## Eduard Jan Dijksterhuis's books

We give below a list of some of Eduard Jan Dijksterhuis's books, some in Dutch, and some English translations. We give extracts from some reviews of these books and in a few cases some additional information. It is worth commenting on the fact that these history of mathematics books are reviewed in many more journals that is the case with other mathematics books. Here we have reviews from mathematics journals, science journals, history of science journals, history journals, classics journals etc. Of course this adds interest in that a classics reviewer, for example, would clearly look for something different from a mathematics reviewer.

**1. Val en Worp. Een Bijdrage tot de Geschiedenis der Mechanica van Aristoteles tot Newton (1925), by E J Dijksterhuis.**

**1.1. Review by: Heinrich Wieleitner.**

*Isis*

**8**(2) (1926), 378-379.

There are significant and "significant" historians. Among those in quote marks I mean the illustrious men who have written thick volumes that are in the hands of all, but annoyed at your own inquiries whenever you pick them up, as there are always this and that, if not false, it is still weak or crooked (

*nomina sunt odiosa*). The important historians without quote marks may have written a lot (such as Paul Tannery); but everything they wrote was well thought out, even if it was hypothetical, everything factually well founded, the sources as fully, carefully, and critically as possible read. It is a pleasure to study such a historian for decades to come. The present work on the development of the laws of falling objects immediately places the author in the class of important historians without quote marks. Employed in the small town of Tilburg, he had to get every book from abroad. What he has nevertheless contributed to the most remote literature, borders on the incredible.

**2. Archimedes (1938), by E J Dijksterhuis.**

**2.1. Review by: Louis Charles Karpinski.**

*Amer. Math. Monthly*

**46**(1) (1939), 41.

At the present time historical studies on the evolution of mathematical science have found new centres of activity in the low countries. The Historical Library of the Exact Sciences, of which series this first part on Archimedes is the sixth volume, is distinguished by careful and scholarly editing, combined with fine printing and substantial and colourful binding. The first five volumes deal with Euclid (I, III) , Non-Euclidean Geometry (II) , and Newton's Principia (IV, V), all six parts appearing over a period of ten years. After giving a preliminary list of works to be cited in this volume on Archimedes, the author gives briefly an account of the life and the works of Archimedes, with sufficient and correct bibliographical references. Upon this follows an excellent summary (pp. 44-133),

*The Elements of the Work of Archimedes*, employing modern symbolism. The Dutch version of the texts of Archimedes, represented in this volume by the two books,

*On the Sphere and the Cylinder*, concentrates on the modern interpretation, algebraic and geometric, of the propositions rather than the literal translation. This will make the work really more valuable for the Dutch teachers of mathematics as the historical connections are also clearly indicated.

**3. De mechanisering van het wereldbeeld (1950), by E J Dijksterhuis.**

**3.1. Review by: Dirk Jan Struik.**

*Isis*

**42**(1) (1951), 66-67.

This is an excellent book, written with full mastery both of the source material and of the secondary literature. It is long, but concise; though much of the subject matter is far from easy, the book is eminently readable. The many facts concerning the gradual unfolding of the mechanical conception of the universe are presented with exceptional lucidity. As an introduction into one of the most vital chapters of the history of philosophy it ranks with the very best; as a book of reference on the philosophies of nature from the Greeks to Newton it is a precious addition to any library provided its owner is not scared by a book in the language of the Netherlands. The author has already established an enviable reputation as a competent historian of science by means of many essays and such books as

*Val en Worp*(which deals with the genesis of the law of falling bodies,

*Isis*

**8**, 378-79) and Simon Stevin (

*Isis*

**40**, 269-70).

**3.2. Review by: N L.**

*Tijdschrift voor Philosophie*

**15**(1) (1953), 137-138.

This bulky book gives us the history of the emergence of the mechanical worldview and thus actually the emergence process of exact science. Starting from Greek antiquity, through the Middle Ages and the Renaissance, we follow the development of scientific thinking up to the crowning of classical physics in the figure of Newton. Although the author repeatedly points out that it must remain very incomplete or that he cannot elaborate on technical details, a very detailed explanation of the growth of science is given here. Completeness of course a very relative concept! Extremely pleasant and reassuring work gives an all-round balanced treatment. There is nowhere to be found here that easy, all-too-simplified and one-sided interpreter, who is all too often found in common representations of the development of the sciences.

**3.3. Review by: Johan Adriaan Vollgraff.**

*Revue d'histoire des sciences et de leurs applications*

**3**(3) (1950), 290-291.

The title of this book, which is not addressed to specialists and therefore contains only a few very basic calculations, agrees with that of 1938 (

*Die Mechanisierung des Weltbildes*) by Anneliese Maier which M Dijksterhuis - without anyway forgetting P Duhem - considers the work, thanks to the great knowledge that this person possesses of medieval manuscripts, as the best source of information on the state of the natural sciences in the scholastic period. It is not, however, the history of this epoch which occupies the greatest place in the work of M Dijksterhuis: pp. 109-241 dealing with the Middle Ages (the Arabs are mentioned only briefly) are preceded by a warning of four pages and a First Part devoted to the Greeks; the Third and Fourth Parts are entitled: Preparation for the Development (pp. 245-313) ... and: Birth of Classical Science (pp. 317-539). In an Epilogue of eight pages the author expresses the conviction that there is an essential difference between classical science and that of the Middle Ages, while between classical science - that of Newton - and modern science it does not exist.

