A CATALOGUE OF THE POETSMOUTH COLLECTION OF BOOKS AND PAPERS WRITTEN BY OR BELONGING TO SIR ISAAC NEWTON C. J. CLAY AND SONS, CAMBEIDGE UNIVEBSITY PKESS WAEEHOUSE, AVE MARIA LANE. DEIGHTON, BELL, AND CO. F. A. BEOCKHAUS. A CATALOGUE OF THE PORTSMOUTH COLLECTION OF BOOKS AND PAPERS WBITTEN BY OB BELONGING TO SIE ISAAC NEWTON THE SCIENTIFIC POKTION OF WHICH HAS BEEN PRESENTED BY THE EARL OF PORTSMOUTH TO THE UNIVERSITY OF CAMBRIDGE DRAWN UP BY THE SYNDICATE APPOINTED THE Qth NOVEMBER 1872 CAMBRIDGE AT THE UNIVERSITY PRESS 1888 CAMBRIDGE: PRINTED BY C. J. CLAY,' M.A. AND SONS, AT THE UNIVERSITY PRESS. CONTENTS. PKEFACE . . . . . ix APPENDIX TO PREFACE , . . . . xxi CATALOGUE. SECTION I. PAGE MATHEMATICS. I. Early papers by Newton ........ 1 II. Elementary Mathematics . ...... . . .2 III. Fluxions . . , '..... . . . ib. IV. Enumeration of Lines of the Third Order ... . . ib. V. On the Quadrature of Curves . ' . . . . : .3 VI. Papers relating to Geometry . . . . ' . , . . . ib. VII. Miscellaneous Mathematical subjects . . '. . . .4 VIII. Papers connected with the' Principia.' A. General . . . ib. IX. B. Lunar Theory . . 5 X. C. Mathematical Problems 6 XI. Papers relating to the dispute respecting the invention of Fluxions . . . . . . . '. . . . ib. XII. Astronomy . . *. . ... . .. .'. 9 XIII. Hydrostatics, Optics, Sound, and Heat . . . . . ib. XIV. Miscellaneous copies of Letters and Papers . . ... .10 XV. Papers on finding the Longitude at Sea ib. SECTION II. CHEMISTRY. *I. Parcels containing Transcripts from Alchemical authors . . 11 *II. Papers on Alchemy .... .... 18 *III. Books on Alchemy . ...... 19 IV. Notes of Experiments . . . . . . . . ib. V. Miscellaneous Notes . r 20 VI. A MS. Note-book ' . .2] * These have been returned to Lord Portsmouth. 253259 VI CONTENTS. * SECTION III. PAGE CHBONOLOGY . . . ' . .25 * SECTION IV. HISTORY . . . . 26 * SECTION V. MISCELLANEOUS PAPERS, chiefly on Theological Subjects . . . .29 SECTION VI. LETTERS. I. Correspondence with Oldenburg 32 II. Correspondence with Collins and Wallis ib. III. Letters of A. Storer to Dr Babington and to Newton . . .33 IV. Correspondence with Flamsteed 34 V. Letters of Gregory to Newton 35 VI. Letters from Halley to Newton on the first publication of the ' Principia ' ib. VII. Letters of Halley to Newton about Comets' Orbits . . .36 *VIII. Letters of Halley to Newton and Molyneux, relating to the Chester Mint ib. IX. Letters from Cotes to Newton on the 2nd edition of the 'Principia' 37 X. Hough drafts of some of Newton's Letters to Cotes . .38 XI. Letters of Keill to Newton 39 XII. Letters of Pemberton to Newton while editing the 3rd edition of the ' Principia ' ib. *XIII. Letters of N. Facio Duillier to Newton and others . . . 40 *XIV. Miscellaneous Letters ib. *XV. Copies of Newton's Letters, published in the Macclesfield Cor- respondence 45 SECTION VII. BOOKS. [Some of these have been returned to Lord Portsmouth.] . . 46 SECTION VIII. MISCELLANEOUS PAPERS. [Some of these have been returned to Lord Ports- mouth.] .49 * These have been returned to Lord Portsmouth. CONTENTS. Vll SECTION IX. PAGE Correspondence, Articles of Agreement, &c., about the publication of Flamsteed's Observations 51 * SECTION X. I. Correspondence between Conduitt and Fontenelle about the Eloge 52 II. Conduitt's Memoirs of Newton ib. III. London Gazette with account of Newton's funeral . . . ib. * SECTION XI. Drafts of Fragments of Conduitt's intended Life of Newton . . . .53 * SECTION XII. Letters and Memoranda relating to Newton after his death . . . .54 * SECTION XIII. Papers on Newton's family matters and on the Mint . . . . .55 * SECTION XI Y. Books and Papers not by Newton . . . . . -.. . .55 * SECTION XV. Complimentary Letters to Newton from distinguished foreigners . . .56 * These have been returned to Lord Portsmouth. PREFACE. IT has been long known that Sir Isaac Newton left, at his death, a large mass of papers, consisting partly of copies of his works written out or corrected for the press, partly of notes relating to the various subjects in which he was interested, and of an extensive correspondence with English and Foreign mathematicians. These came immediately on his death into the possession of Mr Conduitt, who married Catharine Barton, Newton's favourite and accomplished niece. By the marriage of their only child to the first Lord Lymington, they passed into the hands of the first Lord Lymington, and we find them in October 1751 in the hands of Mr Saunderson of Sheer Lane, for Lord Lymington 1 . Since that time they have remained in the possession of the Portsmouth family. Several years ago the present Earl of Portsmouth expressed a wish to present to the University all that portion of the papers and correspondence which related to science, as he felt that these would find a more appropriate home in the Library of Newton's own University than in that of a private individual. Lord Portsmouth entrusted the whole collection of papers to the University, and the present syndicate was appointed to examine, classify, and divide them. This has proved a lengthy and laborious business, as many of the papers were found to be in great confusion mathematical notes being often inserted in the middle of theological treatises, and even numbered leaves of MSS. having got out of order. Moreover a large portion of the collection has been grievously damaged by fire and damp. The 1 See Stukeley's Memoirs (Surt. Soc., 1887) iii. p. 15. X PREFACE. correspondence, however, is in a very fair condition throughout, and had been arranged in an orderly manner. On receiving a preliminary report on the contents of the collection, Lord Portsmouth expressed a wish that the papers relating to Theology, Chronology, History, and Alchemy, should be returned to him at Hurstbourne, where they would be care- fully preserved. On account of his connection with the Newton family, Lord Portsmouth also naturally wished to have returned to him all the papers relating to private, personal, and family matters. These, however, are comparatively few, and not of much interest, with the exception of a short note from Newton's mother, written to him when a boy at College. Although till the present time the papers have never been thoroughly examined, they have been looked at and partially used by various persons since Newton's death. When that occurred (in 1727) Dr Pellett was appointed by the executors to examine them and to select such as he deemed fit for publica- tion. A rough catalogue of the papers is appended to a bond given by Mr Conduitt to the administrators of Newton's estate, in which he binds himself to account for any profit he may make by their publication. This list, with some remarks of Dr Pellett, will be found in Hutton's Mathematical Dictionary. All which Dr Pellett deemed fit to be printed were An Abstract of the Chronology in 12 half-sheets folio, and The Chronology of Ancient Kingdoms Amended in 92 half-sheets folio; and these were printed in 1728 under the care of Mr Conduitt. The whole collection was inspected by Dr Horsley, who edited in 1779 the well-known edition of Newton's works in five quarto volumes. He left a few unimportant remarks on some of the papers, but he made no use of them in his edition. It was again placed in the hands of Sir David Brewster, for his second and elaborate life of Newton in 1855; he made some use of the scattered mathematical notes and papers, and printed a considerable portion of the correspondence. The character of the collection will be made clear by the catalogue which is now put forth. It divides itself (excluding the correspondence) into the heads of Mathematics, Chemistry PREFACE. XI and Alchemy, Chronology, History, and Theology. Many of the Mathematical papers contain Newton's preparations for the Principia, and notes which spring out of questions that were started by his correspondents. It must be recollected that Newton practically gave up his mathematical studies after 1696, even the superintendence of the second edition of the Principia being given to Cotes, and thus that after this date there is little of value in these subjects ; and as most of what is contained in them, especially all that relates to the revision of the Principia, has been published, there is little to be found beyond what has already appeared. The case is different, however, with respect to the papers referring to three subjects, viz. 1st, the Lunar Theory, 2nd, the Theory of Atmospheric Refraction, and 3rd, the Determination of the Form of the Solid of Least Resistance. It is expressly stated by Newton himself that the Lunar Theory as given in his Principia is a mere specimen or fragment of the subject, intended to show how some of the more prominent lunar inequalities could be traced to the disturbing action of the Sun, and how their amounts could be calculated approxi- mately by theory. The only part which is developed with any fulness of detail is that relating to the inequality called the variation, and also that which treats of the motion of the node and the change of inclination of the orbit to the ecliptic. In a short scholium given in the first edition of the Principia, Newton mentions that by similar computations he has found the motion of the moon's apogee, and he states some of the numerical results which he has obtained, but he does not give the calculations themselves, as he considers them too complicated and not sufficiently accurate. In the second edition this short scholium is replaced by a long one, in which Newton states many of the principal results of the Lunar Theory, partly as found from theory alone and partly as deduced by combining his theory with observation ; but he confines himself to results alone, and does not give the method by which these results have been obtained. Unfortunately also, the statement given in the first edition, as to the result which Xll PREFACE. he had found by theory for the motion of the moon's apogee, is omitted in the new scholium. It is interesting to find among the papers on the Lunar Theory a good many containing Newton's calculations relating to the inequalities which are described in the above scholium. These papers are unfortunately very imperfect, and they have greatly suffered from fire and damp, but there is enough re- maining to give a general idea of Newton's mode of proceeding. The most interesting of these papers relate to the motion of the moon's apogee. Two lemmas are first established which give the motion of the apogee in an elliptic orbit of very small eccentricity due to given small disturbing forces acting, (1) in the direction of the radius vector, and (2) in the direction perpendicular to it. These lemmas are carefully written out, as if in preparation for the press, and they were probably at first intended to form part of the Principia. Next follows the application of the lemmas to the particular case of the Moon, in which the supposition that the disturbances are represented by changes in the elements of a purely elliptic orbit of small eccentricity would lead to practical inconvenience, and consequently Newton is led to modify that supposition. In the Principia he shows that if the moon's orbit be supposed to have no independent eccentricity, its form will be approxi- mately an oval with the earth in the centre, the smaller axis being in the line of syzygies and the larger in that of quadra- tures, the ratio of these axes being nearly that of 69 to 70. Now when the proper eccentricity of