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I see in many essays about Newton's Principia how it was very difficult to read and follow, so I was wondering if any of you know of any quotes from mathematicians of the time to that effect.

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It would probably not have been easy for a contemporary mathematician to formulate a direct critique that Newton was difficult to understand without also 'reflecting' unwanted discredit on the skill or level of understanding of the critic. I can't recall seeing such a direct critique, but what can be found perhaps more easily are statements pointing more-or-less indirectly to an early reputation of the 'Principia' for difficulty. Material of this kind from Newton's lifetime, or subsequent decades, includes statements of three sorts:

1 * A-B comparison with a conclusion about which presentation is 'easier': Under this heading (and perhaps nearest to a direct statement of the kind sought by the question), there is the preface to the Marquis de l'Hospital's 1696 book "Analyse des infiniment petits" (Infinitesimal analysis). The focus here is on the content of calculus in the 'Principia', as compared with Leibniz's calculus. The writer of the 1696 preface says:

"the learned M. Neuwton" ... "had found something similar to the differential Calculus, as appears by the excellent book entitled 'Philosophia naturalis principia Mathematica', which he gave us in 1687, of which almost all is of this calculus." ['lequel est presque tout de ce calcul']. "However, the notation of Mr. Leibnis makes his much easier and more expeditious ...".

Thus, by implication, Newton's Principia, at least in its presentation of matters related to the calculus, was being politely described as much more difficult.

2 * Anecdotes which might be enjoyably told by raconteurs without personally admitting any lack in their own understanding: Under this heading there is an anecdote of a remark supposedly overheard in Cambridge while Newton was there: "There goes the man that writt a book that neither he nor any one else understands." (recorded by John Conduitt, MSS at King's College, Cambridge, Keynes 130.6, 130.5, quoted by D T Whiteside (1970), J Hist Astron 1: 116.)

3 * Simplified explanations written ostensibly for students or 'for ladies', carrying indirect implication that some of the material was too difficult to include. Under this heading fall two books of the early 18th-c:

1720: Willem 's Gravesande (1688-1742) wrote an introduction to Newton's physics in which some of the more difficult mathematical material was omitted and replaced by description of experiments to illustrate relevant points ("Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam"; English translation by W T Desaguliers "Mathematical Elements of Natural Philosophy, Confirmed by Experiments; or, an Introduction to Newtonian Philosophy").

1739: "Il Newtonianismo per le Dame ... " ('Newtonianism for Ladies, ... Dialogues about Light, Colours, and Attraction') by Francesco Algarotti (mostly about Newton's optics, and less about the supposedly more difficult gravitation).

One should also mention a statement by Newton himself. His introduction to Book 3 of the Principia included often-quoted remarks that easily attract criticism that his presentation was deliberately made hard to understand:

"I composed an earlier version of book 3 in popular form, so that it might be more widely read. But those who have not sufficiently grasped the principles set down here will certainly not perceive the force of the conclusions, nor will they lay aside the preconceptions to which they have become accustomed over many years; and therefore, to avoid lengthy disputations, I have translated the substance of the earlier version into propositions in a mathematical style, so that they may be read only by those who have first mastered the principles." (from I B Cohen's 1999 translation of the Principia, at page 793.)

(The early version 'in popular form' and presumably easier to understand had been written in 1685 by Newton: it was superseded but not destroyed, and was retrieved and published after his death, both in Latin, and also in English as Newton's 'System of the World' (1728, 1731, 1740).)

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  • $\begingroup$ Thank you very much, that is very helpful, I'm trying to write an essay on how Euler's theory of mechanics is an improvement on Newton's. I saw a comment on an essay saying that including quotes from Euler or Clairaut’s on how difficult the Principia is to read would be useful evidence so I was wondering if there was anything from those two in particular. If not I will use one of the sources you suggested $\endgroup$ – Bradley Hill Oct 22 '17 at 19:33
  • $\begingroup$ I doubt you'll find Euler or Clairaut admitting they could not understand Newton. Their time was one of great sci/math rivalries and they could not afford to lose face. Clairaut claimed to understand and criticize Newton even where his critique was very arguably incorrect. Newton's antique and geometrical style seems to have put them off and may have inhibited them from reading in full. $\endgroup$ – terry-s Oct 22 '17 at 20:09
  • $\begingroup$ Euler's mechanics was 'Newtonian' with supplements, Euler made important improvements in handling trigonometry and calculus (see V J Katz 1987 Hist.math v14 311-324), and second some improvements in theory of motions of extended massive bodies (inertia, rotations &c), but the latter were pioneered before Euler by d'Alembert's work on precession and nutation of the earth's axis ('Recherches sur la precession des equinoxes...' 1749). Some modern studies credit Euler with perceptions actually in Newton; Euler may have reached them independently without fully reading Newton. $\endgroup$ – terry-s Oct 22 '17 at 20:09

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