**3.4. Review by: Madeleine Francès.**

*Revue Philosophique de la France et de l'Étranger*

**148**(1958), 101.

To the problem of the mechanistic interpretation of the world - a subject nowadays of controversy as we know - Dr E J Dijksterhuis makes a valuable contribution, in the form of a basic historical work:

*The mechanization of the representation of the world*. The serious, well-documented book, provided with all the critical apparatus intended to render its consultation easy, reads with interest from one end to the other. Not that he claims to innovate in the main lines of novel sensation. From the Greek origins to the Middle Ages, the Renaissance, the Modern Age, the author analyses the characteristic evolution - which has already attracted the attention of so many specialists in the history of science and philosophy, in different countries. But, although he took great care to pay tribute to his predecessors, Dr Dijksterhuis frequently succeeds in renewing in detail certain conventional points of view. For example, in the book under review, he examines again the role played, from the angle of this problem, by such artists and such scientists. The studies devoted to Leonardo da Vinci, Isaac Beeckman, Galileo, Christiaan Huygens, etc ..., come out - by force of appreciation and precision - paths too beaten. No doubt, the work, particularly the conclusion, offers a certain amount of thought for the cultivated public. Yet, in spite of its clarity, Dr Dijksterhuis's contribution is as remote as possible from a banal extension. Students, philosophers, and scholars will appreciate both his method and his great simplicity.

**3.5. Review by: Pieter H Kollewijn.**

*Books Abroad*

**25**(3) (1951), 292.

The book is announced as having social significance, which it has not; frankly this is just as well. It purports to cover the history of science up to 1700 but the author, a mathematician and physicist, slights the science of the structure of matter very badly as indicated by the references which do not mention such names as Strunz and Berthelot. The main subjects are mathematics, astronomy and some physics but the author's long studies of the history of mathematics keep interfering with the other subjects. He subdivides science into ancient, classical, and modern, with the line between the latter two placed approximately in the late 1920's. Classical science, based on the discoveries of Copernicus, Newton, Dalton, and Descartes respectively in the fields of astronomy, physics, chemistry, and mathematics, ends with the new - should we say dualistic? - theories of Einstein and possibly Planck.

**4. Descartes et le Cartésianisme Hollandais. Etudes et Documents (1951), by E J Dijksterhuis et al.**

**4.1. Review by: J N Wright.**

*The Philosophical Quarterly (1950-)*

**3**(10) (1953), 82-83.

The book is a miscellany comprising two essays devoted specifically to Descartes's philosophy,

*La complexité de la philosophie de Descartes*, by H J Pos, and

*La Méthode et les Essais de Descartes*, by E J Dijksterhuis; an extract from Dr Cornelia Serrurier's book,

*Descartes, l'homme et le penseur*; a hitherto unpublished letter from Descartes to Huygens written about six weeks before Descartes's death, and two other fragments of unpublished letters;

*Observations sur la philosophie de Descartes*, by Du Vaucel, from the Archives Nationales de La Haye; and two long essays,

*Augustinisme et Cartésianisme a Port Royal*, by Geneviève Lewis, and

*Le Cartésianisme aux Pays-bas*, by C L Thijessen-Schoute. Finally, there are 40 pages of notes on

*Les cartésiens hollandais*. .... In Mr Dijksterhuis's essay on the

*Method*and the

*Essays*which follow, much useful information is given on certain obscure passages in both the

*Method*and the

*Regulae*on 'the Analysis of the Ancients and the Algebra of the moderns' and, to mention one point only, of the relation between Descartes's discoveries in mathematics and his stress on intuition and deduction as part of one and the same process. He also claims that the four rules in the

*Discourse*are simply general rules of procedure: the important special rules are to be found elsewhere. These may be summed up as follows: find in each science the axioms which seem indubitable, deduce from these their consequences, form quantitatively the questions which arise and treat them mathematically, i.e. algebraically in accordance with

*la Mathématique Universelle*. Mr Dijksterhuis's notes, of

*La Geometrie*"c'est un ouvrage passionant qui mériterait qu'on en fit une édition moderne commentée." It is urgently needed.

**5. The Principal Works of Simon Stevin. Vol. I: General Introduction - Mechanics (1955), by E J Dijksterhuis.**

**5.1. From the Introduction.**

Modern science was born in the period beginning with Copernicus'

*De Revolutionibus Orbium Coelestium*(1543) and ending with Newton's

*Philosophiae Naturalis Principia Mathematica*(1687).

For reasons we shall not enter into here medieval Scholasticism had not succeeded in finding an effective method for the investigation of natural phenomena. Nor had Humanism been able to find the new paths science had to follow, though it was indirectly instrumental in promoting natural science by fostering the study of Greek originals on mathematics, mechanics and astronomy. The conviction shared by both movements that science was something mankind had once possessed but lost since, led to the conviction that it had to be rediscovered in ancient books, and so turned men's eyes toward the past instead of to the future, where it was to be found.

The creation of modern science required a different mental attitude. Men had to realize that, if science were to grow, each generation had to make its own contribution and that all the wisdom of Antiquity was useful only as a starting point for new research.

In the development of this view the universities, which had always been the bulwarks of medieval science, could play none but a minor part. Naturally inclined to conservatism, they on the whole exerted a retarding influence. For the greater part the revival of learning was the work of individual scholars who, in full possession of traditional science, took the initiative of transcending its boundaries and venturing into unexplored realms of scientific thought.