the orbit is taken into account, supposing that eccentricity to be small, Newton assumes that the form of the orbit in which the moon really moves will be related to the form of the oval orbit before mentioned, nearly as an elliptic orbit of small eccentricity with the earth in its focus is related to a circular orbit about the earth in the centre. He then attempts to deduce the horary motion of the moon's apogee for any given position of the apogee with respect to the sun, and his conclusion is that if C denote the cosine of double the angle of elongation of the sun from the moon's apogee, then the mean hourly motion of the PREFACE. Xlll moon's apogee when in that position is to the mean hourly motion of the moon as l + Jf<7 : 238^. The investigation on this point is not entirely satisfactory, and from the alterations made in the MS. Newton evidently felt doubts about the correctness of the coefficient ^ which occurs in this formula. From this, however, he deduces quite correctly that the mean annual motion of the apogee resulting would amount to 38 51' 51", whereas the annual motion given in the Astro- nomical Tables is 40 41f . The result stated in the scholium to the 1st Edition appears to have been found by a more complete and probably a much more complicated investigation than that contained in the extant MSS. The papers also contain a long list of propositions in the Lunar Theory which were evidently intended to be inserted in a second edition, upon which Newton appears to have been engaged in 1694. This list, together with the two lemmas on the motion of the apogee mentioned above, will be found in the Appendix. Halley inserted in the Philosophical Transactiom of 1721 a Table of Refractions by Newton, without giving any idea of the method of its formation. Kramp, in his Analyse des Refractions, published in 1799, investigates by a new and powerful analytical method the law of atmospheric refraction for rays in the neighbourhood of the horizon. On comparing his theoretical results with Newton's Table, he finds a remarkably close agreement, which is enough to show that the Table was also the result of theory, and therefore that Newton must have had some method of his own of solving the difficult problem of horizontal refraction. Nothing was known of this method, however, until the pub- lication of the correspondence between Newton and Flamsteed by Mr Baily in 1835. In a letter to Flamsteed, dated De- cember 20th, 1694 1 , Newton tries to explain the foundation of 1 Baily's Flamsteed p. 145. XIV PEE FACE. his theory of refraction by giving a theorem from which it is clear that Newton then understood how to form the differential equation to the path of a ray of light through our atmosphere. It is true that, for the sake of greater simplicity in this com- munication to Flamsteed, Newton restricts the enunciation of his theorem to the particular case where the density decreases uniformly as the height increases, but it is obvious from the form of'the enunciation of Newton's theorem that the method is general, provided that the differential of the density which is appropriate to any given law of diminution be employed in finding the corresponding differential of the refraction. In an interesting article in the Journal des Savants for 1836, M. Biot directs particular attention to this subject, and tries to repro- duce the method which Newton may be supposed to have employed in order to calculate his table of refractions. M. Biot closes his article in the following terms : "II est done prouve, par ce qui precede, que Newton a forme 1'equation differentielle exacte de la refraction pour les atmospheres de composition uniforme; qu'il Fa appliquee exactement au cas ou les densites des couches sont proportionelles aux pressions, ce qui rend leur temperature constante; et qu'enfm, pour ce cas, il a obtenu les vraies valeurs des refractions a toute distance du zenith, sans avoir eu besoin d'employer les integrations analytiques qu'il a du tres-vraisemblablement ignorer. II est done le createur de cette theorie importante de 1'astronomie physique, qui serait probablement aujourd'hui plus perfectionee, si Ton avait connu plus tot ses premiers efforts." Judging from Newton's account of the time which he employed in making these calculations, there must have been a considerable mass of papers devoted to them which have not been preserved. Fortunately, however, among the Portsmouth papers we find a detailed calculation of the refraction corre- sponding to the altitudes 0, 3, 12 and 30. In order to make this calculation the path of a ray of light through the atmosphere is divided into a number of parts subtending given small angles at the centre of the earth. Hence are found by the fluxional method quantities which are proportional to the refractions suffered by the ray in passing over the successive PREFACE. XV portions of the path, and from these the actual refractions in passing over these portions are derived by making the total horizontal refraction equal to the amount given by observation. It should be remarked that the above calculation requires an approximate knowledge of the path of the ray, whereas this path is at first unknown, and cannot be accurately determined without a knowledge of the refraction itself. Newton solves the difficulty by an indirect method, making repeated ap- proximations to the form of the path, and thus at length succeeding in satisfying all the required conditions. The papers show that the well-known approximate formula for refraction commonly known as Bradley's was really due to Newton. This formula is only applicable when the object is not very near to the horizon, but the method of calculation employed by Newton is equally valid whatever be the apparent zenith distance. It is well known that in the Principia Newton determines the form of the solid of least resistance, thus affording the first example of a class of problems which we now solve by means of the Calculus of Variations. He there gives what is equivalent to the differential equation to the curve by the revolution of which the above-named solid is generated, without explaining the method by which he has obtained it. Now among the Newton papers we have found the draft of a letter to a correspondent at Oxford, no doubt Professor David Gregory, in which Newton gives a clear explanation of his method, which is very simple and ingenious. The draft has no date, but from internal evidence it was probably written about 1694. A small part of the letter has perished but it is very easy to restore the missing portion. The letter will be found in the Appendix at the end of this preface. It may be remarked that a similar method is immediately applicable to the problem of finding the line of quickest descent. A great many of the Newton papers relate to the dis- pute with Leibnitz about the discovery of Fluxions or the Differential Calculus. They show that Newton's feelings were greatly excited on this subject, and that he considered that N. b XVI PKEFACE. Leibnitz had shown towards him in reference to it great unfairness and want of candour. Newton always maintained that Leibnitz was the aggressor in this dispute, and that he had, by his language in the Leipsic Acts, covertly accused him of plagiarism, whereas he might have known from the corre- spondence that formerly took place between them, that Newton's method was in his possession long before he himself became acquainted with the Differential Calculus. On the other hand Leibnitz, without avowing himself the author of the article in the Leipsic Acts, denied that it really bore the meaning attributed to it by Newton, and maintained that Newton had either been deceived by a false friend into imagining that he had been accused of plagiarism, or else that he was not sorry to find a pretext for attributing to himself the invention of the new Calculus, contrary to the avowal he had made in the Scholium in the 1st Edition of the Principia. From a paper by Leibnitz, which has been published by Dr Gerhardt, it appears that the article in the Leipsic Acts, of which Newton complained, was really written by Leibnitz, and it also seems probable that the ambiguity of its language was not unintentional. We cannot wonder, then, that Newton, firmly believing that Leibnitz had charged him with plagiarism, should have experienced a strong feeling of resentment, and should have been induced to retort the charge upon his accuser 1 . It was not unnatural that this embittered feeling should still survive even after the death of Leibnitz. , It is clear from these Portsmouth papers that Newton believed that Leibnitz, during his second visit to England in October 1676, had obtained access to his MS. entitled De Analysi per Equationes numero terminorum infinitas, which was in the hands of Collins, and that he had thus been materially assisted in discovering the Differential Calculus. This tract of Newton's is printed in full in the Commercium Epistolicum, and is there used merely in order to prove Newton's priority to Leibnitz. It is nowhere asserted or even implied in the Commercium that this tract of Newton had ever 1 In connection with this Newton makes the following quotation from Ovid : "Nee lex est justior ilia, etc." (Artis Amatorice, i. 656.) PREFACE. XV11 been seen by Leibnitz. There can now be no doubt, however, that Newton was right in thinking that Leibnitz had been shown this MS., since a copy of part of it, in Leibnitz's hand, has been found among the papers of Leibnitz preserved in the Royal Library at Hanover 1 . It is, of course, possible that at the time when this copy was taken Leibnitz was already acquainted in some degree with the Differential Calculus, but it is difficult to acquit him of a want of candour in never avowing in the course of the long controversy respecting the discovery of Fluxions, that he had not only seen this tract of Newton's, but had actually taken a copy of part of it. He must have seen, also, at the same time, that the MS. was an old one, and although it does not contain the pointed letters which Newton sometimes but by no means invariably employed to denote Fluxions, Leibnitz could hardly fail to see, if he was acquainted with the Differential Calculus, that the principle of Newton's method was the same as that of his own. It is repeatedly stated by Newton that what he claims is the first invention of the method, and that he does not dispute about the particular signs and symbols in which the method may be expressed. Again, he often states that although, in the sense which he employs, the method can have but one inventor, yet the method may be improved, and the improvements belong to those who make them. In some of these papers relating to the dispute with Leib- nitz, Newton gives us some interesting information respecting the times when several of his discoveries were made. Thus in a passage, which has been quoted by Brewster 2 , he states that he wrote the Principia in seventeen or eighteen months, begin- ning in the end of December 1684, and sending it to the Royal Society in May 1686, excepting that about ten or twelve of the propositions were composed before, viz. the 1st and llth in December 1679, the 6th, 7th, 8th, 9th, 10th, 12th, 13th and 17th, Lib. i, and the 1st, 2nd, 3rd and 4th, Lib. II, in June and July 1684. The following extract will give an idea of Newton's pro- digious mental activity at an earlier period of his life. 1 See Gerhardt, Mathem. Schriften Leibnitzens, i. p. 7. 