, Galileo, Huygens, Newton; but rather to a collective effort in which genes are just the tip of the iceberg. So next to the texts and v

vi Preface letters of the greats, even those of minor figures, indeed of all scholars, are considered. The development of educational institutions assumes relevance and with them the textbooks; tools already in use in general history become so essential, such as statistical analyses. Obviously the material, intellectual political aspects of society are considered, but this had already been made by historians of Marxist inspiration of the second half of the nineteenth century. 5. The establishment of a relativistic conception of science is also stressed, broadly interpreted as a knowledge of nature developed on a rational basis. This does furnish dignity to some form of knowledge, even though today it could appear unscientific, as the standards of modern science are not adhered to. Such is the case with magic, astrology and alchemy. A similar argument may be made regarding the approaches to a study of nature as developed outside Europe such as in China and India. This book does not pretend to provide an exhaustive explanation of the process that in the early modern era led to a profound transformation of the study of nature, which one is tempted to qualify as revolution. More simply, it aims to lend credence to historiographic hypotheses that assume: 1. Modern European science (Galileo s placet) originated from Hellenistic mathematics, not so much because of its rediscovery but, rather, because its applied components, namely mechanics, optics, harmonics and astronomy ( old sciences ), continued to be transmitted to us throughout the Middle Ages without any serious interruption. 2. New sciences, such as dynamics, acoustics, hydraulics, pneumatics and chemistry (modern meaning), had exactly the same methodology and logic organization of old sciences : they were applied mathematics. The difference was in the different phenomena of the natural world examined and in the richer deductive mathematical apparatus with the use of algebra, calculus and analytical geometry. 3. Old sciences played a role as a whole. New mechanics, for instance, derived not only from old mechanics but also from harmonics, optics and astronomy. 4. Most protagonists of the new sciences could be qualified as mathematicians. 5. The way of reasoning typical of mathematics, proceeding from clear definitions and strict reasonings, was adopted by some new philosophers, which gave raise to the experimental philosophy and/or mechanism. This made easy the appropriation by mathematicians of all fields of natural philosophy. Naturally in the background there were the social, political, economical, technological and ideological dynamics. They influenced and were influenced by the development of the new sciences. Little if any attempt however is made here to suggest hypotheses on this point. Greek mathematics was born at the same time as astronomy, harmonics, mechanics, optics and surveying. Only later began a process of abstraction that

Preface vii eliminated, but not completely, the sensitive basis; thus separating pure from impure mathematics (contaminated by the senses). Impure, or applied, mathematics, or mixed mathematics as referred to in this text, applying a terminology used in Renaissance, continued to exist and were generally studied by the same scholars who dealt with pure mathematics. This without a sharp distinction of roles and status between them. People practicing of mathematics (mathematicians broad sense), generally were not specialists, that is they were not mathematicians in the modern (strict) sense; many of them shared interest in natural philosophy, epistemology, technology, medicine, law. For instance, Copernicus was not only an astronomer and mathematician; a label that would have astonished his contemporaries and, most probably, Copernicus himself. He was also a canon in a cathedral chapter, studied medicine and law, occupied himself with theoretical and practical economics and he was also interested in mathematics and astronomy. Mathematicians (broad sense) were thus able to develop ideas about the nature of the world independent enough of those of professional philosophers and theologians. They went some way to build a community with shared values; they knew each other both diachronically and synchronically, criticizing or esteeming but in any case commenting on each others works. This community pursued its science not only for the love of knowledge and to know the fact and the reasoned fact as philosophers did, but also with the aim to make predictions, which only allowed the improvement of technology. In the Renaissance, the applied components of mathematics underwent an adjustment by interacting with some new and old conceptions of natural philosophers, or some new concepts elaborated by engineers and other practitioners, that became the background knowledge for many mathematicians, along with changes in the mathematics itself. An important role was, however, played by the recovery of Hellenist texts of applied mathematics (Archimedes, Euclid, Pappus) and the development of new mathematical techniques (new theory of proportions, algebra, calculus). At the beginning the interaction of mathematics with physics was restricted to traditional mixed mathematics and some other disciplines close to them, such as surveying, architecture and ballistic. For other disciplines, traditionally fully framed into the natural philosophy, mainly based on experience and experiment, such as magnetism, electricity, thermology, alchemy/chemistry, biology and physiology, the role of mathematics was different and the interaction was slower. What was taken from mathematics was the way of reasoning; that is the use of clear definitions, assumptions derived from experiments and considered as true; the use of a deductive approach for proving propositions, even without the explicit use of geometry or arithmetics. For some sciences the evolution toward a form of mixed mathematics, started partially in the seventeenth century, lasted at least until the nineteenth century; this was the case of disciplines founded on quantitative descriptions such as magnetism, electricity and chemistry. Other sciences, where the use of quantity was negligible, such as structural botany and zoology, philology and morphology, that could be classified as qualitative sciences, did not reach, and