During the sixteenth century these pioneers of .modern science are to be found all over Europe. The Italians Tartaglia, Cardano, Benedetti took the lead in the domains of mathematics and mechanics. A new era in astronomy was opened by Copernicus in Prussia and by Tycho Brahe in Denmark. In France the mathematician Vieta prepared the way for the great progress in algebra that was to be accomplished in the seventeenth century.

The work of these prominent scholars was supplemented by the activity of numerous craftsmen who, urged on by economic necessity, tried to put science to practical use. Some of them were well-known artists (like Leonardo da Vinci and Albrecht Durer), who at the same time worked as engineers planning or constructing canals, locks, dikes and fortifications. For the greater part, however, their names do not survive; they were the numerous makers of clockworks and nautical or astronomical instruments, the cartographers and, somewhat later, the grinders of lenses and the makers of telescopes and microscopes.

Simon Stevin acquired his honourable position in the history of civilization by working both in theoretical science and in engineering. This combination of faculties was prophetical: modern science truly required the cooperation of theory and practice. It could only come into being by theoretical speculation on data furnished by experience. Matter, being obstinate and unwilling to yield its secrets to pure reasoning; can only be forced to disclose its properties if submitted to experimental research. However, to perform experiments, technical skill in constructing and using instruments is wanted. On the other band the accumulation of empirical data is not in itself sufficient. Only mathematical formulation of quantitative relations leads to theories, the consequences of which can be put to the test in newly devised experiments. Thus the evolution of science can only proceed by .a constant interaction between theory and practice.

The role of the technician is by no means exhausted with his contributions to the experimental side of science. His help is needed again when the results achieved are to be applied for the benefit of humanity.

In later centuries the various departments of scientific work were as a rule separated, most scientists concentrating either on theoretical or on experimental research or on the application of science in technical inventions. In the age of pioneers, however, their concentration in one person was not yet uncommon. Stevin was an example of this, and be appears to have been fully aware of the significance the combination had for the growth of natural science.

We shall not endeavour to depict in this biography the intellectual atmosphere in which he accomplished his work as a scientist and an engineer; this will be done, as far as necessary, in the introductions to the works that will be published in this edition. A few words on the political background of his career in the Low Countries will be given in the description of his life, to which we will now pass on.

**5.2. Review by: I Bernard Cohen.**

*Isis*

**47**(4) (1956), 447-448.

The first volume of the new edition of Stevin is devoted to mechanics. It contains a general introduction by the distinguished historian of science, E J Dijksterhuis, who is known for his writings in Dutch on the history of mechanics, on Stevin, and on the revolution in physical thought which he has appropriately called, "The mechanization of the world view," (reviewed in

*Isis*, 1951,

**42**: 66-67; it is pleasant to be able to report that this book is soon to appear in an English translation, and also in a German translation to be published by Springer-Verlag). In the general introduction to the volume of Stevin's works on mechanics, Dijksterhuis presents biographical information concerning the life of Stevin, his political background, and his ideas on language. This is followed by a brief and succinct account of Stevin's achievements in various fields, mathematics, mechanics, hydrostatics, astronomy, geography, navigation, technology, military science, book-keeping, architecture, music, civic matters, and logic. There follows a general conclusion and appreciation in which Dijksterhuis develops the dual aspect of Stevin, the "prototype of the engineer, of the perfect technologist, who deals with practical problems in a scientific way." Dijksterhuis calls attention to the oscillations of Stevin between "what he calls spiegeling (speculation, i.e., theoretical investigation) and daet (practical activity)." In a most valuable appendix, in which a bibliography lists the titles of all of Stevin's works, together with their reprints and translations.

**6. Archimedes (1956), by E J Dijksterhuis.**

**6.1. From the Preface.**

This book is an attempt to bring the work of Archimedes, which is one of the high-water marks of the mathematical culture of Greek Antiquity, nearer to the understanding and the appreciation of the modern reader. Such an attempt has been made twice before, in a way so excellent that I can scarcely hope to equal it: by T L Heath in

*The Works of Archimedes*and by P Ver Eecke in

*Les Oeuvres Complète d'Archimède*. My belief that I might be excused for adding to these two excellent editions a new adaptation of the writings of the great Greek mathematician finds its justification in the consideration that the method of treatment here chosen differs fundamentally from the one followed by Heath as well as from that applied by Ver Eecke. As a matter of fact, Heath represents Archimedes' argument in modern notation. Ver Eecke gives a literal translation of his writings. Both methods have their disadvantages: in a representation of Greek proofs in the symbolism of modem algebra it is often precisely the most characteristic qualities of the classical argument which are lost, so that the reader is not sufficiently obliged to enter into the train of thought of the original; the literal translation, on the other hand, which like the Greek text says in words everything that we, spoiled as we have been by the development of mathematical symbolism, can grasp and understand so much more easily in symbols, perhaps helps the present-day reader too little to overcome the peculiar difficulties which are inevitably involved in the reading of the Greek mathematical authors and which certainly are not due exclusively, nay, not even primarily, to the fact that they wrote in Greek.

The method applied in the present book attempts to combine the advantages and avoid the disadvantages of the two methods just outlined. The exposition follows the Greek text closely, but only the propositions are given in a literal translation; after that the proofs are set forth in a symbolical notation specially devised for the purpose, which makes it possible to follow the line of reasoning step by step. This system of notation, which was also used in my work

*De Elementen van Euclides*(The Elements of Euclid) (Groningen, 1929, 1931), in long practice has been found a useful aid in the explanation of Greek mathematical arguments.