2 Brewster's Life, Vol. i. p. 471. XV111 PREFACE. "In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve : and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666 ^ for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 2 1 found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 3 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposi- tion in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method." The above extract has been given here on account of its intrinsic interest, although in writing it so many years after 1 In 1666 Newton was in the 24th year of his age. 2 Probably this should be changed to 1679 and 1680. 3 Probably this should be changed to 1684 and 1685. PREFACE. XIX the events to which it relates, Newton appears to have made one or two mistakes of date, and probably for this reason has drawn his pen through the entire passage. Newton's manuscripts on Alchemy are of very little interest in themselves. He seems to have made transcripts from a variety of authors, and, if we may judge by the number of praxes of their contents which he began and left unfinished, he seems to have striven in vain to trace a connected system in the processes described. He has left, however, notes of a number of his own chemical experiments made at various dates between 1678 and 1696. Some of these are quantitative. Those of most interest relate to alloys. He mentions several easily fusible alloys of bismuth, tin and lead, and gives as the most fusible that which contains 5 parts of lead + 7 of tin + 12 of bismuth. He says that an alloy consisting of 2 parts of lead + 3 of tin + 4 of bismuth will melt in the sun in summer. The alloy which goes by his name is not in the proportions of either of these two ; but, as he states that tinglas (bismuth) is more fusible than tin, he could not have used pure metal. The note-book which contains the longest record of his chemical experiments contains also the account of a few optical and other physical experiments and the paper on the decussa- tion of the optic nerve published by Harris and from him by Brewster. Harris, according to Brewster, published from a copy in the Macclesfield Collection; but the copy seems to have been identical with that in this book, except that a paragraph at the end is omitted. Brewster overlooked the paper in this book, though he has quoted from other parts of the book. The Historical and Theological MSS. cannot be considered of any great value. A great portion of Newton's later years must have been spent in writing and rewriting his ideas on certain points of Theology and Chronology. Much is written out, as if prepared for the press, much apparently from the mere love of writing. His power of writing a beautiful hand was evidently a snare to him. And his fastidiousness as to the expression of what he wrote comes out very curiously in these XX PREFACE. papers; thus there are six drafts of the scheme for founding the Royal Society, seven drafts of his remarks on the chronology published under his name at Paris (which made him very angry), many of the Observations on the Prophecies, several of the scheme of mathematical learning proposed for Christ's Hospital, &c. The four elaborately bound volumes, containing ' the Chro- nology of Ancient Kingdoms Amended/ the Chronicle to the Conquest of Persia by Alexander, Observations on the Prophe- cies, and the treatise " De Mundi Systemate," are very remark- able specimens of their author's care in writing out his works, and of his beautiful handwriting ( vii. 2). They are all con- tained in Horsley's collection. It is believed that in the present catalogue nothing has been omitted, and that thus a very fair idea may be obtained of what occupied Newton's time throughout his life. The papers date from his earliest time, giving his accounts when first he began college life as a sizar of Trinity College, and his mathe- matical notes while still an undergraduate: and they continue till his death. All the papers or books which have been re- turned to Lord Portsmouth are marked with an asterisk * in the catalogue. Of the more important letters, which have not been retained by the University, copies have been taken by the permission of Lord Portsmouth, and these are retained with the portion of the MSS. presented by him to the University. In addition to this a copy of Brewster's Life of Newton has been placed with the collection, in which the letters there given have been carefully collated with their originals ; so that prac- tically the student of Newton's works has all the scientific correspondence at his command. H. R. LUARD. G. G. STOKES. J. C. ADAMS. G. D. LIVEING. CAMBRIDGE, 26 May 1888. APPENDIX TO THE PREFACE. IT may be interesting to give a few extracts from the Newton papers on some of the subjects which have been referred to in the above Preface. These relate to I. The form of the Solid of Least Resistance. Principia, Lib. II. Prop. 35, Schol. II. A List of Propositions in the Lunar Theory intended to be inserted in a second edition of the Principia. III. The motion of the Apogee in an elliptic orbit of very small eccentricity, caused by given disturbing forces. I. ON THE FORM OF THE SOLID OF LEAST RESISTANCE. LIB. II., PROP. XXXV. SCHOL., p. 326, 1st Ed. Draft of a Letter in Newton's hand, no doubt to Professor David Gregory, and probably written in 1694. SIR, I now thank you heartily both for the very kind visit you made me here and for the errata you gave me notice of in my book and also for your care of Mr Paget's business. The Lem. 1 in the third book I could not recover as tis there stated, but I have don't another way with a Demonstration, and altered very much the Proposition which follows upon it concerning the precession of the Equinox. The whole is too long to set down. The figure which feels the least resistance in the Schol. of Prop. xxxv. Lib. n. is demonstrable by these steps. XX11 APPENDIX TO THE PREFACE. 1. If upon EM be erected infinitely narrow parallelograms BGhb and MNom and their distance Mb and altitudes MN, BG be Mm + Bb . given, and the semi sum of their bases be also given and called s and their semi difference - - be called x : and if the 2i lines BG, bh, MN, mo, butt upon the curve nNgG in the points n, N, g, and G, and the infinitely little lines on and kg be equal to one another and called c, and the figure mnNgGB be turned about its axis BM to generate a solid, and this solid move uniformly in water from M to B according to the direction of its axis BM : m M the summ of the resistances of the two surfaces generated by the infinitely little lines Gg, Nn shall be least when gG qq is to nN n as BG x Bb to MN x Mm. For the resistances of the surfaces generated by the revolution of Gg and Nn are as and , that is, if and be called p and a. as and - and their summ P 9 BG MN . , , A , a . x , -- 1 - is least when the fluxion thereot p q BGxp MNxq nothing, or -- f = + - - . pp qq pp qq is p = Gcfi& = Bbwiid + ^^quad _ ss _ % sx + X x + cc and there- fore p "2sx + 2xx, and by the same argument q = 2sx + 2xx and BG x 2sx - 2xx MNx2sx+2xx BG x T^x MNxs+x therefore - - = - , or pp qq pp qq and thence pp is to qq as BG x s x to MN x s + x, that is, gG qq to nN qq as BG x Bb to MN x Mm. APPENDIX TO THE PREFACE. XX111 2. If the curve line DnNgG be such that the surface of the solid generated by its revolution feels the least resistance of any solid with the same top and bottom BG and CD, then the resistance of the two narrow annular surfaces generated by the revolution of the [infinitely little lines nN~\ and Gg is less then if the intermediate solid bgNM be removed [along CB without altering Mb, until bg comes [to BG], supposing as before that on is equal to Jig,] and by consequence it is the least that can be, and therefore gG qq is to nN qq as BG x Bb [is to MN x Mm]. *[Also if] gh be equal to hG so that the angle [gGh is 45 de s r ] then will Bb qq be [to nN qq as BG x Bb is to] MN x Mm, and by conse- quence BG qq is to GR qq as BG q is to MN x BR or BG q x BR is to GR^ [as GR to MN}. Whence the proposition to be demonstrated easily follows. But its to be noted that in the booke pag 327 lin. 7 instead of Quod si figura DNFB it should be written Quod si figura DNFGB, and that DNFG is an uniform curve meeting with the right line GB in G in an angle of 135degr. I have not yet made any experiments about the resistance of the air and water nor am resolved to see Oxford this year. But perhaps the next year I may. I had answered your letter sooner but that I wanted time to examin this Theorem and the Lem. 1 in the 3 d Book. I do not see how to derive the resistance of the air from the ascent of water. The reasoning which must be about it seems too complicate to come under an exact calculus, and what allowance must be made for the retardation of the water by the contact of the pipe or hole at its going out of the vessel is hard to know. II. LIST OF PROPOSITIONS APPARENTLY INTENDED TO BE INSERTED IN A 2ND EDITION OF THE PRINCIPIA. In Theoria Lunae tractentur hae Propositiones. 8 PROP. XXV. PROB. v. PAGE 434, PRINCIP. Orbem Lunae ad aequilibrium reducere. * If the altitude of the frustum of the cone spoken of in the preceding para- graph be infinitely small, the semi-angle of the cone becomes equal to 45. Hence when the total resistance is a minimum, the curve meets the extreme ordinate GB at an angle of 45. XXIV APPENDIX TO THE PREFACE. 5 PROP. XXVI. Aream orbis totius Lunaris in piano immobili descriptam mensi synodico proportionalem esse. 6 PROP. XXVII. Invenire distantiam mediam Lunae a Terra. 7 PROP. XXVIII. Invenire motum medium Lunae. I PROP. XXIX. In mediocri distantia Terrae a Sole invenire vires solis tarn ad perturbandos motus Lunae quam ad mare movendum. 2 PROP. Invenire vires Lunae ad mare movendum. 3 PROP. XXX. Invenire incrementum horarium areae quam Luna in orbe non excentrico revolvens radio ad terrain ducto in piano immobili describit. 4 PROP. XXXI. Ex motu horario Lunae invenire distantiam ejus a terra. 10 PROP. Invenire formam orbis Lunaris non excentrici. II PROP. Invenire variationem Lunae in orbe non excentrico. 9 PROP. Invenire aequationem parallacticam. 12 PROP. Invenire formam orbis Lunaris excentrici. 13 PROP. Invenire incrementum horarium areae quam Luna in orbe excen- trico revolvens radio ad terram ducto in piano immobili describit. 