viii Preface up today have not yet reached, the status of mixed mathematics. For them the use of symbolic logic however allowed and yet allows, at least in principle, an approach that has a similar deductive structure of that of mixed mathematics. Mixed mathematics had a uniform organization, the same that is found in modern science; there was an empirical basis that worked as a starting point for a mathematical theory that provided explanations and predictions about the real world. This approach was transmitted unchanged, with periods of more or less darkness, until the sixteenth century. Since then mixed mathematics widened their scope and started to encroach on the whole philosophy of nature which ceased to be the object of study of professional philosophers. The so-called scientific revolution consisted thus in a lengthy process of adjustment of mixed mathematics pursued by mathematicians, that, ideally, started just prior to Galileo and lasted for the entire seventeenth century, concluding with Newton. This book furnishes hints on how this process took place and on its continuity with antiquity. Only a short historical period is explored with some completeness, a few generations before and after Galileo, as well as his friends (more or less direct disciples) and enemies (mostly from the Jesuit order). The study is conducted by examining the contribution of various specialists of the period, not only major figures but minor too often regardless of their actual value investigating their formation, and thus highlighting the general concepts that were relevant to the science of the day. The focus is primarily on the evolution of the traditional mixed mathematics, in particular, mechanics intended as a set of procedures addressing motion and equilibrium of solid and fluid bodies, that was not included in a single discipline prior to the nineteenth century. The assumed historiographic hypotheses are validated against the evidences resulting from the exploration of the following aspects: 1. The epistemology of the traditional mixed mathematics. On the one hand, optics and mechanics adopted principles representing some statements of empirical facts, whose truths were not questioned; for example, that light propagates in a straight line, that a weight tends to drop downward, and so on. On the other hand, astronomy (and harmonics), which had as basic principles one or more plausible but not certain hypotheses, which had to justify the phenomena. In these justifications mathematicians used measures (a quantitative approach) that were also very accurate. 2. The emergence of new mixed mathematics. This included ballistics (Tartaglia and Galilei), the strength of materials (Galilei), hydraulics (Castelli), pneumatics (Torricelli). The position of mathematics in the Renaissance, with attention both to that studied in universities and to that taught in the abacus schools. 3. The diffusion of some form of skepticism about metaphysics and natural philosophy (due either to revival of some form of ancient skepticism or simply by pragmatic reasons, encouraged by social needs, for instance to avoid censure from the church). The possibility that this encouraged a positivistic view and the birth of the experimental philosophy where only facts were relevant, whose regularity could be studied with mathematics.