Apart from the introduction of this aid, I have also tried to meet in another way the difficulties which I know from experience are encountered by present-day mathematicians reading Greek authors. In fact, the Greek mathematicians in their works are wont to give, without a single word of elucidation about the object in view, a dry-as-dust string of propositions and proofs, in which not the slightest distinction is made between lemmas and fundamental theorems, while the general trend of the argument is often very difficult to discover. In order to bring this trend out more clearly I have collected in a separate chapter (Chapter III) all those theorems which in relation to the nucleus of a treatise have the function of elements; with each individual work the argument could then be summarized much more briefly, because all the lemmas had already been discussed previously. A decimal classification of Chapter III makes it possible to trace these lemmas quickly, if desired, and to find out how they can be proved. Through this arrangement the additional advantage has been gained that each of Archimedes' treatises can be studied separately.

**6.2. Review by: Daniel C Lewis.**

*The American Journal of Philology*

**79**(2) (1958), 221-222.

In the Preface, the author begins with a word of homage to T L Heath, whose well-known work on Archimedes might well render superfluous any further attempt to interpret for modern readers the genius of this greatest of all ancient mathematicians. Bur Professor E J Dijksterhuis asserts that his work differs fundamentally from that of T L Heath in that the latter interprets the work of Archimedes in modern notation and thus tends to miss the actual process of Archimedian thinking, whereas Dijksterhuis, although he too seeks by using notational abbreviation to avoid the cumbersome expression of mathematical concepts in ordinary language, carefully tries to avoid modern mathematical notation as an aid to mathematical thinking in the hope that he will thus more nearly produce in the reader the spirit of the original thinker. This reviewer has given serious consideration to this claim and has examined in parallel studies the treatment of several topics as expounded by Archimedes himself, as interpreted by T L Heath, and as reinterpreted by the author. The superficial difference in the three treatments is at once obvious, but the reviewer finds it hard to feel that there is really a fundamental difference. ... Many ... features ... are scattered throughout the book. Each is in itself quite minor; but each is ensconced in sound scholarship; and the totality of them all is extremely impressive and constitutes, in the reviewer's opinion, the chief merit of the work of Professor Dijksterhuis rather than any exaggerated claim that he may have contributed anything fundamentally different.

**6.3. Review by: Jean Itard.**

*Revue d'histoire des sciences et de leurs applications*

**9**(4) (1956), 366-371.

This work is the translation, in English, by Miss C Dikshoorn of the

*Archimedes*of E J Dijksterhuis published in Dutch, in 1938, at Noordhoff, Groningen, in a volume of 213 pages and which was completed between 1938 and 1944 in volumes XVII and XX of the

*Euclides*journal. The current edition, which faithfully follows the original text with some additions, will make it accessible to a larger audience. It is not strictly speaking an edition of Archimedes' works, but a continuous commentary which is always very close to the text, and which is directly understandable by the modern reader. Already in

*De Elementen van Euclides*(Groningen, I, 1929 and II, 1930) the author had accomplished a very similar and very successful work. A difference, however, is to be noted. In the study on Euclid the statements of very many propositions are given, both in Greek and in Dutch. For Archimedes, on the contrary, the Greek text has almost completely disappeared.

**6.4. Review by: Ivor Bulmer-Thomas.**

*The Classical Review, New Series*

**8**(1) (1958), 43-45.

That every traduttore must be to some extent a traditore is accepted, but the rendering of Greek mathematical works offers one opportunity of faithlessness not open to other translators. The Greeks never developed any symbolism except the most rudimentary, and the most complicated mathematical expressions are set out in full literary form. A single enunciation by Apollonius of Perga may run to eighteen lines of the Teubner text, and by the time the modern reader has reached the end he may not remember where he began. Is the translator to follow the literary form of the Greek closely? This is the course taken by Paul Ver Eecke in

*Les Oeuvres complètes d'Archimède*(Paris, Brussels, 1921). Or is the translator free to take advantage of modern symbolism for the purpose of shortening his own task and helping the reader's understanding? This is the practice adopted by Sir Thomas Heath in

*The Works of Archimedes*(Cambridge, 1897) and, less drastically, in the Loeb

*Greek Mathematical Works*, vol. ii (London, 1941). Professor E J Dijksterhuis, for whom the chair of the History of Mathematics and Natural Sciences was created in the University of Utrecht in 1953, has tried to steer a mean between these courses. He gives the propositions in full literary form, but in the proofs, while following Archimedes' line of reasoning closely, he uses a notation of his own, already employed in his

*De Elementen van Euclides*(Groningen, 1929, 1931).

**6.5. Review by: Israel Edward Drabkin.**

*Science, New Series*

**125**(3250) (1957), 702.

In setting forth the mathematical arguments, E J Dijksterhuis employs a notation of his own devising, which is somewhat between the modern symbolic notation of T L Heath's English version and the nonsymbolic verbal mathematics of Paul Ver Eecke's literal French translation. The bulk of the work is a discussion of all the writings of Archimedes, proposition by proposition. As a rule, only the enunciation of the proposition is actually translated; the rest is generally paraphrased, summarized, and commented on. In addition, there are chapters on Archimedes' life and works and on the basic concepts and lemmas that he employs. With this book, Dijksterhuis has put all students of Greek mathematics in his debt. The modern reader who approaches an author as profound as Archimedes needs every help he can get, and he is indeed fortunate, now, to be able to consult Dijksterhuis along with the standard editions of Heath and Ver Eecke. The new work is so very valuable for what it seeks to do - that is, to make more understandable the actual mathematics of Archimedes - that it may seem ungracious to ask for more. Yet a consideration of Archimedes' work suggests many topics (some of them outside the boundaries of technical mathematics) which have not been adequately dealt with in any of the standard treatises on Archimedes.

