## Isaaci Newton, Matheseos Professoris Cantabrigiensis, & Regiae Societatis Anglicanae Socii, Philosophiae Naturalis Principia Mathematica. Londoni, jussu Soc. Regiae, 1687, in 4.

Leipzig: Grossius and J.F. Gleditsch, 1688.

First edition of the important *Acta Eruditorum* review of the *Principia*. There were four reviews of the *Principia*, of which this is chronologically the third. It is “the most detailed and serious of the four reviews. It was comprehensive enough to provide many people in Europe without access to the *Principia *itself with a fairly full account of its contents” (Gjertsen, *Newton Handbook, *p. 472). The first review appeared in issue no. 186 of the *Philosophical Transactions*, January – March, 1687: “not only did [Edmund] Halley finance, edit, publish and distribute *Principia*, he also reviewed it, anonymously, in *P*[*hilosophical*]* T*[*ransactions*]. It is little more than a summary interspersed with expressions of praise” (*ibid*.). The second appeared in the issue of *Bibliothèque Universelle *of March 1688, consisting “of nothing more than the headings of the sections of Books I and II translated into French. There is also a summary of Book III, and an introductory paragraph ...” (*ibid*.). The final review was that in the *Journal des Sçavans*, August, 1688, in which “Newton’s hypothesis was dismissed as arbitrary, unproven and belonging to geometry rather than mechanics” (*ibid*.). The *Acta* review is anonymous, but “new evidence has recently enabled the author of this book review to be identified as Christoph Pfautz (1645-1711), a professor of mathematics at the University of Leipzig ... From the correspondence of [Otto] Mencke, the editor of the *Acta*, and from notes of his grandson, we may learn that Pfautz and Mencke were closely associated in many ways. They were members of the same ‘collegium’ in the university. Additionally, in 1684, five years before the publication of the *Principia*, Pfautz and Mencke went on a trip together to Holland and to England ... Pfautz was a logical choice to be the reviewer of the *Principia*. He was a professional mathematician interested in astronomy. He was also a close associate of Mencke, and was a regular reviewer of the *Acta *… Pfautz’s review achieved a special importance in 1689, when Lebniz referred to it in one of three articles he published in the *Acta*: the ‘Tentamen de Motuum Coelestium Causis’ (Essay on the Causes of the Motions of the Heavenly Bodies). In this work, Leibniz set forth an alternative explanation to Newton’s” (Cohen).

[Pfautz] “begins: ‘It has seemed best to the distinguished author, a first-rate mathematician of our time, to emulate the zeal and industry of the ancients and moderns together in promoting natural science, and to exhibit for the public good an outstanding example of it in this work of profound learning.’ He then proceeds to summarize Newton’s Preface, paraphrasing Newton’s definition of ‘rational mechanics’ as ‘the science of motions due to any forces, and of forces required for any motions.’ He follows Newton in observing that in the three books comprising the *Principia*, Newton ‘has undertaken to discuss matters relating to gravity and levity, elastic force, the resistance of fluids, and other forces of this sort – whether attractive or repulsive – and indeed the motion of bodies.’ He then says that Newton has applied these principles and ‘general propositions’ to ‘a clear model of the system of the world’, setting forth ‘by what forces of gravity bodies tend toward the sun and toward the other planets, in agreement with the celestial phenomena, and how the motions of the planets, moon, comets, and the sea follow from this.’

“Continuing with his summary-paraphrase, Pfautz turns to the Definitions and Axioms. He mentions the definitions given by Newton of ‘quantity of matter and of motion’, of the ‘inherent [or innate], impressed, and centripetal force’. He does not give the reader either extracts of paraphrases of Newton’s definition of these quantities, nor does he comment on their possible novelty or originality, but merely echoes Newton to the effect that these are among the ‘less commonly used terms’ and therefore are to be defined. He then summarizes the scholium on space and time, stressing Newton’s distinction between ‘relative’ or ‘measured’ and ‘absolute’ quantities. No critical comments are made concerning Newton’s views on absolute and relative space and time.