14 PROP. Invenire variationem Lunae in orbe excentrico. APPENDIX TO THE PREFACE. XXV PROP. Inveiiire aequationem parallacticam in orbe excentrico. PROP. Inveiiire parallaxim solis. PROP. Invenire motum horarium Apogaei Lunaris in Quadraturis con- sis tentis. PROP. Invenire motum horarium Apogaei Lunaris in conjunctione et oppositione consistentis. PROP. Ex motu medio Apogaei invenire ejus motum verum. De Sole. PROP. Invenire locum solis. Ex Solis motu medio et prostaphaeresi dabitur locus centri gravi- tatis Terrae et Lunae deinde ex hoc loco et parallaxi menstrua (quae in quadraturis Lunae est 20" vel 30" circiter) dabitur locus terrae cum loco opposite solis. PROP. Invenire motum Apheliorum. PROP. Invenire motum nodorum. Nodus orbium Jovis et Saturni movetur in piano immobili quod transit per nodum ilium & secat angulum orbium in ratione corporum in distantias ductorum inverse, id est in ratione equalitatis circiter, existente angulo quern hoc planum continet cum angulo orbis Jovis minore quam angulo altero quern continet cum orbe Saturni. Serventur forte inclinationes orbium omnium ad hoc planum, & quaerantur motus intersectionum quas orbes cum ipso faciunt et habebuntur motus planorum orbium respectu fixarum. PROP. Invenire perturbationes Orbis Saturni ab ejus gravitate in Jovem oriundas. XXVI APPENDIX TO THE PKEFACE. PROP. Invenire perturbationes Orbis Jovis ab ejus gravitate in Saturnum oriundas. PROB. In systemate Planetarum in venire planum immobile. A centre solis per orbes Planetarum ducatur linea recta sic ut si Planetae singuli in minimas suas ab hac linea distantias ducantur, summa contentorum ad unam lineae partem aequetur summa con- ten torum ad alteram; et haec linea jacebit in piano immobili quam proxime. Yel sic accuratius : Per solem et orbes Planetarum et commune centrum gravitatis eorum omnium ducatur linea recta sic ut si sol et semisses Plane- taram in minimis orbium ab hac linea distantiis ad utramque solis partem siti augeantur vel minuantur in ratione distantiarum verarum a centro solis ad distantias mediocres ab eodem centro, deinde ducan- tur in distantias suas ab hac linea : summa productorum ab una rectse parte et ab una etiam parte communis centri gravitatis, conjuncta cum summa productorum ex altera utriusque parte aequetur surnmae productorum reliquorum : jacebit haec recta in piano immobili, et hujusmodi rectae duae planum illud determinabunt. III. ON THE MOTION OF THE APOGEE IN AN ELLIPTIC ORBIT OF VERY SMALL ECCENTRICITY. From a somewhat mutilated MS. vihich seems to have been prepared for the press. LEMMA. Si Luna P in orbe elliptico QPR axem QE, umbilicos S, F habente, revolvatur circa Terram S et interea vi aliqua V a pondere suo in Terram diversa continub impellatur versus Terram; sit autem umbilicorum distantia SF infinite parva : erit motus Apogaei ab im- pulsibus illis oriundus ad motum medium Lunae circa Terram in ratione composita ex ratione duplae vis V ad Lunae pondus mediocre APPENDIX TO THE PREFACE. XXV11 P, et ratione lineae SE quae centre Terrae et perpendiculo PE inter- jacet ad umbilicorum distantiam SF. N D CAS. 1. Fingamus vires P & V non esse continuas sed singulis temporis particulis aequalibus et quam niinimis semel agere, agat autem vis utraque in P sintque irP particulae ellipseos quas Lima praecedente temporis particula descripsit. Pp particula ejusdem Ellipseos [quam Luna] per impulsum vis solius P absque impulsu vis V posteriore temporis particula describere deberet et PG parti- cula orbis novi quern Luna per impulsum vis utriusque V & P in loco P factum eadem posteriore temporis particula describit. Et erit angulus pPG ad angulum quern lineola pP cum lineola proximo ante appulsum Lunae ad locum P descripta et producta contineat, id est ad angulum PSG seu motum angularem Lunae ut vis V qua angulus prior genitus est ad vim ponderis P qua angulus posterior genitus est. Agatur Pf ea lege ut angulus fPG- complementum sit anguli SPG ad duos rectos et P/"transibit per umbilicum superiorem Ellipseos novae, et quoniam angulus FPp, (ex natura Ellipseos) complementum sit anguli SPp ad duos rectos, angulus FPf duiplo major erit angulojt?P6r, adeoque earn habebit rationem ad angulum PSG quam habet vis 2 V ad vim P. Sit f umbilicus iste superior, et in PF ac Pf demittantur perpendicula SK et Sk, quorum Sk secet ' PF in I. Et per ea quae in Prop. LIB. 1 ostensa sunt, erit PF ad SP + PF ut ellipseos XXviii APPENDIX TO THE PREFACE. latus rectum quod nominabimus L ad 2/SP + 2PK, et divisim PF ferit adl SP ut L ad 2SP + 2PK- L, seu PF aeq ualis .., * ,. r , -Z/jjT 4- 2iJrJ\. Li et [eodlem argumento Pf aequalis ^-^D ~^ -- 5^. Nam latus rectum quod sit (per Prop. Lib. 1. Princip.) in duplicata ratione arese quam Luna radio ad terrain ducto singulis temporis particulis describit, et quantitas arese illius per impulsum vis V nil mutetur, idem manet in Ellipsi utraque. Cum autem 2SP et L ob in- finite parvam distantiarn SF aequentur, deleatur 2SP L et erit FP aequalis -=-=. et Pf aequalis ^=- quarum differentia est Jr i\. 1 K seu IK. Est autem IK ad Ik ut SK ad Pk, ideoque (ob infinite parvam SF) est IK infinite minor quam Ik seu Ff, et propterea Ff perpendicularis est ad PK. Quare si jungatur Ef t anguli FEf & FPf, in segmento circuli per puncta P, E, F, f transeuntis con- sistentes, aequales erunt inter se. Ideoque cum angulus FSfsit ad angulum FEf ut FE vel SE ad FS seu 20 S, et angulus FPf supra fuerit ad angulum PSG ut vis 2V ad vim P: erit ex aequo angulus FSf ad angulum PSG, id est motus Apogaei ad motum medium Lunae ut 2V*SE ad PxSF seu VxSE ad PxOS. Concipe jam numerum impulsuum augeri et intervalla diniinui in infinitum ut actiones virium V et P reddantur continuae et constabit Propositio. Q.E.D. COROL. Valet Propositio quam proxime ubi excentricitas finitae est magnitudinis, si modo parva sit. LEMMA. Si Luna P in orbe Elliptico QPR axem QR et umbilicos S, F habente revolvatur circa Terram, et interea vi aliqua W a pondere suo diversa secundum lineam distantiae SP perpendicularem impella- tur ; sit autem excentricitas OS infinite parva : erit motus Aphelii J ab impulsu illo oriundus ad motum medium Lunae in ratione composita ex ratione quadruplae vis W ad pondus P et ratione perpendiculi PE ad excentricitatem OS. 2 1 This should be Apogasi. 2 This should be umbilicorum distantiam SF. APPENDIX TO THE PREFACE. XXIX CAS. 1. Distinguatur enim tern pus in particulas aequales et quam minimas, et agat vis W non continue sed singulis temporis particulis semel. Sit autem T velocitas Lunae [in] P ante impulsum vis W ibi factum et t incrementum [velojcitatis ex impulsu et L latus rectum Orbis Lunaris ante [impulsum]. Et quoniam area quam Luna radio ad Terrain [ducto singulis temjporis particulis aequalibus describit, sit ante impulsum ad eandem aream post im- pulsum ut T ad T + t, et latus rectum (per Prop. xiv. Lib. i. Princip.) sit in duplicata ratione arese, erit (per Lem. Lib. n. Princip.) fjl . o^ O/ L seu L + ^= L latus rectum post impulsum. Est autem (ut in Lemmate superiore) ^-^ ^^ T longitude PF qua Luna distabat A&jT 4- ArJi. Li ab umbilico superiore ante impulsum ; et propterea cum situs lineae PF, si modo excentricitas SF infinite parva sit, ex impulsu illo nil mutetur, ideoque PK maneat eadem quae prius et solum L mutetur, si producatur PF ad ut sit umbilicus superior post impulsum; erit Pcf> aequalis 9 . De hac longitudine subdu- catur longitude ipsius PF superius inventa, nempe -~p- 2SP+2PK-L' et interea in utraque pro 2SP + ZPK scribatur 2L & nianebit differentia F aequalis SP seu SP. Unde longitude per- pendiculi g quod in diametrum QR ab umbilico (f> demittitur, erit 4t PE. Jam vero in Lemmate superiore, velocitas quam vis V impulsu unico generare potest, est ad velocitatem Lunae ut lineola pG quam Luna vi impulsus illius dato tern pore describere posset ad lineolam Pp quam Luna velocitate sua data T eodem tempore descri- bat, id est ut Ff&d PF. 1 Ideoque si velocitas prior nominetur S erit 2SxPF Ff aequalis ^ - ob angulum FPf anguli GPp duplum, et per- pendiculum fJi quod ab umbilico f in ellipseos axem QR demittitur o & aequale -= EF. Proinde cum angulus SF sit ad angulum FSf ut g ad fh, et angulus FSf ad angulum PSp ut V x SE ad P x OS, 1 This should be pG ad Pp. XXX APPENDIX TO THE PREFACE. erit angulus SF ad angulum PSp, hoc est motus Apogaei a vi W genitus ad niotum medium Lunae ut -= PE ad EF et V x SE ad P x OS conjunctim, id est (ob aequales EF ad SE et proportionales t & S, W & V) ut 2W x PE ad P x OS. Q.E.D. COROL. Obtinet etiam Propositio quam proxime ubi [quam minima sit] excentricitas etiamsi non sit infinite parva. SECTION I. MATHEMATICS. I. EARLY PAPERS BY NEWTON. (Holograph.) 1. Extracts by Newton From Hooke's Micrographia, From the History of the Royal Society, From the Philosophical Transactions. Notes of some Mines in Derbyshire and Cardiganshire. 2. Scraps and Extracts made by Newton, including two little notes on tangents arid musical semi-tones. 3. A tract in English written in 1666, entitled "To resolve pro- blems by Motion." Also short tracts entitled De Solutione Problematum per Motuin. De Gravitate Conicarum. Problems of Curves. 4. Calculation of the Area of the Hyperbola. 5. On the Laws of Motion. On the Laws of Reflection. On Motion in a Cycloid. 6. Problems in Geometrical Optics. N. 2 CATALOGUE OF NEWTON PAPERS. II. ELEMENTARY MATHEMATICS. (Holograph.) 1. Observations on the Algebra of Kinckhuysen. 2. The first Ten Propositions of the 2nd book of Euclid, suc- cinctly enunciated and demonstrated. 3. Theorem on the Area of a Triangle. 4. Trigonometria succincte proposita et nova methodo demon- strata a S* Joanne Hareo Arm. 5. A few MS. leaves, containing Compendium Trigonometriae. It includes Spherical Trigonometry. Intended for learners. 6. Table of sines to every half degree. III. FLUXIONS. 1. Transcript of a Tract on Fluxions said to have been written by Newton in November, 1666. 2. Tract relating to the History of Fluxions, transcribed from one which was probably written by Jones. 3. Part of Newton's method of Fluxions and Infinite Series, with a fragment of the same treatise. (Holograph. ) 4. Part of a Tract on Fluxions. 5. Some Propositions in Fluxions. ["I think this fragment very proper to be published." Horsley, Oct. 22, 1777.] 6. Analysis per quantitates fluentes et eorum momenta. 7. Method of Fluxions and Infinite Series. 8. On the solution of Fluxional Equations. 9. Fluxions applied to Curves. 10. Propositions in the Method of Fluxions (dotted letters em- ployed). 11. Propositions in Fluxions (dotted letters employed). 12. An early paper on deducing the subnormal in a curve from a given rational relation between x and y, and the converse operation. 1 3. Fragments on Fluxions. 14. Method of Curves and Infinite Series, and application to the Geometry of Curves. Complete all but the 1st leaf. IV. ENUMERATION OF LINES OF THE THIRD ORDER. (Holograph/ 1. An early copy. 2. A later copy. SECTION I. MATHEMATICS. 6 3. On the curves of the third order, produced by the projections of the Parabola Neiliana. 4. Fragments concerning lines of the third order, and some mis- takes of Descartes ["not worth publishing." S. Horsley, Oct. 23, 1777]. V. ON THE QUADRATURE OF CURVES. (Holograph.) 1. A copy which appears to be pretty complete. 2. A fragment on the same subject. 3. Scattered papers on the same subject, in great confusion 4. Another fragment on the same. 5. Note on Quadrature of Curves, intended as a Supplement to Section 10 of Book I. of the Principia. 6. Fragment on the Quadrature of Curves whose equations con- sist of but three terms. VI. PAPERS RELATING TO GEOMETRY. (Holograph.) 1. De Problematum resolutione Synthetica. 2. Geometria. Liber 1. A fragment. 3. Geometry, a fragment on Porisms. 4. Analysis Geometrica. Regula Datorum. 5. Newton's Regula Fratrum. 6. Fragment relating to Curves. 7. Geometria Curvilinea and Fluxions. 8. Scraps containing Propositions in Geometry ; viz. : (a) To describe a Conic Section through five given points ; and (b) To describe a Conic Section passing through two points and touching three given straight lines. 9. Tract on the construction of Equations, unfinished. 10. On the Properties of Curves. 11. Part of a Treatise on Geometry (in Latin). 12. De Compositione Locorum Solidorum. 13. Solutio Problematis Veterum de Loco Solido. 14. Fragments relating to the writings of the Ancients in general, but especially to the Porisms of Euclid, and the Loci of 12 4 CATALOGUE OF NEWTON PAPERS. Apollonius ["very curious and fit to be published." S. Horsley, Oct. 26, 1777]. 