**6.6. Review by: Oskar Becker.**

*Gnomon*

**29**(5) (1957), 329-332.

The original Dutch-language work by E J Dijksterhuis is fortunately now in a good English translation (by C Dikshoorn). In its 1st Chapter it contains a biography of the great mathematician and engineer, carefully constructed from the sources, in which his various mechanical constructions, as far as the oft-failing sources allow, are extensively and critically discussed. An overview of the preserved and lost manuscripts and the editions of the mathematical works is contained in its 2nd Chapter. The peculiarity of the book, however, only comes into effect in the third chapter.

**6.7. Review by: Marshall Clagett.**

*Isis*

**49**(1) (1958), 91-92.

Professor Dijksterhuis' new and important book on Archimedes is an English version (with some changes) of a Dutch original that appeared earlier. It will immediately establish itself as a companion to T L Heath's English paraphrase of the works of Archimedes. It does, however, have certain advantages over the version of Heath: (i) being written a half-century later than Heath's work, it naturally has all the fruits of the last half century of Archimedean research; it thus represents the most recent and authoritative summary of scholarly opinions on Archimedes; (2) while like Heath's version, it, too, is a paraphrase rather than a literal translation in the manner of Ver Eecke's French version, it nevertheless keeps closer to the spirit of Archimedes' works than does Heath. It does this in part by substituting a new system of symbolism that Dijksterhuis feels catches the essential characteristics of the Greek proofs better than the modem symbolism employed by Heath.

**6.8. Review by: James R Newman.**

*Scientific American*

**197**(1) (1957), 170.

Dijksterhuis presents a new edition of Archimedes' work, which attempts "to bring it nearer to the understanding and appreciation of the modern reader." The exposition follows the Greek text closely, but the propositions are given in a literal translation. The proofs are set forth "in a symbolical notation specially devised for the purpose, which makes it possible to follow the line of reasoning step by step." The entire work has been translated into English by Miss C Dikshoorn. This is a well printed, very attractive edition which students of Archimedes will cherish, but it must not be supposed that, despite the new symbolism and the editor's very helpful comments and explanations, this text opens Archimedes for the millions.

**6.9. Review by: W van der Wielen.**

*Mnemosyne, Fourth Series*

**11**(4) (1958), 361-363.

Dijksterhuis has devised a very original notation which has the brevity and the lucidity of modern mathematical notation and at the same time saves the typical Greek reasoning. This notation has been published for the first time in Dijksterhuis'

*"Elementen van Euclides"*(Groningen, 1929, 1931) and has been summarized in the third chapter of his "Archimedes". Thanks to this notation it is possible for the modern reader to get an exact idea of Archimedes' works without the risk of getting lost in the complexity of the original. This same third chapter (

*"The Elements of the Work of Archimedes"*) has a second function in the whole. The student, who, with a fair knowledge of the contents of Euclid's Elements undertakes to read Archimedes, meets with two difficulties, apart from the one already mentioned. In the first place he finds out that Archimedes takes for granted a thorough knowledge of, and in some places (e.g. Quadratura Parabolae, Prop. 3, ad fin.) quotes, a lost work,

*"Elements of Conies"*. In the second place Archimedes has the habit of giving, at the very beginning of most of his books, a series of lemmata, the purpose of which is not evident until much later on and which, at first sight, are rather confusing. In this chapter Dijksterhuis has given an excellent summary of (a) the notation just mentioned, (b) the propositions not given by Euclid, but taken for granted by Archimedes, among others those which must have been given in the "Elements of Conies", (c) the lemmata given by Archimedes himself. [The reviewer shows his] admiration for this brilliant book, which one cannot take up without impressed by the thorough knowledge the author has of his and by the lucid way in which he treats it. At last we are book on one of the greatest minds of ancient Greece, which him accessible to many people. We may be sure that for years to come Dijksterhuis' Archimedes will be the authoritative work on the great mathematician of Syracus.

**6.10. Review by: Vera Sanford.**

*Amer. Math. Monthly*

**65**(9) (1958), 721.

It is inevitable that this volume be compared with

*The Works of Archimedes*by Sir Thomas Heath (1897, recently reissued by Dover, New York). Heath describes his book as "a reproduction of the extant works of perhaps the greatest mathematical genius that the world has ever seen." Dr Dijksterhuis says that his is "an attempt to bring the work of Archimedes ... nearer to the understanding and appreciation of the modern world." The points of difference are important. In the matter of mathematical notation, Dr Dijksterhuis believes that Heath's use of modern symbols masks the characteristic qualities of the classical argument. Accordingly he has utilized a notation of his own invention which he had found useful in his translation of Euclid. This innovation, however, did not appeal to Dr van der Waerden who said, in

*Science Awakening*, that this is not necessary "provided we take good care not to use algebraic transformations which cannot immediately be reformulated in the Greek terminology." In view of the scant acquaintance of American readers with the Greek alphabet, it is unfortunate that Dr Dijksterhuis used capital letters from this alphabet in his diagrams. Heath did not. Another important difference in the two books is in the treatment of the material with which Archimedes begins many of his works, theorems discovered by his predecessors and others of his own, essential to the work that follows. Heath compares this to a master piece of strategy. Dijksterhuis believes that it tends to obscure Archimedes' purpose. Accordingly he arranges these theorems in a logically constructed system, coded for reference and preceding his treatment of the text of Archimedes. As a third point of difference, Dijksterhuis gives a running commentary with each translation. Heath makes sparing use of footnotes, relying on his introductory chapters for fuller explanation. Which work should a student consult? Both!