“The ‘Axioms’ or ‘Laws of Motion’ are treated at greater length. Each of the three laws of motion is quoted as are the corollaries. Thus the parallelogram law is stated and also Newton’s result that ‘the common center of gravity of all bodies acting on one another (external actions and impediments excluded) either is at rest or moves uniformly straight forward’. The scholium following the laws is paraphrased at great length.

“It is evident that Pfautz is making a careful and complete paraphrase or summary or ‘epitome’ (as we shall see Newton call it) of the *Principia*, much like an extended and detailed table of contents. This is his method, once again, in dealing with Section One, on ‘first’ and ‘last’ ratios, where he paraphrases each of Newton’s lemmas concerning limits and also Newton’s statements concerning the reasons why he has rejected the method of indivisibles. As a trained practicing mathematician and a university teacher of mathematics, Pfautz was able to grasp the principal features of Newton’s treatment of limits and to appreciate the significance of the purely mathematical features of Newton’s presentation.

“This brings Pfautz to Section Two and Proposition 1, the beginning of Newton’s development of rational mechanics. On this score Pfautz says he had ‘decided to present to the reader’ the arguments of the first two books ‘arranged in order’, and with ‘as much abridgement as possible.’ But, as he was ‘making a synopsis of this material, which extends through various categories and relations of bodies and motions combined with one another in various ways,’ the ‘writing grew to such a bulk that it far exceeded the limit which I had set for myself.’ And thus he ‘had to fear that the annoyance caused to the reader by such a long description of general propositions, so varied and not adapted to concrete things, … might be greater than the loss caused by a disconnected review skimming only the main topics.’

“From this point on, the presentation takes on more of a general summary character, in which Pfautz will not present the content of the *Principia *proposition by proposition and section by section. Adopting this more general tone, Pfautz observes that in the first two books ‘motions of bodies of every kind are discussed – spherical and non-spherical, ascending and descending, projected, pendulous, fluid, and agitated by any kind of forces; motions in a straight line, in curved lines; motions circular, spiral, in conic sections – concentric with the center of forces and eccentric – in moving or unmoving orbits; progressive motions; motions propagated through fluids; likewise the centripetal, absolute, and accelerative forces of motions; times, velocities, and the increase and decrease of the latter; centers, areas, places, apsides, spaces, mediums, and the densities and resistances of mediums.’ These, we are told, are all ‘set forth in an investigation worthy of so great a mathematician.’ Pfautz adds that interspersed among the propositions there are important lemmas on geometry, especially the geometry of conics, and also scholiums giving ‘philosophical’ (i.e., physical) examples of the abstract mathematical principles being expounded so that the latter will not appear sterile.

“Following an extended summary of the many different topics explored by Newton, Pfautz reaches the conclusion of Book Two. He fully appreciates the significance of Newton’s demonstration that the speed of planets in their orbits, moving ‘more slowly in their aphelia and more swiftly in their perihelia’ is ‘the opposite of what ought to happen according to the mechanical laws of vortices.’ He apparently can find no fault with Newton’s ringing conclusion that the planetary speeds in Cartesian vortices contradict the celestial phenomena, even though he does not comment on the significance of the dreadful blow that Newton has dealt to Cartesian physics …

“Turning to Book Three, Pfautz observes that Newton ‘lays down as foundation for the book’ a set of ‘hypotheses, partly physical, partly relying upon astronomical observations.’ After summarizing these ‘hypotheses’, he gets to the heart of Book Three. Here, he says, Newton uses these astronomical data and the mathematical results of the first two books to ‘demonstrate that the forces by which the circumjovial planets, the primary planets, and the moon are continually drawn off from their rectilinear motions and kept in their orbits are from their gravitation toward Jupiter, the sun, and the earth, and are reciprocally as the squares of the distances from the center of Jupiter, of the sun, and of the earth; that all bodies gravitate toward each of the planets, and that their weights toward any single planet, at equal distances from the center of the planet, are proportional to the quantity of matter in each one (from which he further infers that the weights of bodies do not depend upon their forms and textures, that a vacuum is necessarily given …).’ Here is an admirable summary statement of some of the principal new aspects of the Newtonian system of the world …

“Pfautz carefully drew out of Newton’s text not only the primary features of Newton’s system of the world but also many important details of Newton’s presentation. These include Newton’s results concerning the relative densities of the planets, the motions of the planets, the shape of the earth as an oblate spheroid, the precession of the equinoxes as a gravitational consequence of the earth’s shape, the variation in weight with latitude, the inequalities of the motion of the moon explained by gravitational forces, and the ebb and flow of the sea also explained.