15. Remarks on the nature and objects of Arithmetic, Geometry, and Mechanics. 16. A fragment, relating to the Comparison of Curved Superficies. VII. MISCELLANEOUS MATHEMATICAL SUBJECTS. (Holograph, exc. 7.) 1. Problemata Numeralia. 2. Arithmetica Universalis. A chapter on the limits of the roots of equations (see p. 184 of Leyden Ed. of Univ. Arith. 1732). 3. De serierum proprietatibus. 4. On Quadrature by Ordinates. 5. Regula differentiarum &c. 6. Bernoulli's problem on drawing lines cutting a series of curves according to any given law. Phil. Trans. 1716. 7. Errata in Dr Barrow's Conicks and in his Archimedes, with a letter to Newton about the latter Errata. 8. Scraps of calculations. VIII. PAPERS CONNECTED WITH THE PRINCIPIA. (Mostly Holograph.) A. General. 1. Propositions on Elliptic Motion. 2. A fragment in which Fluxions are employed in finding the Centripetal force in an Orbit. 3. Propositions afterwards included in the Principia, but differently numbered. 4. A small fragment (early) of the Principia. 5. De Motu Corporum. 6. Propositiones De Motu Corporum. The references do not agree with the Principia. 7. Propositiones de Motu. Several copies differing somewhat from each other, of which one is printed in Rigaud's " Historical Essay" Appendix, No 1. 8. Corrections to copy of Propositions on Motion forming pro- bably an early draft of part of the Principia. 9. Proposed Corrections probably for 1st Edition of the Principia. 10. On the Resistance of fluids ; account of Hauksbee's experi- ments, with Newton's deductions ; chiefly rough notes. SECTION I. MATHEMATICS. 5 11. Revision of the Principia. Notes relating to Calculation of orbits of Comets. 12. Additions and Corrections to 1st Edition of the Principia. 13. Additions and Corrections to the 2nd Edition of the Principia. 14. Observations and Calculations about Comets. 15. Draft of part of the Preface to the 1st Edition of the Principia. Not quite as printed, in part fuller. 1 6. Preface and Preparations for 3rd Edition of the Principia. 17. Very rough fragments relating to the Principia. 18. Miscellaneous Calculations. 19. Corrections to 1st Edition of the Principia (terribly damaged by fire). 20. Dr Halley's account of the Principia given to K. James II. IX. PAPERS CONNECTED WITH THE PRINCIPIA. B. Lunar Theory. 1. Papers on the Lunar Theory found in interleaved copy of 1st Edition of Principia (damaged by fire). 2. Propositions prepared to be used in the Lunar Theory (greatly damaged by fire). 3. Fragments on the Lunar Theory (greatly damaged by fire). 4. Propositions in the Lunar Theory, found on loose sheets placed at the end of the interleaved copy of the 1st Edition of the Principia. These were probably intended to be employed in a 2nd Edition, but the design was not carried out. 5. Notes on the law of change of the Moon's variation according to the change of the Sun's distance; and on the mutual action of Jupiter and Saturn. 6. Unarranged fragments connected with points of the Lunar Theory. 7. On change of the variation in an excentric orbit, and on the motion of the Moon's Apogee. 8. A list of Propositions in the Lunar Theory, prepared for a 2nd Edition of the Principia, but not used. 6 CATALOGUE OF NEWTON PAPERS. 9. Propositions relating to the Lunar Theory, including a Scholium, differing from that inserted in the 2nd Edition. 10. On the Theory of the Moon. (Various statements of the principal points of this Theory.) 11. Propositions ' De motu nodorum Lunse,' prepared for the 3rd Edition of the Principia. 12. Motion of the Moon's Apogee. This consists of two Lemmas, prepared for press; two Propositions, in duplicate ; and an imperfect copy of one of these propositions, with a rough draft of an investiga- tion of the horary variation of the Inclination. The Propositions are not numbered, and therefore they were perhaps intended to be worked up for the 1st Edition. 13. Calculations for forming Lunar Tables. 14. Various Lunar Tables. 15. Comparisons of calculated places of the Moon with Obser- vations. X. PAPERS CONNECTED WITH THE PRINCIPIA. C. Mathematical Problems. 1. To find the True Anomaly from the Mean. 2. Fragment on the Solid of least resistance. 3. Atmospheric Refraction, with detailed calculation of the Refraction at the altitudes 0, 3, 12 and 30. 4. Altitudes by the Barometer. XI. PAPERS RELATING TO THE DISPUTE RESPECTING THE INVENTION OF FLUXIONS. 1. Apographum Schediasmatis a Newtono olim scripti, 13 Nov. 1665. 2. Printed Title-page of the 1st Edition of the Commercium Epistolicum, with proposed additions to the Title of the 2nd Edition. 3. Notes on the Correspondence in Wallis's Works, Vol. 3. 4. Notae ad Acta Eruditorum. 5. Rough drafts of the Leibnitz Scholium in the 2nd Edition of the Principia, and proposed additions to it. SECTION I. MATHEMATICS. 7 6. Enarratio plenior Scholii prsecedentis. 7. Mens Scholii prsecedentis. 8. An account of the Commercium Epistolicum (several vary- ing copies). 9. Papers relating to the origin of the Dispute. 10. Collations for the History of the Infinitesimal Analysis. 11. Fragment of "An account of the Differential Method from the year 1677 inclusively." 12. History of the Method of Fluxions. (Several copies with varying Titles.) 13. "Historia Methodi Infinitesimalis" (several varying copies), with Corrigenda to the English copy of the " Recensio" published in Phil. Trans. Jan., Feb., 1714-5. 14. Annotationes in Commercium Epistolicum. 15. Appendix containing Newton's proofs of his priority to Leibnitz, &c. (A fragment.) 16. Newton's Statement of the case in dispute between Leibnitz and himself. 17. Draft (holograph) of Newton's Letter to the Editor of Memoirs of Literature, May, 1712 (never published). (See Brewster, ii. 283.) 18. Copy in Newton's hand of Leibnitz's letter to Hans Sloan, 29th Dec., 1711. 19. References to the original letters contained, or intended to be contained, in the Commercium Epistolicum. 20. Latin translation (copy) of the Recensio given in Phil. Trans. No. 342, differing from that given in the Second Edition of the Commercium Epistolicum. 21. ' Ad Lectorem,' prefixed to the 2nd Edition of the Com- mercium Epistolicum. (Several drafts.) 22. Latin letter (copy) of John Keill to Hans Sloan. May, 1711. 23. Keill's letter (copy) to John Bernouilli, translated into French after July, 1716, with some notes on it in Newton's hand. 24. Extract from a letter of Leibnitz complaining of an attack on his " bonne foi." 25. Bernoulli's problem in the Acta Eruditorum for Oct. 1698. 26. Historical Annotations on the Elogium of Leibnitz. 8 CATALOGUE OF NEWTON PAPERS. 27. Several drafts of letters of Newton to Des Maizeaux after the death of Leibnitz. (Holograph.) 28. Remarks on Leibnitz's first Letter to the Abb6 Conti. 29. Proposed addition to the "Remarks" on Leibnitz's second Letter to the Abbe Conti after Leibnitz's death. (Des Maizeaux, Vol. 2, pp. 82-106.) 30. Drafts of a letter to a friend of Leibnitz (probably Cham- berlayne), defending Keill. Also copy of English translation of Leibnitz's letter to Chamberlayne (in Newton's hand). 31. Copy by Newton of Leibnitz's letter of 9th Ap. 1716, to De Monmort, and draft of Newton's Observations upon it given in Raphson's Hist, of Fluxions, App. p. 111. 32. Newton's observations on the Synopsis given in the Leipzic Acts of Jones's "Analysis per quantitatum Series," &c. (Lond. 1711). 33. Animadversions on Monmort's letter to N. Bernouilli, dated 20th Aug. 1713, and printed in the 2nd Edition of his Analysis upon the play of Hazard. 34. John Bernouilli's letter of 7th June, 1713, with Newton's Observations upon it. 35. Extract from Bernouilli's Notice of July, 1713 (the Charta Volans), and "Remarques sur la dispute entre Mons. Leibnitz et Mons. Newton," &c., with Newton's Observations upon them. 36. Contents of Des Maizeaux's Recueil, &c. Copies of letters which are published in Des Maizeaux's Recueil. 37. Several drafts of an intended Preface to the Commercium Epistolicum. 38. Letter of Newton to the Abbe Conti in reply to the Post- script of Leibnitz to the same. This letter refers to the 1st Postscript given in Des Maizeaux. 39. Draft of part of the "Account of the Commercium Epi- stolicum," &c., inserted in the Phil. Trans. 40. Errata in Raphson's History of Fluxions. 41. Unarranged fragments relating to the dispute with Leibnitz. 42. Drafts of Letters of Newton to Yarignon and others, relating to Bernouilli's Letter of 7 June, 1713, which had been disavowed by the writer. SECTION I. MATHEMATICS. XII. ASTKONOMY. 1. Astronomical communications from Flamsteed, including longitudes and latitudes of stars for 1686, and of 21 stars compared with the comet of 1680. 2. Lunar distances in 1677 and in 1685, by Flamsteed, with copies of these two papers, one by Newton. 3. Equations of Moon's Apogee. Table by Newton for Flamsteed. Elements of the Comets of 1472, 1580, 1585, 1652, 1661, 1665, 1672, 1677, and 1686, as calculated by Halley. 4. Eclipse Tables for a period of 18 years, by Halley. 5. Observations of Eclipses, sent to Newton from various quarters, with a diagram of the annular eclipse of 1686 * by E. de Louville (Paris). 6. Transits of Satellites of Jupiter and of their shadows across the disc of the planet, observed by Pound at Wanstead. 7. Table of Declinations of every 5 th degree of the Zodiac. XIII. HYDROSTATICS, OPTICS, SOUND, AND HEAT. 1. A treatise, with a table, on the Division of a Monochord. Not in Newton's hand, but apparently of his composition. Followed by an extract in his hand " out of Mr Sympson's Division Violist." 2. Scrap relating to the velocity of sound; also on the back a note on the proportionality of mass to weight. 3. Manuscript copy of Newton's Optical writings, and of con- troversies about them. 4. Latin draft of the Opticks, Book I., Part I. (1 sheet). 5. Answer to objections made to Newton's Optical Theories. Also a scrap with memoranda about the Newtonian telescope. 6. Scrap. Memorandum of observations on the colours of thick plates. 7. Fragments on Light and Heat. 8. Proposed addition to Newton's Opticks. On the Refraction, observed in Iceland Spar, and Note "to the Reader" relating to it. 10 CATALOGUE OF NEWTON PAPERS. 9. Fragments on Opticks. 10. Optical experiments. 11. Figure and description of a sheep's eye. Printed by Brewster i. 420. 12. Speculations as to the constitution of matter and the nature of the action of heat. XIY. MISCELLANEOUS COPIES OF LETTERS AND PAPERS. 1. Copies of Letters from Leibnitz, Slusius, &c. to Oldenburgh. 2. Copies of various Mathematical papers by Tschirnhausen, Leibnitz, Slusius, &c. 3. "Sur la Cubature du coin Spherique" par M. de Lagny. 4. Fragments on Mathematical subjects by Cassini, Craig, and Morland. XV. PAPERS ON FINDING THE LONGITUDE AT SEA. 1. Various proposals for finding the Longitude at Sea. 2. Several drafts of a Report by Newton to the Lords of the Admiralty on the different projects for determining the Longitude at Sea. 3. Draft of a letter by Newton on the same subject. 4. Two shorter drafts of the same letter. SECTION II. CHEMISTRY. *I. FIVE PARCELS CONTAINING TRANSCRIPTS FROM VARIOUS ALCHEMICAL AUTHORS IN NEWTON'S HANDWRITING, WITH NOTES AND ABSTRACTS. (1) 1. Notes out of Philalethes. 2. On Ripley's Vision; 'Sir G. Ripley his letter to K. Ed. IV. unfolded.' 3. 3 tracts. De metallorum metamorphosi, Brevis manductio ad rubinum cselestem, Fons Chemicse Philosophise. 4. Extracts from Raymond Lully. 5. an author unnamed. 6. various authors. 