**7. Die Mechanisierung des Weltbildes (1956), by E J Dijksterhuis.**

**7.1. Review by: Serge Moscovivi.**

*Revue d'histoire des sciences et de leurs applications*

**13**(2) (1960), 149-151.

Mr Dijksterhuis's book is a remarkable book. It should be considered only from this angle, whatever criticism that can be brought to it. Besides, can one criticize such a work? We have no other option than to discuss it. What is precisely its value? The qualities of the author are obvious to those who stop on any paragraph or chapter: extensive information, clarity of exposition, pedagogical gift to condense in pleasing formulas very difficult theories and that we find in confused form among the authors. The genesis of the mechanization of the image of the universe, Mr Dijksterhuis seeks the beginnings of philosophical reflection.

**8. The Mechanization of the World Picture (1961), by E J Dijksterhuis.**

**8.1. Review by: A Rupert Hall.**

*Scientific American*

**205**(6) (1961), 177-183.

Few readers who pick up this solid volume will be deceived by its author's manner of address to the general reader into supposing that this is a trivial work. It is a major contribution to the history of science whose ready availability in English has been eagerly awaited for several years. It should be remarked at once that the translation by Miss C Dikshoorn is excellent. This is a book for serious study, and one that well repays the effort. Its author expects a fair amount of mathematical and physical understanding on the part of his readers, and by no means fails in respect to his subject by sliding over its difficulties. The reader must be prepared to grapple with ideas, and sometimes terminologies, that demand concentrated attention. The main steps in

*The Mechanization of the World Picture*are not difficult to pick out, though no short summary can do justice to Dijksterhuis' learned and enlightening study of the original texts.

**8.2. Review by: Marshall Clagett.**

*Science, New Series*

**134**(3491) (1961), 1684.

All students of the history of science concerned with the so-called Scientific Revolution of the 17th century will welcome this English translation of Dijksterhuis'

*De Mechanisering van het Wereldbeeld*(Amsterdam, 1950). This work both in its original form and in the German translation (1955), has already become a classic, for its author is one of the most profound interpreters of the history of mathematics and mechanics. The author modestly claims that his interpretation of the mechanization of physical science is not "intended as a handbook for historians of science; [that] it has been written for the general reader with a broad interest in the subject." But let me assure the readers of this review that many historians of science have already learned much from it and many more will learn from it.

**8.3. Review by: Hugh Francis Kearney.**

*The Economic History Review, New Series*

**15**(3) (1963), 590-59.

Dijksterhuis, an expert on Copernicus, Stevin and Descartes as well as Archimedes and Euclid, enables his readers to trace the continuity of European science from the Greeks, through the revival of Greek thought in the thirteenth century and its further reinforcement in the sixteenth, to the achievement of the scientific revolution itself. The combination of detail with range is remarkable. The clarity of his sympathetic exposition of Aristotelian science is combined with an assured discussion of Newtonian physics. Perhaps most striking of all is the chapter on Galileo, which is surely the best short treatment of this subject in English. The second feature of the book is its rare combination of sweetness and astringency. The mathematics are there but the general historian, for whom the book is intended, never feels completely out of his depth. Some reassuring phrase is always to be found near at hand. But there is no false simplicity. Each thinker from the Greeks onwards is treated on his own terms and in the account of; for example, the late scholastic Terminists, something is conveyed of the intellectual calibre of the men concerned, mistaken though their views appear in retrospect.

**8.4. Review by: Michael A Hoskin.**

*The English Historical Review*

**79**(311) (1964), 391.

It is more than a decade since E J Dijksterhuis's

*The Mechanization of the World Picture*, a survey of the history of physics from the Greeks to Newton, first appeared in Dutch. It now appears in an English version, translated by C Dikshoorn (Clarendon Press: Oxford University Press, I961). The author, a distinguished historian of science and the leading authority on Simon Stevin, has been prevented by reasons of health from taking into account for this edition the work published since 1950. In so young a subject ten years is a long time, but this substantial volume of a quarter of a million words remains a mine of information that will be of great value to all serious students of the subject.

**8.5. Review by: Niels H de V Heathcote.**

*History*

**49**(165) (1964), 130.

In this scholarly work, first published in 1950 in Dutch, Professor Dijksterhuis, Professor of the History of Science in the University of Utrecht, describes those major developments in the history of the physical sciences that led eventually to the mechanistic description of the universe, a term which he defines in the last few lines of the book as 'a description of nature with the aid of the mathematical concepts of classical mechanics'. The subject is treated under four main headings: the Legacy of Antiquity, Science in the Middle Ages, the Prelude to the Growth of Classical Science, the Evolution of Classical Science. Of these the last (pp. 287-491) covers the crucial period from Copernicus to the publication in 1687 of Newton's

*Principia*, the starting point of the 'classical' mechanics that dominated physical science until the opening years of the present century. Though the book is primarily concerned with the 'mathematization' of the physical sciences, no special knowledge of either mathematics or physics is required. What Professor Dijksterhuis does, and does most admirably, is to present an overall picture of the various influences at work, both within and without the main stream of scientific thought, that either retarded or accelerated the trend towards mathematization. His profound and sympathetic understanding of these influences is evident throughout, but especially in his treatment of that difficult period, the Middle Ages. All historians, whether historians of science or not, will welcome this masterly exposition of an aspect of man's intellectual activity that has played so important a part in the history of civilization.