“The review ends with a number of pages summarizing Newton’s findings about comets. Here is a portion of Pfautz’s summary in his own words. ‘Concerning comets: that they are higher than the moon (the evidence being the lack of diurnal parallax) and they are in the region of the planets (their annual parallax proving this). He infers that the comets shine with light reflected from the sun and that in the circumsolar region many more are seen than in the region opposite the sun. Further, from their motions, in every way very free, preserved for a very long time even contrary to the motions of the planets, he concludes that the aether has no resistance … He concludes that comets are a kind of planet, returning by continual motion into orbit and that they move in conic sections (ellipses but so like a parabola that parabolas can be used in their place without sensible error) having their focus in the center of the sun and that by radii drawn to the sun they describe areas proportional to the times.’ Pfautz observes that Newton found ‘an analogy with the planets’ in that those comets ‘are smaller which revolve in orbits that are smaller and closer to the sun’” (*ibid*.).

As already mentioned, Leibniz referred to Pfautz’s review in his article ‘Tentamina de Motuum Colestium Causis’, published in the *Acta* a year after the review. “Leibniz explained that while in Rome he had ‘come upon an account of the celebrated Isaac Newton’s Mathematical Principles of Nature’ in the June 1688 issue of the *Acta*. Although the topic of the causes of celestial motions was at that time ‘far removed from my present line of thought’, he wrote, his reading of the account of Newton’s book recalled to mind some work he had done in Paris twelve years earlier. At that time he had decided not to publish his ideas on this subject, waiting until he could have the opportunity ‘to make a more careful comparison of the geometrical laws with the most recent observations of astronomers.’ But now, after reading about Newton’s work, he had been stimulated to write up and publish his own very different explanations … Newton never believed that Leibniz’s theorem, published in the *Acta* in 1689, had truly been found earlier and independently of the *Principia*. In fact, he even declared that Leibniz’s theorems ‘(Errors and Trifles excepted) are Mr. Newton’s (or easy Corollaries from them).’ In another document, in which Newton referred to Pfautz’s review as ‘an epitome’ of the *Principia*, Newton said that Leibniz read the review and then proceeded to compose the three essays for the *Acta* ‘as if he himself had discovered the principal propositions of Newton concerning these matters, and had done so by a different method, and had not yet seen Newton’s book’ … For two centuries there had been no way of telling whether or not Leibniz had actually seen the *Principia* before writing his three articles, whether or not he had derived his information about Newton’s results exclusively from Pfautz’s review … More recently, however, the profound investigations of Domenico Bertoloni Meli have uncovered some hitherto unnoticed notes by Leibniz. By a combination of careful analysis and deep historical insight, Bertoloni Meli has been able to identify these notes, to assign a date to them, and to determine their significance. They leave no doubt that Leibniz had been carefully reading the *Principia *before writing and publishing the three articles in the *Acta*” (*ibid*.).

This volume of the *Acta* also contains three articles by Denis Papin (1647-1713) in which he outlines a new method of transmitting power from one point to another by means of an air-pump; two articles by the astronomer Gottfried Kirch (1639-1710) in which the *Sceptrum Brandenburgicum*, a star constellation, is first described; and three articles by Jakob Bernoulli (1655-1705).

Bernard Cohen, ‘The review of the first edition of Newton’s *Principia *in the *Acta Eruditorum*, with notes on the other reviews,’ pp. 323-336 in: *The investigation of difficult Things. Essays on Newton and the History of the Exact Sciences*, 1992. Not in Babson or Wallis.

Pp. 303-315 in: Acta Eruditorum Anno M DC LXXXVIII publicata… 4to, pp. [viii], 672, [viii], with 13 engraved plates. Contemporary vellum, manuscript title on spine (small stamp to title page and library label to front paste-down, deaccessioned).

Item #4463

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Price:
$6,000.00
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