Preface ix 4. The evolution of the concept of experience and its evaluation; in particular the development of the contrived experiment on the study of natural phenomena using measuring instruments such as clocks and rulers. This kind of experiment was often performed in laboratories, with particular attention to the specific conditions under which this occurred, foreshadowing the possibility of repetition. 5. The innovations introduced by and in the philosophy of nature. The focus is on the most important acquisitions, including the possibility of a motion without a cause, the possibility of a vacuum, the denial of the quality of lightness, the recognition that there are no qualitative differences between earth and heaven. A most important change in the philosophy of nature was the birth of mechanism which became soon dominant. It explained the phenomena of the material world by means of (material) efficient causes only, avoiding most of the metaphysical considerations of philosophers and thus becoming more accessible to mathematicians. 6. The innovations introduced in mathematics. A new role of the proportions, the development of algebra and calculus with the replacement of the potential infinity of Greek mathematics with the actual infinity. The study was conducted on original sources, mostly printed texts, which are, however, numerous and in many cases poorly studied. From Galileo on, schools or scientific associations are referred to rather than individual scholars. Among those mentioned are the Galilean school, the Jesuit school, the Accademia del cimento and the Royal society of London. Chapter 1 presents the mixed mathematics of antiquity, with a greater focus on how these were considered by mathematicians rather than by philosophers. Chapter 2 refers to the situation in the Renaissance Italy considering new approaches to the world of the emerging middle classes, including merchants, artists, engineers, and physicians. Chapter 3 presents the change in the philosophy of nature with the emergence of the mechanist philosophy, the new mixed mathematics and the establishment of an experimental approach. Chapter 4 refers to Galileo and his school, particularly on methodological and epistemological aspects. Chapter 5 lends its title to the book and considers the adoption of Galileo s approach by his immediate successors, little studied to date. Chapter 6 presents some concluding remarks. I want to acknowledge Paolo Bussotti for his comments on some parts of my book that allowed me to avoid some inconsistencies and to fill some gaps. Editorial Considerations Most figures related to quotations are redrawn to allow a better comprehension. They are however as much possible close to the original ones. Symbols of formulas are those of the authors, except cases easily identifiable. Translations of texts from

x Preface various languages are as much as possible close to the original. For the Latin, Italian of the XV and XVI centuries a critical transcription has been preferred. In the critical Latin transcription some shortenings are resolved, v is modified in u and vice versa where necessary, ij in ii, following the modern rule; moreover the use of accents is avoided. In the Italian critical transcription some shortenings are resolved, v is modified in u and vice versa when necessary, and a unitary way of writing words is adopted. Books and papers are always reproduced in the original spelling. For the name of the different characters the spelling of their native language is generally preferred, excepting for the ancient Greeks, for which the English spelling is assumed, and some medieval people, for which the Latin spelling is assumed, following the common use. In cases where spelling is not fixed, a modern form is assumed. For instance, Gian Battista, Giovan Battista, all become Giovanni Battista. Through the text I searched to avoid modern terms and expressions as much as possible while referring to ancient theories. In some cases, however, I transgressed this resolution for the sake of simplicity. This concerns the use for instance of terms like mass and work even in the period they were not known. From the context is however clear that they are used with not technical meaning. Rome, Italy March 2017 Danilo Capecchi

Contents 1 Ancient Mixed Mathematics... 1 1.1 Epistemology of Mixed Mathematics.... 1 1.1.1 Aristotelian Subalternate Sciences... 3 1.2 Geometrical Optics.... 5 1.2.1 Euclid s Optics... 6 1.2.2 Further Developments.... 10 1.3 Mechanics, Machines, and Equilibrium... 13 1.3.1 Aristotelian Mechanics... 13 1.3.2 Hellenistic Science of Equilibrium... 15 1.3.3 Inversion in the Role of Mathematics.... 19 1.4 The Science of Harmonics... 21 1.4.1 Fundaments of Greek Harmonics... 22 1.4.2 Rationalist and Empiricist Theoreticians... 25 1.4.3 Ptolemy s Harmonica.... 34 1.5 Observational Astronomy.... 42 1.5.1 Astronomical Hypotheses... 43 1.5.2 Ptolemy s Astronomical System... 46 1.5.3 Astronomy According to Philosophers... 56 1.6 Quotations... 63 References... 64 2 Skills and Mathematics in Renaissance Italy... 69 2.1 Teaching of Mathematics... 69 2.2 Treatises of Abacus... 72 2.2.1 Trattato di Tutta L arte Dell Abacho of Paolo dell Abbaco... 77 2.2.2 Luca Pacioli s Summa... 83 2.3 Artists and Engineers... 95 2.3.1 Leon Battista Alberti... 96 2.3.2 Leonardo da Vinci... 105 xi