**8.6. Review by: G Holt.**

*Physics Today*

**15**(8) (1962), 48.

It is a large imposing volume, characterised by a measured thoroughness in grappling with difficulties that are often slighted (for example, a step-by-step account of Kepler's work on establishing the shape of planetary orbits). It carefully summarises the content and proofs in major scientific documents in physical science over almost 2000 years, and gives full citations of sources. I can here only list some of the parts which struck me as particularly enlightening: A lucid and brief discussion of Aristotelianism and Neoplatonism in Greek philosophy of nature; the consideration of 14th century physics; a perhaps rather brief account of technology as a source of medieval natural science; a detailed probing of the main works of Kepler and of Huygens; and a fine summary of the aims and deficiencies of Newton's scientific work.

**9. A History of Science and Technology (1963), by R J Forbes and E J Dijksterhuis.**

**9.1. Review by: J Morton Briggs, Jr.**

*Isis*

**55**(1) (1964), 101-102.

In the last twenty years, the output of historians of science has increased tremendously to the point where the survey has become a difficult book to write. All of the information known simply will not fit. When technology is appended - and its importance goes without saying - the problems are still greater. The distinguished authors of this two-volume paperback survey have, alas, not been able to overcome the difficulties. There is a wealth of information presented; there is an attempt at narrative; there are only a few mistakes; and yet the flaws vitiate the effort. First of all, the fact that two men wrote the book, and acknowledge only the chapters they individually worked on, is evident and breaks the flow of the history. ... Second, and ultimately more important, the reader becomes terribly bored, not to say annoyed, by the constant apologies that space limitations restrict the authors to only an outline of whatever subject is at hand. Moreover, the truncations of the narrative produced by these brief outlines tend to make for distortion and confusion.

**10. The Mechanization of the World Picture (1969), by E J Dijksterhuis.**

**10.1. Review by: Irving Adler.**

*Science & Society*

**35**(2) (1971), 232-238.

This is a paperback edition of the late book, first published in Dutch in 1950 and English in 1961. ... Dijksterhuis divides the history of physical science into three periods: the ancient period begins with Thales, about 600 B.C.; the classical period begins with Newton's

*Principia*in 1687; the modern period begins with Planck's quantum theory in 1900. The purpose of the book is to trace the genesis during the ancient period of the principal ideas and practices that became the foundation of physical science during the classical period: "experiment as the source of knowledge, mathematical formulation as the descriptive medium, mathematical deduction as the guiding principle in the search for new phenomena to be verified by experimentation." ... Within the limited framework that Dijksterhuis chose for his work he has produced a masterpiece of lasting value. Many characteristics of Dijksterhuis's book contribute to its great merit and combine to make reading it a rewarding experience.

**11. Simon Stevin: Science in the Netherlands around 1600 (1970), by E J Dijksterhuis.**

**11.1. Review by: Albert Van Helden.**

*Isis*

**62**(4) (1971), 544-545.

George Sarton in 1934, lamenting the dearth of literature on Simon Stevin, whom he described as "perhaps the most original man of science in the second half of the sixteenth century," made a plea for a full biography as well as an edition of Stevin's works (Isis, 1934, 21:242). In the intervening years Sarton's plea has not gone unheeded, thanks largely to the efforts of the late E J Dijksterhuis. In 1943 Dijksterhuis published Simon Stevin, the first full-fledged Dutch biography of the man, and when the Royal Netherlands Academy of Sciences and Letters in 1950 appointed a committee to edit Stevin's works for republication, he became its chairman. In that capacity he edited the first volume of

*The Principal Works of Simon Stevin*(5 vols., Amsterdam, 1955-1966) and made valuable contributions to the other volumes. Before his death in 1965 Dijksterhuis had nearly completed an English biography of Stevin which has been brought to fruition by M G J Minneart and R Hooykaas. We can thus fairly say that Stevin has received the recognition Sarton advocated. ... The present book is not a straightforward translation of the Dutch biography. Some material aimed at the Dutch reader has been deleted, while some background material helpful to the foreign reader has been added.

**11.2. Review by: Jon V Pepper.**

*The British Journal for the History of Science*

**5**(4) (1971), 416-417.

The work under review is a shortened version in English of Dijksterhuis' earlier Dutch biography of Stevin. It provides a useful conspectus of Stevin's life and works, and its very shortness, indeed slightness in places, may usefully lead the reader to consult Stevin's work directly, which the English reader may do most conveniently in the recent five-volume collection of his principal works. ... In some parts of this work, Dijksterhuis seems to be rather apologetic in his presentation of Stevin's contributions. This is unnecessary, not because Stevin was a universal genius (which he was not), but because it should not be necessary now to write history of science from the point of view of the major original contributors only. Most workers in science, then as now, were not particularly creative. But history consists in part, at least, of the piecing together of the whole picture, and its subsequent interpretation, and we can gain almost as good a picture of the science of most ages from the average work of the period as from outstanding additions, which usually grow out of the current interests. Indeed, these latter may have their most powerful effect only later. Using this judgment, Stevin is important, not because of new work he did, but because of the coming together in him of many of the threads of contemporary work. Read in this light, Dijksterhuis' little book will be useful, and its subtitle made meaningful.