7. "Artephius, his secret book." 8. Basil Valentine; on the minerals of Hungary, Carinthia &c., and the conditions of their formation, and on the transmutation of metals and the separation of the three principles, and of vitriol. Jodochus a Rehe; Processes for preparing the Philosopher's / stone from MSS. in possession of Dr Twysden. Copies of 4 letters * from Faber to Dr Twysden, 1673 4, recounting success of ex- periments in preparing spirits of mercury. Notes on Faber's work. 9. Hermes. Tabula smaragdina et commentarium. 10. The same in English. 11. "The Epitome of the treasure of health written by Edvardus generosus Anglicus innominatus, who lived A. D. 1562." 12. Hadrian Mynsicht. Aureum seculum redivivum. Testa- mentum de philosophorum lapide. Both in hexameters. 12 CATALOGUE OF NEWTON PAPEKS. 13. Ex Turba philosophorum. 14. Preparatio Mercurii, ex MSS. Philosophi American!. 15. Liber Mercuriorum Corporum. On the back an explanation of the symbols in it. 16. 47 Alchemical recipes, the work of an old Priest, viz. B. 17. Ex Rosario magno. 18. Emblemata Michaelis Maieri, comitis Germani. 1 9. Of chemical authors and their writings. 20. Collectiones ex novo lumine chemico. 21. Ex codicillo R. Lullii (Colon. 1563). 22. Notes mythological and alchemical. 23. Account of furnaces, &c. 24. Extracts from Flamel and several other authors. 25. A page of references to a work not named. 26. Loca difficilia in novo lumine Chymico explicata. 27. Extracts: clavis aureae portse, medulla Alchemiae, de Lapide vegetabili, Pupilla Alchemise, &c. 28. Basil Yalentini Currus triumphalis antimonii. 29. Alphabetical explanation of common chemical words. 30. Miscellaneous references. ^ . 31. Abstract of a treatise on Nature's obvious laws and processes in vegetation. 32. 'Out of Schroder's Pharmacopoeia.' (2) 1. The book of N. Flamel, in English. 2. The metamorphoses of the planets, with two folios of notes which are in the nature of memoranda of points adverted to in the treatise. 3. Maier's tracts: Symbola aurese mensse duodecim nationum (an account of chemical writers in 1 2 books). Lusus serius. (On the medicinal virtues of mercury, tutty, &c.) Atalanta fugiens. Yiatorium. (A chemical interpretation of some parts of ancient mythology.) Septimana philosophica, 6 days, 7th day wanting. SECTION II. CHEMISTRY. 13- 4. Notanda chymica. Out of Maier (1 f.). 5. Regulse...de lapide philosophico authore anon, and Maier's figures prefixed to Valentine's keys (If.). 6. Ex Epistola Edm. Dickenson ad Theodoruin Mundanum (2 f.). 7. Tabula Smaragdina and other extracts. Hieroglypliica Plane- tarum (If.). 8. Extracts apparently from Van Helmont. On the 3rd page, last line but two, occurs "Terra juxta parallelos rotunda est, juxta meridianos ovalis. Hallucinatur." 9. Notes chiefly from Philalethes on Bipley. 10. On Bipley's gates (2 f.). 11. Kipley expounded (2f.). 12. Notes on Bipley (an abstract). 13. Thesaurus thesaurorum, in English (If.). 14. A key to Snyders. 15. Sententise notabiles expositse (If.). 16. Sententise luciferse et conclusiones notabiles (4 f.). A note relating to mint affairs on top of first page. 17. Practica Marise Prophetissse in artem Alchemicam (If.). 18. De igne sophorum et materia quam calefacit (1 f.) extr. from various authors. 19. Notanda chemica from various authors (If.). 20. De secreto solutionis (1 f.) from various authors. 21. The three fires. The work with sol vulgar. The several works (If.). 22. "Clavis." 23. Extracts from various authors, chiefly alchemical, but some notes also about the occurrence of minerals (1 f.). 24. Verses at the end of B. Valentine's mystery of the microcosm. 25. The standing of the glass for the time of Putrefaction. The hunting of the Green Lyon, in verse, with some notes by Newton. 26. "Pearce the black monck upon the Elixir" (verse). 27. "Out of Bloomfield's Blossoms, and a short work that beareth the name of Sir George Bipley." 28. Extracts from Norton's ordinal, Chaucer's tale of the Chanon's yeoman, the work of Richard Carpenter, Dastin's dream. 29. Several questions concerning the Philosopher's stone, no author named (1 f.). 14 CATALOGUE OF NEWTON PAPERS. 30. Observations of the matter in the glass, Authore Anonymo ; also a recipe for an elixir (If.). 31. Sendivogius explained (4f.). 32. The same in Latin, an abstract (2 f.). 33. Epistola ad veros Hermetis discipulos. S. Didier. 34. The seven chapters of Hermes, with part of an unfinished letter on the back. 35. Latin letter communicated by Frederick duke of Holstein, 1656, giving an account of the death of a Jewish magician, of his oratory, instruments, perpetual fire in a crystal, &c. with no writer's name (If.). (3) 1. Jodochus a Rehe. Precede universelle. 2. Artephius, de arte occulta lib. secretus. 3. Abstract of Flamel's account of his hieroglyphics with a sketch of the figures. 4. Novum lumen Chymicum Sendivogii (abstract). 5. Extracts from Joh. Spagnetus. Enchiridion Physicse, ar- canum Hermeticse Philosophise opus. 6. Extracts from Norton's Ordinal, Dastin's dream, Black monk, the hunting of the Green Lyon, Eipley, &c. 7. Ex Augurelli Chrysopceia, and the Marrow of Alchemy. 8. Extracts from Ripley and others. Tabula Smaragdina, and De metallorum metamorphosi (a leaf missing at the beginning). 9. Observanda. Instructio de Arbore Solari. Area Arcani. Epistola Grasseei. Occultae naturae mysterium. Appendix ad aurum potabile. Lucerna salis philosophorum. Auriga chemicus. Rosarium magnum. 10. Snyders' Commentatio de Pharmaco Catholico. 11. References to B. Valentine's works, his process, 12 keys, and Extracts from his Testament. 12. Miscellaneous Notes and quotations. 13. Note of information received from a Londoner as to pre- cautions in preparation of the philosopher's stone. Mar. 3, 1695 6. 14. Notes de scriptoribus chemicis. 15. Notes and memoranda relating to alchemy (2 ). SECTION II. CHEMISTRY. 15 16. Table of contents of some work on Alchemy. 17. Notes and memoranda (2 f.). 18. Abstract of some work, with commencement of a letter to Mr Proctor an attorney relating to a bond of Mr Tongue to Newton on the back. 19. Annotationes, being extracts from several works. 20. Account of S. Didier's keys, and what various other authors have written on the same subject. This seems to be an attempt to co-ordinate the accounts of processes described mystically by the several authors (5 f.). 21. Chemical nomenclature of the Egyptians, and a praxis of alchemy extracted from various authors, with a duplicate folio partly cancelled. 22. De mineralibus. Extracts from Geber and others. References and extracts (one on the back of a letter). 23. Diagram of lapis philosophicus cum rotis elementaribus. 24. Memoranda about chemicals. 25. Notes of some process. On the back of memoranda of sums owing from Mr George Gates, Mr Day, and Richard Rawlins. 26. Receipt for some compound of sulphur, mercury, antimony and silver, apparently with a view to multiplication of the silver. 27. Alchemical receipts. 28. Receipts for medicines, ink, etc. 29. Table of contents of some work. 30. Part of a treatise, containing Lapidis compositio, out of L. Ventura, Elementorum conversio, from the same, Regimen ignis, from the same and Is. Hollandus, Materia, out of Philalethes and others, Decoctio, Regimen Mercurii, Saturni, Jovis, Lunse, Veneris, Martis, et Solis, out of various authors, and a rough copy of part of the Decoctio. 31. Another treatise in the form of extracts from various authors, some parts repeated, altered, and fragmentary; part Latin, part English, but no original matter. 32. Tables of contents to a similar treatise. 33. Another treatise, apparently earlier, edges partly burnt. 16 CATALOGUE OF NEWTON PAPERS. 34. Table of contents, with a chapter de virga mercurii. 35. A collection of nine papers in a cover (originally ten), con- sisting of notes and extracts, the 10th paper, of ancient hieroglyphics, missing. 36. Three odd papers on the Regimen. (*) 1. A common-place book, in paper cover, containing notanda and sententise notabiles from various alchemical authors. Greater part blank. 2. A list of chemical authors. 3. Several Indices Chemici. 4. De peste. Van Helmont. 5. Note as to Terra lemna, and Terra sigillata, with Leibnitz's address. 6. List of books on Chemistry with shelf-marks (perhaps in Trinity Library). 7. An alchemical recipe headed " Roth Mallor's work." On the back of the folio a recipe for making aqua regia from calcium chloride and aqua fortis, and for another menstruum which seems to be a solution of antimony chloride. The 2nd Period (a part of the foregoing recipe), but not in Newton's hand. 8. Notes of reference to some alchemical works. Diagrams of furnaces. Sundry recipes for making clay for furnaces and lutes. Note that "for rectifying spirits and ethereal oyles, nothing is better than the bladder of an ox or hogg," and a recipe for calcining gold which seems only getting it into a fine powder. 9. Dr Goddard's experiments of refining gold with antimony, extracted from Phil. Trans. 10. Part of a letter ordering some one to procure for Newton from Hamburg various metallic ores. On the back a note about something being true when angles due to difference of refraction are taken small enough, and a recipe for some plaster. 11. Notes of stannic chloride, and some chemical reactions. 12. An alchemical experiment, not in Newton's hand, which seems part of some larger work. There is a note in Newton's hand on it relating to quantities obtained in some distillation. SECTION II. CHEMISTRY. 17 (5) 1. Anagrams of " Isaacus Newtonus " on draft of a letter to the Council about some matter at the Mint. Note of quotations in ludo puerorum, scala philosophorum, and rosario. 2. Directions as to some details of an alchemical process given by a Londoner acquainted with Mr Boyle and Dr Dickinson. On the back the beginning of a letter in which mention is made of Mr Pepys asking Sir I. N. for a method of finding the longitude at sea. 3. List of Alchemical works. A classification of the same with dates. On the back an account of gold and silver moneys coined since Christmas (no year), in which the guinea is put at 21s. 6d. 4. Another list of Alchemical authors with dates. 5. Another list of Alchemical authors, with extracts from Act of Parl. 5 Car. II., on coinage, on the back. 6. Extracts " ex lumine de tenebris." 7. A treatise on Chemistry, extracted from various authors, similar to nos. 18, 31, above ; with some odd papers partly duplicates. 8. Two chapters apparently of another such treatise, headed " Reductio et sublimatio " (2 fol.), and " Separatio elementorum" (1 fol.) compiled as before. 9. Recipes for cements. Address of 2 stampmakers. Mathemati- cal diagrams and lists of alchemical works. 10. Opus Galli Anonymi. With a note by Newton " Simile est hoc opus operi Fabri..." It gives a recipe for the Philosopher's stone \J and medicine but it does not state what the material operated on is ; the preparation consists in repeated digestions and distillations. 11. Alchemical operations references to the pages of several books. 12. Experimenta Raymundi (2 fol.). 13. Observationes (heads of Alchemical process). 14. Ex Fabri Hydrographo Spagyrico (1 f.). 15. Ex Hercule prochymico (1 f.). 16. Miscellanea from Raymund and others (1 f.). 17. The Regimen, in seven aphorisms and notes thereon (2 f.). 18. Index chemicus (commencement only). 19. Various extracts from alchemical works (9 f.). N. 2 18 CATALOGUE OF NEWTON PAPERS. 20. Out of ' La Lumiere sortant des Tenebres ' [above, no. 6], and commentary thereon (1 f.), but incomplete. 