xii Contents 2.4 Alchemy, Magic, and Medicine... 115 2.4.1 Alchemy.... 115 2.4.2 Natural Magic.... 118 2.4.3 Medicine... 125 2.5 Quotations... 138 References... 142 3 New Forms of Natural Philosophy and Mixed Mathematics... 147 3.1 Schools of Philosophy in the Renaissance... 147 3.1.1 Humanism and Platonism... 148 3.1.2 Evolution of Aristotelianisms... 149 3.2 Updating Classical Mixed Mathematics... 155 3.2.1 A Heated Debate of Philosophers on the Epistemology of Mixed Mathematics... 155 3.2.2 A Renewed Theory of Proportions... 158 3.2.3 Mechanical Disciplines.... 166 3.2.4 Harmonics and Acoustics... 183 3.2.5 Optics: Theories of Vision and Light... 207 3.3 Mechanical Philosophy... 230 3.3.1 Early Mechanical Philosophers.... 233 3.3.2 Mechanism and Mathematics... 238 3.4 The Emergence of Physico-Mathematica... 240 3.5 Quotations... 244 References... 250 4 Galilean Epistemology... 261 4.1 Basic Galilean Ontology and Epistemology... 261 4.1.1 Definition and Essence... 265 4.2 Method of Scientific Research... 272 4.2.1 Possible Hellenistic Influence... 272 4.2.2 Possible Influences of Jesuit Philosophers... 274 4.2.3 Possible Influence of Mathematicians... 276 4.3 Experiment and Experience... 278 4.3.1 Ascertainment of Empirical Laws.... 284 4.3.2 Overcoming Incompleteness of Mathematics... 286 4.3.3 Thought Experiments... 289 4.4 The Role of Causes... 292 4.4.1 Explanations Through Causes.... 295 4.4.2 Causes and Experiments... 304 4.5 The Role of Disciples... 309 4.5.1 Bonaventura Cavalieri... 309 4.5.2 Evangelista Torricelli... 315 4.5.3 Benedetto Castelli.... 325 4.5.4 Vincenzo Viviani... 333

Contents xiii 4.6 Quotations... 339 References... 346 5 Post-Galilean Epistemology. Experimental Physico-Mathematica... 353 5.1 Galileo s Entourage... 353 5.1.1 Alfonso Borelli. The Last Heir... 353 5.1.2 Experiments, Mathematics, and Principles of Natural Philosophy in Giovanni Battista Baliani... 373 5.1.3 Marin Mersenne s Universal Harmony... 385 5.2 Jesuitical Tradition... 400 5.2.1 Jesuit Epistemology... 402 5.2.2 Production of Experience. Giovanni Battista Riccioli... 415 5.2.3 Production of Experience. Fancesco Maria Grimaldi... 428 5.3 Experimental Philosophy... 438 5.3.1 The Accademia del Cimento... 440 5.3.2 The Royal Society... 449 5.3.3 Robert Boyle... 466 5.4 Quotations... 484 References... 489 6 Concluding Remarks... 495 6.1 Toward Physica Mathematica... 495 6.2 René Descartes System of Natural Philosophy.... 500 6.2.1 The Role of Experience... 501 6.2.2 Purely Deductive Mixed Mathematics... 510 6.3 Quotations... 525 References... 526 Index... 529