The renovation of the arts and sciences by the Renaissance has been especially glorious in Italy and the Netherlands. Among the outstanding scholars of that period Simon Stevin, born at Bruges and living at Lelden, is one of the most interesting. Although little is known about his life, his marked personality speaks clear I y to us through his writings. He wrote on Mathematics, Mechanics, Hydrostatics, Astronomy, Navigation and technical and military matters; he introduced decimal fractions and measures; he prepared the theorem of the parallelogram of forces; he established fundamental laws in hydrostatics; he was one of the early defenders of the Copernican system and he explained loxodromic sailing, improved the windmills, proposed equal temperament in music and improved the construction of fortifications. He always combined purely theoretical investigations with their practical applications. A survey of his work conveys at the same time a vivid picture of the exact sciences about 1600. The author, the late E. J. Dijksterhuis (1892-1965), was a professor of history of science at the universities of Utrecht and Leyden. He wrote books on Euclid and on ArchImedes' mathematics and mechanics, and he became widely known outside the circle of historians of SCience by his extensive study on "The Mechanization of the World Picture" (1950; engl. transl. 1961). Of his standard work on Simon Stevin (written In the Dutch language), the present book Is a shortened version In English, adapted to the educated, non-specialist reader.
SIMON STEVIN
Plate 1. Portrait of Simon Stevin by an unknown artist. Library of Leyden University.
SIMON STEVIN Science in the Netherlands around 1600 BY E. J. DIJKSTERHUIS MARTINUS NIJHOFF / THE HAGUE 1970
ISBN-13: 978-94-010-3209-4 e-isbn-13: 978-94-010-3207-0 DOl: 10.1007/978-94-010-3207-0 1970 by Martinus NijhojJ, The Hague, Netherlands All rights reserved, including the right to translate or to reproduce this book or parts thereof in any form
CONTENTS EDITORS' PREFACE INTRODUCTION 1 1. STEVINS' LIFE 4 II. MATHEMATICS 14 Introduction 14 Sixteenth-Century Mathematics 14 Stevin's Mathematical Work 16 1. De Thiende 16 2. Tables of Interest 20 3. Arithmetic and Algebra 21 3.1 Introduction 21 3.2 Geometrical Numbers 22 3.3 Algebraic Numbers 23 3.4 Equations 25 3.5 The Quadratic Equation 27 3.6 The Cubic Equation 31 3.7 Negative Roots 33 3.8 The Equation of the Fourth Degree 33 3.9 The Rule "Algebra" 34 3.10 New Methods 35 3.11 The Translation of Diophantus's Algebra 36 3.12 The Practice of Arithmetic 37 3.13 The Doctrine of Ratios 38 3.14 Theory of Irrational Quantities 38 4. Geometry 39 4.1 Introduction 39 4.2 Geometrical Problems 40 4.3 Geometrical Instruments 40 4.4 Trigonometry 42 4.5 Construction of an Ellipse 42 4.6 Didactics 43 IX
VI CONTENTS 4.7 Semi-regular Polyhedra 43 4.8 Augmented Polyhedra 45 4.9 Perspective 46 III. MECHANICS 48 1. Introduction 48 2. Aristotelean and Archimedean Mechanics 48 3. Stevin's Criticism of the Principle of Virtual Displacements 49 4. The Art of Weighing (De Weeghconst) 50 4.1 Definitions and Postulates. The Theory of the Lever 50 4.2 The Wreath of Spheres (Clootcrans) 52 4.3 Oblique Forces 54 4.4 Three Forces in Equilibrium 57 4.5 Centres of Gravity 57 5. The Practice of Weighing (Weeghdaet) 59 5.1 Resistances 59 5.2 An Experiment on Falling Bodies 59 5.3 Instruments and Machines 60 5.4 The Pressure of the Bridle (Toomprang) 61 IV. HYDROSTATICS 64 1. Introduction 64 2. The Archimedean Principle 65 3. The Force Exerted on the Bottom 66 4, The Force Exerted on the Walls 68 5. The Problem of the Diver 68 6. On Floating Top-heaviness (Vlietende Topswaerheyt) 69 7. Summary 69 V. AsTRONOMY 70 1. Introduction 70 2. The Heavenly Motions (Hemelloop) 74 3. Stevin's Method 74 4. The Plan of the Work 76 5. Copernican Astronomy 76 6. Theological Opposition 78 7. The Nova Zembla Phenomenon 79 8. The Tides 80 VI. NAVIGATION 83 1. Introduction 83 2. The Sailings (Zeylstreken) 83 3. Great-circle Sailing 84 4. Loxodromic Sailing 84 5. The Haven-finding Art (Havenvinding) 87 5.1 Introduction 87
CONTENTS VII 5.2 The Memoir of Plancius 88 5.3 Stevin's Method of Haven-finding 88 VII. TECHNOLOGY 93 1. Introduction 93 2. Mills 93 2.1 Introduction 93 2.2 The Mechanism of a Water-miII 93 2.3 Theory of the MiII 95 2.4 Stevin on MiIIs (Van de Molens) 96 3. Sluices and Locks 98 3.1 Various Kinds of Sluices 98 3.2 The Swivel-gate Lock 99 4. Hydraulic Engineering 100 5. Geomorphology 102 6. The Sailing Chariot 104 VIII. MILITARY SCIENCE 106 A. Fortification 106 B. The Marking out of Army Camps (Castrametatio) 110 IX. ARCHITECTURE 113 1. Introduction 113 2. Town-Planning 115 3. House-Building 115 X. DOUBLE-ENTRY BOOK-KEEPING 117 1. Introduction 117 2. Mercantile Book-keeping 117 3. Princely Book-keeping 118 XI. MUSIC 120 XII. CIVIC MATTERS 123 A. The Citizen 123 B. The Prince 124 XIII. STEVIN AND THE DUTCH LANGUAGE 126 XIV. STEVIN'S PERSONALITY 130 XV. STEVIN'S WORKS 134
PREFACE The works of Simon Stevin are most interesting for the history of science, because they have such a wide scope and reflect so clearly the development of scientific knowledge around 1600 in central Europe. The recent publication of his Principal Works, with an English translation, has again attracted attention to his fascinating personality. The book on Stevin by Professor E. J. Dijksterhuis, originally published in the Dutch language, is an excellent introduction to the life and works of this remarkable Netherlander. Dijksterhuis prepared a somewhat condensed English edition, adapted to the foreign reader. Because of his untimely death, publication had to be deferred until the undersigned were able to undertake the editorial work. The Royal Netherlands Academy of Sciences, Amsterdam, allowed a grant, through which a linguistic revision of the text was made possible. We are very grateful to Miss C. Dikshoorn for the care with which she carried out this task and prepared the text for the press. A few supplementary notes have been added, for which we are personally responsible and which have been marked with our initials (R.H. or M.M.). Messrs Martinus Nijhoff, The Hague, who published the original Dutch edition, have kindly agreed to bring out also the English version and have given all their attention to this publication. R. HOOYKAAS M. G. J. MINNAERT