21. Fragment out of some treatise with pictures no beginning or end. 22. Recipes for lutes, with some addresses on the back. 23. Recipes for some alchemical medicines, with address of a druggist. 24. Other alchemical operations, one a translation, and one not in Newton's hand. 25. Abstract of Yarworth's " Processus " incomplete, extending to Chap. v. 26. An alchemical tract entitled " Manna," not in Newton's hand, but with additions and notes at the end in his hand. 27. Recipe for Regulus Martis; on the back some arithmetical calculation. 28. Copy (not in Newton's handwriting) of a letter from Mr John Casswell, Oxford, Oct. 14, 1694, to Mr John Flamsteed, giving an account of some observations on magnetism. 29. Account of a method for making aqua fortis and for re- fining silver, in Conduitt's hand. 30. "Experimentum Bellini." 31. Theatrum Astronomies Terrestris. Packet marked VI. containing the following papers on Alchemy : 1. Some alchemical receipts, not in Newton's hand. 2. Queries, not in Newton's hand. 3. A medicine to transmute copper, ditto. 4. Alchemical receipts, ditto. 5. To make artificial pearl, ditto. 6. No. 73. An incomplete copy (76 pp.) of Yarworth's "Processus," not in Newton's hand. N.B. The several copies of Yarworth are not identical. SECTION II. CHEMISTRY. 19 *rn. Two bound MS. copies of Yarworth's "Processus," both incomplete. A MS. book on Alchemy, containing The apocalyps or revelation of the secret spirit, by an un- known author. Quotations from divers writers on alchemy. An unknown author upon the philosopher's stone. Ex epistola Johannis pauperis. De Alkymiae veritate Se Aa7rtSi/3vs &c. The breefe of Sir Edward Vere's book. Aug. 18, 1610. IV. NOTES OF EXPERIMENTS, ALL IN NEWTON'S HAND. 1. Dec. 10. 1678 to Jan. 15. Subliming antimony with salam- moniac. Alloying antimony with lead and other metals. (No definite result of value.) 2. Jan. 1679 80. Subliming antimonial sublimate with lead antimoniate &c. Jan. 22. Action of nitric acid and salammoniac on antimony sulphide &c. and further sublimations. (Most of these experiments are roughly quantitative.) 3. Feb. 1679 80. Fusing antimony with vitriol and other things. Sublimation of various metals by help of antimony and salammoniac &c. Action of oil of vitriol on galena, of nitric acid on sublimate of antimony, and others of a like kind. 4. Aug. 1682. Similar experiments; some on lead ore, others on an alloy of tin and bismuth which he seems to call Diana. 5. July 10 (no year), "vidi >j }> Oct. 5, referred to in p. 37 J> J> Oct. 26, March 31, 1711 40 )> June 4, )> J> JJ June 9, 42 only a fragment in Edleston. 55 ?) June 23, 44 Crownfield (printer) to Newton July 11, 1711 Cotes to Newton. July 19, ... 50 July 30, ... 52 Sept. 4, ... 54 Oct. 25, not in Edleston. Feb. 7, 171112 ... 57 Feb. 16, ... 61 Feb. 28, ... 75 March 13, ... 79 April 14, 1712 ... 91 April 15, ... 93 April 26, ... 100 May in MS. wrongly. May 1, ... 103 May 3, ... 106 38 CATALOGUE OF NEWTON PAPEKS. Edleston. Page Cotes to Newton, May 13, 1712 ... 114 Aug. 10, ... 121 Aug. 17, ... 127 Aug. 28, ... 132 Sept. 6, ... 136 Sept. 15, ... 140 Oct. 23, ... 143 Cotes to Bentley. March 10,171213 ... 149 Dec. 22, 1713 ... 166 Cotes to Newton. April 29, 1715, On the Eclipse of the Sun, 22nd April, partly given in Edleston, p. 179. Robert Smith to Newton, relating to the publication of Cotes's works, Dec. -23, 1718; Aug. 12, 1720. Robert mith to John Conduitt, Esq re ., Feb. 4, 1732 3, asking for the loan to him of the foregoing letter of Cotes on the Eclipse. Also a memorandum dated June 6, 1738, acknowledging the receipt of certain letters of Cotes to Newton lent to him by Mrs Conduitt. X. ROUGH DRAFTS OF SOME OF NEWTON'S LETTERS TO COTES. The letters in Edleston and the pages to which these drafts relate are given in the following list : Letter VI. page 1 4 5) VIII 19 J5 XI 24 w XIII 27 XV 30 55 XLII 83 XLIII 89 JJ XLVI 94-98 LXI 129 LXXXI 154 This is rather fuller than the letter printed by Edleston. Letter LXXXII page 156 SECTION VI. LETTERS. 39 XI. KEILL TO NEWTON. Keill to Newton, April 3, 1711. Copy of Keill's answer to the letter u pro eminente Mathematico," in the Journal Litteraire, 29th July, 1713. Keill to Newton, Nov. 9, 1713. Feb. 8, 1713-4. Answer in Edleston, Cor- respondence of Newton and Cotes, p. 169, dated April 2. Johnson to Keill, Feb. 9, 1713-4. Keill to Newton, April 20, 1714. Answer in Edleston, p. 170. May 2, 1714. May 14, 1714. (Draft of a letter from Newton to Keill dated May 15, 1714, is printed in Edleston, p. 176.) Keill to Newton, May 17, 1714. May 21, 1714. May 25, 1714. June 2, 1714. June 24, 1714. Aug. 6, 1714. Oct. 29, 1715. Nov. 10, 1715. May 17, 1717. May 23, 1718. (On the back of Keill's letter of Oct. 29, 1715, there is a scrap in Newton's hand in answer to an objection of Bernouilli.) XII. PEMBERTON'S LETTERS TO NEWTON WHILE EDITING THE 3RD EDITION OF THE 'PRINCIPIA.' Pemberton to Newton, Feb. 11, 1723-4. Feb. 18, 1723-4. May 17, 1725. Monday, May 31, 1725. Tuesday Morning, June 22, 1725. July 17, 1725. Feb. 9, 1725-6. Besides these, 16 undated letters and 7 sheets of queries. 40 CATALOGUE OF NEWTON PAPERS. LETTERS FROM N. FACIO DUILLIER TO NEWTON AND OTHERS. N. Eacio Duillier to Newton, Nov. 17, 1 692. Nov. 22, 1692. May 4, 1693. June 15, 1717. April 1, 1724. N. Eacio Duillier to Conduitt, Aug. 8, 1730 (with proposed Epitaphs on Newton). N. Eacio Duillier to Conduitt, Aug. 12, 1730. Aug. 26, 1730. Abstract of Facio's Letter to Dr Worth, Jan. 26, 1731-2. N. Eacio Duillier to Conduitt, April 5, 1732. , April 10, 1732. April 12, 1732, with enclosed petition to the king. Petition to the Commons. A printed copy of a Latin Eclogue on Newton by M. Eacio de Duillier. *XIV. MISCELLANEOUS LETTERS. 1. Venan(?) to Huyghens, Aug. 20, 1664. 2. Borellius to Wallis (Latin), Dec. 6, 1670. 3. Collins to Borellius, Junii 8, 1672. 4. Robert Hooke to Newton, Feb. 16756. Brewster, i. 140. 5. Newton to Hook (on thin plates), Feb. 5, 1675 6. Brewster, i. 141. 6. Thomas Burnet to Newton, Jan. 13, 1680-81. 7. Newton to Thomas Burnet, s. d. (Jan. 1 680 1 ?). Brewster, ii. 447. 8. Boyle to Newton, Aug. 19, 1682. 9. Newton to Jan. 11, 16878 (dated, but not signed). Brewster, ii. 546. SECTION VI. LETTERS. 41 10. Gilbert Clerke to Newton, on difficulties in the Principia, 26 Sept. 1687, with draft of Newton's answer. Gilbert Clerke to Newton, Oct. 3, 1687. Nov. 7, 1687. Nov. 21, 1687. 11. John Locke to Newton, July 26 [1692]. Brewster, ii. 461. 12. Richard Bentley to Newton, Feb. 18, 1692-3. Brewster, ii. 463. 13. John Mill to Newton, Nov. 7, 1693. Brewster, ii. 472. 14. Samuel Pepys to Newton, Dec. 21, 1693. Brewster, ii. 471. 15. Nath. Hawes to Newton, May 29, 1694. 16. Basnage de Bonval to Newton, Aug. 22 (no year), De la Haye. 17. Charles Montague to Newton, March 19, 1695 (offering the mastership of the Mint). Brewster, ii. 191. 18. Cassini to Newton, April 6, 1698, on the Satellites of Saturn. 19. Truchet to Newton (no date), acknowledgment of a copy of Newton's Optics translated into French. 20. T. Home to Newton, Aug. 22 (no year). 21. John Hockett to Newton, Sept. 14, 1699 (asking interest for his son at Trinity, with some chron. notes of Newton on the back). 22. to Lady Norris, proposing marriage (copy in Conduct's hand), 17034. Brewster, ii. 211. 23. Lord Halifax to Newton, March 17 [17045]. Brewster, ii. 216. 24. Lord Halifax to Newton, May 5, 1705. Brewster, ii. 217. 25. 26. Two drafts of Newton's letter to a friend at Cambridge, about the election [1705]. Brewster, ii. 215. 27. Draft of part of a letter from Newton to [F. Godolphin?] [1705.] 28. D. Gregory to Newton, Sept. 16, 1707, about the Scottish coinage. 29. R. Bentley to Newton, June 10, 1708. Brewster, ii. 248. 30. Oct. 20, 1709. Brewster, ii. 250. 31. Remond de Monmort to Newton, Feb. 16, 1709-10. 32. ,, ,, to Newton, giving an account of the quarrel between Drs Sloane and Woodward, about stones in the gall-bladder, March 28, 1711. Brewster, ii. 244. 42 CATALOGUE OF NEWTON PAPERS. 33. J. Derham to Newton, Feb. 20, 17123. Brewster, ii. 519. 34. R. Bentley to Newton, July 1 [1713]. Brewster, ii. 254. 35. The Abbe Bignon to Newton, Nov. 30, 1713. 36. 37. Draft of a letter from Newton to the Abbe Bignon, with a copy by Conduitt. 38. Varignon to Newton, Dec. 5, 1713. 39. R. Bentley to Newton, Jan. 6, 1713-4. 40. J. Derhain to Newton, about his physico-theology, May 11, 1714 (with some notes by Newton on Osiris, the length of the year, etc.). 41. John Chamberlayne to Newton, May 20, 1714. 42. Fontenelle to Newton, June 9, 1714. 43. A. Menzikoff to Newton, asking admission to the Royal Society, Aug. 23, 1714. 44. Three drafts of Newton's answer, Oct. 21, 1714. 45. John Chamberlayne to Newton, Oct. 28, 1714. 46. (no date) Friday morning. 47. Varignon to Newton, Nov. 18, 1714. 48. Fontenelle to Newton, Feb. 4, 17145. Brewster, ii. 518. 49. Sir Alex. Cunningham to Newton, Feb. 21, 1716. Venice. 50. Draft of letter from Newton to Bernouilli about the omission of his name from the list of Fellows of the Royal Society. 51. Brook Taylor to Newton, April 22, 1716. Brewster, ii. 509. 52 Sir Alex. Cunningham to Newton, May 1, 1716. Venice. 53. Conti to Newton, Dec. 10, 1716. Brewster, ii. 434. 54. Letter of Remond de Montmort to Newton, dated Paris, Feb. 25, 1716-7. 55. John Bernouilli to R. de Monmort, Apr. 8, 1717 (copy, with an addition by Newton). Brewster, ii. 437. 56. Nich. Bernouilli to Newton, May 31, 1717. 57. Fontenelle to Chamberlayne, July 6, 1717 (extract in Mrs Barton's hand). Brewster, ii. 289. 58. Remond de Monmort to Newton, March 27, 1718. 59. Letter from Brook Taylor to Mr Innys, dated Aug. 12, 1718, containing an extract of a letter from M. Riccati to M. Poleni forwarded by M. Montmort, 5 Aug. 1718. 60. Newton to Varignon, Oct. 13, 1718. Draft. SECTION VI. LETTERS. 43 61. Varignon to Newton, Nov. 17, 1718. 62. Remond de Monmort to Taylor, Dec. 18, 1718. (Copy.) Brewster, ii. 511. 63. Yarignon to Newton, July 26, 1719. 64. Newton to Varignon, 1719. Draft. Answer to 63, printed Maccl. Corres. Yol. n. p. 436. 65. James Stirling to Newton, Aug. 17, 1719. Brewster, ii. 516 66. A. H. de Sallengre to Newton, Sept. 22, 1719. 67. Joh. Bernouilli to Newton, Dec. 21, 1719. Brewster, ii. 504. 68. Newton, in. Non. Quintil. [July 5] 1719. Brewster, ii. 502. 69. Job. Bernouilli to Newton. Copy of latter part of do. in Newton's hand. 70. Yarignon to Newton, after April 28, 1720. 71. Nov. 28, 1720. Brewster, ii. 496. 72. James Wilson to Newton, Dec. 15, 1720 (signed A. B.). Brewster, ii. 440. 73. Rizzetti to the Royal Society, containing objections to Newton's Optical Experiments (s. d.). Also a letter of Rizzetti to Christine Martinello, of Yenice, on the same subject. 74. James Wilson to Newton, Jan. 21, 1720 1. Brewster, ii. 443. 75. Cotet to Newton, on the edition of Newton's Opticks printing at Paris, Aug. 16, 1721. 76. G. J. Gravesande to Newton, Aug. 18, 1721. 77. Yarignon to Newton, Sept. 18, 1721. 78. Oct. 2, 1721. 79. Letter from Hen. Fr. Daguesseau to Newton, Oct. 1721. 80. Yarignon to Newton, Dec. 9, 1721. 81. 82. Yarignon to Bernouilli, 2 copies, April 4, 1722. 83. Yarignon to Newton, April 4, 1722. 84. April 28, 1722. 85. Aug. 4, 1722. 86. Newton to Yarignon. Draft reply to 83. 87. July 0)13, 1722. 44 CATALOGUE OF NEWTON PAPERS. 88, 89. Newton to Varignon. Draft. About August, 1722. 2 copies. 90. Fontenelle to Newton, Nov. 22, 1722. 