Preface; Editorial Considerations; Contents; 1 Ancient Mixed Mathematics; 1.1 Epistemology of Mixed Mathematics; 1.1.1 Aristotelian Subalternate Sciences; 1.2 Geometrical Optics; 1.2.1 Euclid's Optics; 1.2.2 Further Developments; 1.3 Mechanics, Machines, and Equilibrium; 1.3.1 Aristotelian Mechanics; 1.3.2 Hellenistic Science of Equilibrium; 1.3.3 Inversion in the Role of Mathematics; 1.4 The Science of Harmonics; 1.4.1 Fundaments of Greek Harmonics; 1.4.2 Rationalist and Empiricist Theoreticians; 1.4.3 Ptolemy's Harmonica; 1.5 Observational Astronomy; 1.5.1 Astronomical Hypotheses 1.5.2 Ptolemy's Astronomical System1.5.3 Astronomy According to Philosophers; 1.6 Quotations; References; 2 Skills and Mathematics in Renaissance Italy; 2.1 Teaching of Mathematics; 2.2 Treatises of Abacus; 2.2.1 Trattato di Tutta L'arte Dell'Abacho of Paolo dell'Abbaco; 2.2.2 Luca Pacioli's Summa; 2.3 Artists and Engineers; 2.3.1 Leon Battista Alberti; 2.3.2 Leonardo da Vinci; 2.4 Alchemy, Magic, and Medicine; 2.4.1 Alchemy; 2.4.2 Natural Magic; 2.4.3 Medicine; 2.5 Quotations; References; 3 New Forms of Natural Philosophy and Mixed Mathematics; 3.1 Schools of Philosophy in the Renaissance 3.1.1 Humanism and Platonism3.1.2 Evolution of Aristotelianisms ; 3.2 Updating Classical Mixed Mathematics; 3.2.1 A Heated Debate of Philosophers on the Epistemology of Mixed Mathematics; 3.2.2 A Renewed Theory of Proportions; 3.2.3 Mechanical Disciplines; 3.2.4 Harmonics and Acoustics; 3.2.5 Optics: Theories of Vision and Light; 3.3 Mechanical Philosophy; 3.3.1 Early Mechanical Philosophers; 3.3.2 Mechanism and Mathematics; 3.4 The Emergence of Physico-Mathematica; 3.5 Quotations; References; 4 Galilean Epistemology; 4.1 Basic Galilean Ontology and Epistemology; 4.1.1 Definition and Essence 4.2 Method of Scientific Research4.2.1 Possible Hellenistic Influence; 4.2.2 Possible Influences of Jesuit Philosophers; 4.2.3 Possible Influence of Mathematicians; 4.3 Experiment and Experience; 4.3.1 Ascertainment of Empirical Laws; 4.3.2 Overcoming Incompleteness of Mathematics; 4.3.3 Thought Experiments; 4.4 The Role of Causes; 4.4.1 Explanations Through Causes; 4.4.2 Causes and Experiments; 4.5 The Role of Disciples; 4.5.1 Bonaventura Cavalieri; 4.5.2 Evangelista Torricelli; 4.5.3 Benedetto Castelli; 4.5.4 Vincenzo Viviani; 4.6 Quotations; References 5 Post-Galilean Epistemology. Experimental Physico-Mathematica5.1 Galileo's Entourage; 5.1.1 Alfonso Borelli. The Last Heir; 5.1.2 Experiments, Mathematics, and Principles of Natural Philosophy in Giovanni Battista Baliani; 5.1.3 Marin Mersenne's Universal Harmony; 5.2 Jesuitical Tradition; 5.2.1 Jesuit Epistemology; 5.2.2 Production of Experience. Giovanni Battista Riccioli; 5.2.3 Production of Experience. Fancesco Maria Grimaldi; 5.3 Experimental Philosophy; 5.3.1 The Accademia del Cimento; 5.3.2 The Royal Society; 5.3.3 Robert Boyle; 5.4 Quotations; References; 6 Concluding Remarks
Summary:
This book casts new light on the process that in the sixteenth and seventeenth centuries led to a profound transformation in the study of nature with the emergence of mechanistic philosophy, the new mixed mathematics, and the establishment of the experimental approach. It is argued that modern European science originated from Hellenistic mathematics not so much because of rediscovery of the latter but rather because its "applied" components, namely mechanics, optics, harmonics, and astronomy, and their methodologies continued to be transmitted throughout the Middle Ages without serious interruption. Furthermore, it is proposed that these "applied" components played a role in their entirety; thus, for example, "new" mechanics derived not only from "old" mechanics but also from harmonics, optics, and astronomy. Unlike other texts on the subject, the role of mathematicians is stressed over that of philosophers of nature and the focus is particularly on epistemological aspects. In exploring Galilean and post-Galilean epistemology, attention is paid to the contributions of Galileo's disciples and also the impact of his enemies. The book will appeal to both historians of science and scientists.
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