I sent you by last tuesdays Post the last sheet of ye Principia, & told you that the cut for ye Comet of 1680 was going to be rolled off. But we want the page where it is to be inserted in the book. I think ye page is 462 or 463. Pray send me wch it is, that it may be graved upon the Plate for directing the Bookbinder where to insert it. I am Yor most humble Servant

London 5 March 1713.

IS. NEWTON

I have Sr Isaac's Leave to remind you of what You and I were talking of, An alphabetical Index, & a Preface in your own Name; If you please to draw them up ready for ye press, to be printed after my Return to Cambridg, You will oblige

I received both Your Letters with the last sheet of the Book inclosed in the former of them. The Paragraph beginning with Cæterum Trajectoriam quam Cometa descripsit &c., which is in the 497th page of the former Edition, falls in the 465th page of the new Edition. This is the place to which I suppose You would refer the Cut for the Comet. I intend in a day or two to set about the Alphabetical Index. I will write to Dr Bentley concerning the Preface by ye next Post.

March. 8. 171

I am Sr. Your &c.

I received what You wrote to me in Sr Isaac's Letter. I will set about the Index in a day or two. As to the Preface I should be glad to know from Sr Isaac with what view he thinks proper to have it written. You know the book has been received abroad with some disadvantage, & the cause of it may easily be guess'd at. The Commercium Epistolicum lately publish'd by order of the R. Society gives such indubitable proof of Mr Leibnitz's want of candour that I shall not scruple in the least to speak out the full truth of the matter if it be thought convenient There are some peices of his looking this way which deserve a censure, as his Tentamen de Motuum Cœlestium causis*. If S1 Isaac is willing that something of this nature may be done, I should be glad if, whilst I am making the Index, he would be pleas'd to consider of it & put down a few notes of what he thinks most material to be insisted on. This I say upon supposition that I write the Preface my self. But I think it will be much more adviseable that You or He or both of You should write it whilst You are in Town. You may depend upon it that I will own it & defend it as well as I can if hereafter there be occasion.

I am Sr &c.

Newton had himself drawn up some strictures upon this piece, which were made use of by the editors of the Commercium Epistolicum (p. 97). See the paper entitled "Ex Epistola cujusdam ad Amicum," printed in the Appendix to this work.

Dear Sir,

LETTER LXXIX.

BENTLEY TO COTES.

At S Isaac Newton's March 12.

I communicated your Letter to St. Isaac, who happend to make me a visit this morning, & we appointed to meet this Evening at his House, & there to write you an Answer. For ye Close of your Letter, wch proposes a Preface to be drawn up here, and to be fatherd by you, we will impute it to your Modesty; but You must not press it further, but go about it your self. For ye subject of ye Preface, you know it must be to give an account, first of ye work it self, 2dly of ye improvements of ye New Edition; & then you have St. Isaac's consent to add what you think proper about ye controversy of ye first Invention. You your self are full Master of it, & want no hints to be given you: However when it is drawn up, You shall have His & my Judgment, to suggest any thing yt. may improve it. Tis both our opinions, to spare ye Name of M. Leibnitz, and abstain from all words or Epithets of reproch: for else, yt will be ye reply, (not that its untrue) but yt its rude & uncivil. St. Isaac presents his service to you.

For Mr. ROGER COTES Professor of

Astronomy at Trinity College in
Cambridg.

I am Yours

R. BENTLEY*

* The original of this Letter, which has been already printed in the Bentley Correspondence (p. 460), is in the possession of Dawson Turner, Esq., who has kindly furnished me with a new transcript of it.

I have received Dr Bentlys Letter in answer to that which I wrote to him concerning the Preface. I am very well satisfied with the directions there given, & have accordingly been considering of the Matter. I think it will be proper besides the account of the Book & its improvements, to add something more particularly concerning the manner of Philosophizing made use of & wherein it differs from that of Descartes and Others, I mean in first demonstrating the Principle it employs. This I would not only assert but make evident by a short deduction of the Principle of Gravity from the Phænomena of Nature in a popular way that it may be understood by ordinary readers & may serve at ye same time as a specimen to them of the Method of ye whole Book. That You {may} ye better understand what I aim at I think to proceed in some such manner. [Tis one of ye primary Laws of Nature, that all bodys persevere in their state &c. Hence it follows that Bodys which are moved in curve-lines & continually hindred from going on along the tangents to those curvelines must incessantly be acted upon by some force sufficient for that purpose. The Planets (tis matter of fact) revolve in Curve-lines, therefore. &c. [Again, tis Mathematically demonstrated that Corpus omne, quod movetur &c. Prop. 2 Lib 1, & corpus omne, quod radio &c. prop. 3 Lib 1. Now tis confess'd by all Astronomers that the Primary Planets about ye Sun & the Secondary about their respective primary doe describe areas proportional to the times. Therefore ye force by which they are continually diverted from the tangents of their Orbits is directed & tends towards their central Bodies; which force (from what cause soever it proceeds) may therefore not improperly be

call {ed} Centripetal in respect of the revolving Bodies & Attractive in respect of ye central ones. [Furthermore tis Mathematically demonstrated that. Cor. 6, Prop. 4. Lib. 1 & Cor. 1, Prop. 45, Lib. 1. But tis agreed upon by Astronomers that &c. or &c. Therefore the centripetal forces of the Primary Planets revolving about the Sun & of the Secondary Planets revolving about their Primary ones, are in a duplicate proportion &c. In this manner I would proceed to the 4th Prop of Lib. III & then to the 5th. But in the first corollary of this 5th Proposition I meet with a difficulty*, it lyes in these words [Et cum attractio omnis mutua sit] I am persuaded they are then true when the Attraction may properly be so called, otherwise they may be false. You will understand my meaning by an Example. Suppose two Globes A & B placed at a distance from each other upon a Table, & that whilst ye Globe A remaines at rest the Globe B is moved towards it by an invisible Hand; a by-stander who observes this motion but not the cause of it, will say that ye Globe B does certainly tend to the centre of ye Globe A, & thereupon he may call the force of the invisible hand the centripetal force of B & the Attraction of A since the effect appeares the same as if it did truly proceed from a proper & real Attraction of A. But then I think he cannot by virtue of this Axiom [Attractio omnis mutua est] conclude contrary to his sense & Observation that the Globe A does also move towards the Globe B & will meet it at the common centre of Gravity of both bodies. This is what stops me in the train of

* The difficulty raised by Cotes here affords an instance of the temporary haze which may occasionally obscure the brightest intellects. Compare the story told of Lagrange by Biot (Journal des Savants, 1837, p. 84): "Lagrange tira un jour de sa poche un papier qu'il lut à l'Académie, et qui contenait une démonstration du fameux Postulatum d'Euclide, relatif à la théorie des parallèles. Cette démonstration reposait sur un paralogisme évident, qui parut tel à tout le monde; et probablement Lagrange aussi le reconnut pour tel pendant sa lecture. Car, lorsqu'il eut fini, il remit son papier dans sa poche, et n'en parla plus. Un instant de silence universel suivit, et l'on passa aussitôt à d'autres objets."