**12. Archimedes (Reprint of the 1956 edition) (1987), by E J Dijksterhuis.**

**12.1. From the Publisher.**

This classic study by the eminent Dutch historian of science E J Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the text, and then undertakes a comprehensive examination of all the extant writings.

**12.2. Review by: Gerald James Toomer.**

*Isis*

**80**(2) (1989), 305-306.

E J Dijksterhuis's book, first published in English in 1956 (revised from a Dutch version published between 1938 and 1944), has established itself as the best detailed study of Archimedes' works in any language. After brief chapters on what is known or rumoured of Archimedes' life, and on the transmission of the text and its history of publication, the long Chapter 3 gives an admirable exposition of "the elements of the work of Archimedes," including the basic theorems of conics and other mathematical procedures necessary for understanding the rest of the book. In this discussion Dijksterhuis introduced his own symbolic notation, which he rightly claimed both better represented the Greek methods of "application of areas" than the algebraic symbolism used in most modern translations and avoided the confusion induced in the modern reader by literal translations of the ancient rhetorical exposition. The rest of the book paraphrases and explains each of the surviving works in turn. The last chapter deals briefly with works known only from fragments or from second-hand sources. The bulk of the book remains as valid as when it was written, and it is difficult to foresee its being superseded. Thus the reprint is greatly to be welcomed.

**12.3. Review by: Alexander Jones.**

*American Scientist*

**77**(3) (1989), 302.

Dijksterhuis's Archimedes is both a book about Archimedes and a translation of his works, and in both respects it is outstanding. The translation is not a literal rendering of the Greek mathematical prose; instead Dijksterhuis employs a notation that faithfully and compendiously represents the arguments that Archimedes states in words, without encouraging the reader to import the anachronistic concepts that often creep in when early scientific writings are presented in the garb of modern notation. A preliminary chapter usefully collects the lemmas and non elementary concepts that Archimedes assumes, so that an acquaintance with Euclid's Elements is the only prerequisite to understanding the mathematics. Dijksterhuis's thorough introductory survey of the scattered sources for Archimedes's biography shows much cautious good sense. Thirty years separate the first publication of this book in English and the present reprinting. Although Dijksterhuis's text has not been revised, the publishers have added a useful bibliographical survey of recent Archimedean studies, by a historian who has himself made numerous contributions to the subject. The new edition will expose many new readers to a book.

**13. Clio's stiefkind (1990), by E J Dijksterhuis and K Van Berkel.**

**13.1. Review by: Albert W Grootendorst.**

*Isis*

**85**(2) (1994), 321-322.

E J Dijksterhuis (1892-1965), the Dutch historian of the exact sciences renowned for his

*Mechanisation of the World Picture*(Princeton University Press published an English edition in 1986), was an ardent protagonist of bridging the gap between the "two cultures," the humanities and the exact sciences. In his inaugural lecture at Utrecht University (1952), he raised this question and addressed the

*α*-students as follows: "The river that separates you from it [i.e., the exact sciences] is much too deep. Going upstream, however, you will find a ferry, which can bring you to the other side. This ferry is called 'history of science,' and I will be happy to be the ferryman."

The book reviewed here, Clio's stiefkind (stiefkind = stepchild; Clio is the well-known muse of history), amplifies this view in a well-chosen selection of ten articles. These articles - all in Dutch - cover mathematics as a cultural factor, the role of mathematics in science, and history of science as a bridge between the two cultures. There are also essays on Galileo and Simon Stevin; the first of these was Dijksterhuis's first contribution to the history of science (1920). The introduction by the editor includes a short biography of Dijksterhuis; a selected bibliography of his works and a name index conclude the book. Each article is preceded by a short introduction. This book is very good reading. Its content is fascinating and surely not outdated; the style and wording are excellent, which is to be expected from an author who received a literary prize for a book on science (Mechanisation).

*Clio's stiefkind*is highly recommended to all who are interested in the history of science and share the feeling that the gap between the two cultures must be narrowed, especially in our era.

**13.2. Review by: Willem Hackmann.**

*The British Journal for the History of Science*

**26**(3) (1993), 378-379.

Ten of Dijksterhuis's essays have been selected which highlight his main themes, in particular his interest in the interconnectedness of the arts and the sciences, and in the mathematization of nature which he regarded as the key element in the development of modern science. The editor, Klaas van Berkel, has written a short introduction and a few explanatory endnotes for each essay. He has also modernized the Dutch spelling and syntax, but this does not diminish Dijksterhuis's fluid and lucid style in any way. It is a pity that this can only be appreciated by readers of Dutch, but then most of the material was written for a Dutch audience. The essays are grouped under four broad headings: Mathematics as Cultural Element; Mathematics in Science; Two Important Examples (Galileo's support of Copernicus and the life of Simon Stevin), and History of Science as Bridge Between the Two Cultures. The essays range from Greek mathematics to the purpose and method of the exact sciences. The clever title of the book,

*'Clio's Stepchild'*, is borrowed from the essay in which Dijksterhuis voiced his dissatisfaction with the Dutch educational establishment for treating history of science as the Cinderella of history. Clio, one of the nine muses in Greek mythology, is the patron of history.