91. Draft of a letter from Newton to Fontenelle. No date. 92. Newton to Varignon, Dec. 13, 1722. Draft. 93. Letter from Newton to some one at Paris about Varignon's picture after Varignon's death, which took place Dec. 23, 1722. Brewster, p. 295. 94. Joh. Bernouilli to Newton, Feb. 6, 1723. Brewster, ii. 507. 95. Philip Naude to Newton, on the Calculus, Feb. 6, 1723-4. 96. De L'Isle to Newton, thanking him for his election to the Royal Society, April 2, 1724. 97. G. Cavelier to Newton, on the publication of his Chrono- logy, May 11, 1724. 98. A. F. Marsili to Newton, Aug. 1724. 99. De L'Isle to Newton, Dec. 21, 1724. 100. A. F. Marsili to Newton, March 11, 17245. 101. G. Cavelier to Newton, March 20, 1724 5, about publica- tion of his Chronology. 102. J. T. Desaguliers to Newton, ' April 29, 1725. 103. Jombert to Newton, Sept. 12, 1725. (2 copies.) 104. Draft of a letter from Newton to Daguesseau on Bernoulli's letter, complaining of being called ' eques errationis.' 105. Colin Maclaurin to Newton, Oct. 25, 1725. Brewster, ii. 385. 106. Fontenelle to Newton, acknowledging the receipt of the third edition of the Principia, July 14, 1726. 107. Thomas Mason to Conduitt, March 23, 1726-7. 108. J. Craig to Conduitt, April 7, 1727, partly printed by Brewster, ii. 315. 109. William Stukeley to Dr Mead, June 26, 1727 July 15, 1727, four sheets, written consecutively, but sent at intervals. 110. W. Stukeley to Conduitt, July 15, 1727. 111. July 22, 1727. 112. Memorandums relating to Sir I. N. given to A. Demoivre by Conduitt, Nov. 1727. SECTION VI. LETTERS. 45 *xv. LIST OF THE LETTERS OF NEWTON, MOSTLY PUB- LISHED IN THE MACCLESFIELD CORREPSONDENCE. Newton to Collins These are fair copies. No. Maccl. Corr. ccxxiv Jan. 1669 Feb. 6, 1669 Feb. 23, 1668-9 and comment by Collins Newton to Aston May 18, 1669 Collins Oldenburg Feb. 18, 1669-70 July 11, 1670 July 16, 1670 Sept. 27, 1670 July 20, 1671 Jan. 6, 1671-2 Jan. 18, 1671-2 Jan. 29, 1671-2 Feb. 10, 1671-2 Feb. 20, 1671-2 ccxxv CCXXVI CCXXVII CCXXVII1 CCXXIX CCXXXI CCXXXIII CCXXXIV ccxxxv CCXXXVI CCXXXVII CCXXXVIII Collins Oldenburg CCXXXIX March 26, 1672 Phil. Trans. No. 82, p. 4032 March 30, 1672 No. 82, p. 4034 April 13, 1672 No. 83, p. 4059 May 4, 1672 No. 83, p. 4057 May 21, 1672 not in Phil. Trans. May 25, 1672 Maccl. Corr. CCXLI June 19, 1672 CCXLII July 6, 1672 CCXLIIT July 11, 1672 Phil. Trans. No. 88, p. 5084 a long letter on Optics in reply to Mr Hook's "Con- siderations". Collins July 13, 1672 Maccl. Corr. CCXLV Oldenburg July 13, 1672 CCXLVI Collins July 30, 1672 CCXLVII Oldenburg Sept. 21, 1672 CCXLIX March 8, 1673 CCLI Oldenburg? April 3, 1673 CCLII in answer to Hugenius' letter of Jan. 14, 1673. Newton to Collins April 9, 1673 May 20, 1673 CCLIII CCLIV 46 CATALOGUE OF NEWTON PAPERS. Newton to Collins Sept. 17, 1673 Maccl. Corr. CCLV Nov. 17, 1674 CCLVIII Oldenburg Dec. 9, 1674 CCLIX [printed Dec. 5 in Mace. Corr.] Dary Collins Oldenburg Jan. 22, 1675 Maccl , Corr. CCLX July 24, 1675 ?? CCLXI Aug. 27, 1675 ?, CCLXII Dec. 14, 1675 ,j CCLXIII Dec. 21, 1675 >) j> CCLXIV Jan. 10, 1675-6 >> ?? CCLXV Feb. 15, 1675-6 ,5 ?? CCLXVII Feb. 19, 1676 June 13, 1676. Latin letter for Leib Collins Sept. 5, 1676 Oldenburg (?) Oct. 24, 1676 Oldenburg Nov. 18, 1676 Nov. 28, 1676 Comm. Epist. p. 131 Maccl. Corr. CCLXIX CCLXX CCLXXIII SECTION VII. BOOKS. *1. A Theological Common-place Book, written from both ends, in Newton's hand. 2. Four folio MS. volumes, bound in red morocco, and labelled " John Conduitt," entirely in Newton's hand. (1) The Chronology of Ancient Kingdoms amended. Horsley, v. pp. 28263. (2) i. A short chronicle from the first memory of things in Europe to the conquest of Persia by Alexander the Great. Printed twice by Horsley, v. pp. 3 27 and pp. 267291. ii. Another copy of the Chronology of Ancient Kingdoms amended. (3) Observations on the Prophecies. Horsley, v. pp. 297 491. (4) De motu Corporum Liber Secundus. This is the treatise De Mundi Systemate. Horsley, iii. pp. 180242. *3. A volume of extracts on Alchemical subjects, in Newton's hand. 4. (1) A copy of the 1st edition of the Principia, interleaved with notes in Newton's hand. Among the leaves inserted is the preface to the 3rd edition. In a miserable plight from damp and ill-treatment. (2) A copy of the second edition of the Principia, interleaved with notes and additions in Newton's hand. 5. A MS. copy of a portion of the Arithmetica Universalis, apparently an early copy. 6. A copy of Schooten's edition of Des Cartes' Geometry, Lugd. 1649, with a few notes in Newton's hand. 7. A short treatise on the beginning of Algebra, in Newton's hand : at the other end are extracts from Quintus Curtius, and a long prayer, and a sermon on Lev. xix. 18, not in N.'s hand. 8. A common-place book written from both ends, with " Isaac Newton, Trin. Coll. Cant. 1661," in the beginning. This contains, at one end, Definitions from Aristotle's Organon, an abridgement of the Phisiologia peripatetica of John Magirus, and some Astronomical notes by Newton : at the other, Sentences from Aristotle's Ethicks, Annotationes ex Eustachii Ethic., Axiomata, 48 CATALOGUE OF NEWTON PAPERS. Epitome G. J. Vossii partionum oratoriarum, a note on the word Idea, Remarks on " Qusestiones qusedam Philosophies," details of the observation of the comet of 1664, of the effect of sunlight on the eyes, etc. *9. A copy of " Secrets revealed, or an open entrance to the shut palace of the King," &c., by W. C., London, 1669, with notes in Newton's hand. *10. A bound MS. book containing at one end memoranda of Newton's expenses at College, and at the other a short outline of Trigonometry and Conic Sections in Newton's hand. 11, 12. Two MS. note books, bound, containing a Compendium of Elementary Mathematics, apparently made by St John Hare. In one of the volumes Abotesley is added to the name, and the fol- lowing " Sibi, non aliis hsec." To the other volume the date 1675 is given after the name. 13. Lettres de M. Leibnitz and M. le Chevalier Newton sur 1'invention des Fluxions et du Calcul Differentiel. This is a proof of part of the 1st edition of Desmaizeaux's E/ecueil, with corrections. (Several pages are wanting at the end.) 14. A college note-book, written from both ends, containing early exercises extraction of the square and cube root, elementary Geometry, &c. followed by annotations of Wallis's Arithmetica In- fmitorum. This is preceded by a note of Newton's fixing by an entry in his account-book the date of the annotations as being in the winter 1664 5, at which time he says he found the method of infinite series. Also notes on music, chances, &c. This is the note-book referred to in Brewster's Life of Newton, Vol. i. p. 22. 15. Proof sheets of the edition of Newton's Opticks, with a few MS. additions by Newton. 16. An early copy (MS.) of the Lectiones Opticse, Jan. 1669. 17. A book, containing the commencement of a work on Hydro- statics, the greater part consisting of a dissertation partly meta- physical, partly theistic, on the constitution of matter, motion, the Cartesian philosophy, etc. 18. A common-place book, written originally by B. Smith, D.D., with calculations by Newton written in the blank spaces. This contains Newton's first idea of Fluxions. SECTION VIII. MISCELLANEOUS PAPERS. *1. Copy of the agreement relating to Sir I. Newton's MSS. Copy of bond given by Conduitt in relation to Sir I. Newton's papers. An account of John Conduitt's right to the MSS. of Sir I. Newton. 2. Six drafts (all in Newton's hand) of a scheme for establishing the Royal Society. 3. Two printed copies of Newton's letter to the Abbe Conti dated Feb. 26, 1716, with remarks of Newton on the letter of Leibnitz to the Abbe Conti the latter dated |~f May 1716 (printed in Des Maizeaux. Recueil, Tome ii. pp. 20, 82, 107). 4. Advertisement of the Book "De Systemate Mundi" in Con- duitt's hand, with memoranda and modern letters on Newton's life. 5. On Education, vations. Order to pay 125 to Flamsteed for his first Catalogue of fixed stars. Receipt for the same from Ja. Hodgson. Flamsteed to Newton, April 23, 1716 (asking for the return of his MSS.) printed in Baily's Flamsteed, p. 322. Order by Queen Anne for the appointment of a Board of Visitors of the Royal Observatory dated Dec. 12, 1710. Drafts of Correspondence relating thereto. Petition to the Queen of the President, Council and Fellows of the Royal Society of London, for the grant of a new place of Meeting. * SECTION X. I. CORRESPONDENCE BETWEEN CONDUITT AND FONTENELLE ABOUT THE ^LOGE. Conduitt to Fontenelle, 27th March, 1727. O. S. Fontenelle to Conduitt, 14th April, 1727. N. S. Conduitt to Fontenelle, No date given, but must be about 21st July, 1727. 31st July, 1727. 5th October, 1727. 0. S. Fontenelle to Conduitt, 15 Nov. 1727. N. S. Conduitt to Fontenelle, 23rd Nov. 1727. 1st Jan. 1727-8. The above are inclosed in a portion of Mists' Weekly Journal for Saturday, April 8, 1727, containing Reflections occasioned by the Death of Sir I. Newton. II. Conduitt's Memoirs of Sir I. Newton, sent to Fontenelle for the loge. 1. English copy, containing 29 numbered pages, No. 21 repeated, and 1 page of corrections. 2. French copy, containing 27 pages. This includes a trans- lation of the account of Newton's funeral from the London Gazette of 4th April, 1727. III. A copy of the London Gazette for 4th April, 1727, contain- ing the account of Sir I. Newton's funeral. * SECTION XI. DRAFTS OF FRAGMENTS OF CONDUITT'S INTENDED LIFE OF SIR I. NEWTON. 1. 42 pages, giving an account of Newton's life to the time of his going to Cambridge. 2. 35 J pages, containing a more finished copy of the same. [This was intended to be followed by an account of the state of Philosophy when Newton began his discoveries.] 3. Four copies of suggestions addressed to some one from whom Conduitt expected to obtain a popular account of the state of phi- losophy when Sir I. Newton first appeared, and also a similar account of his discoveries, and of the improvements that several persons have made in various parts of them. 7| pages. 4. 16 pages, relating to his life and work at Cambridge. 5. 17 pages of Miscellanea, containing anecdotes, &c. 6. 17 pages relating to Newton's character. 7. 2 copies, each about 1 \ page, on his love and gratitude to his mother. 8. 2 pages on Sir I. Newton's manual dexterity. 9. 2 copies of 2 pages, each on the same subject, illustrated by a custom in the house of Austria. 10. Paper with date 31st of August, 1726, containing 4 large and 4 small pages, containing anecdotes of Newton, relating to various times. 11. 2 pages, containing an account of a conversation of Conduitt with Newton, on Sunday the 7th March, 1724-5. 12. 2 pages, containing various scraps from Newton's note-books. 13. Scrap of 4 small pages, on Newton's dispute with Hook. 14. Scrap of 2 small pages, in glorification of Newton. 15. Scrap of 1 J large pages, containing rough notes relating to Newton's last illness, and brief references to anecdotes. 16. A compliment on Pope, 17. Sketch of a preface. 18. Extracts from Journal books of the R. Soc. relating to the late Sir I. Newton with a letter from W. Rutty, R. S. Sec. to Conduitt. Dates of what passed at the University (so endorsed by Conduitt). * SECTION XII. LETTERS AND MEMORANDA, RELATING TO NEWTON, AFTER HIS DEATH. 1. Thomas Mason to Coiidnitt, 13 March, 1726-7. 2. J. Craig to Conduitt, 7 Apr. 1727, partly printed by Brewster, ii. 315. 3. Wm. Stukeley to Conduitt, 26 June, 1727. 4. Wm. Stukeley to Dr Mead, 26 June, 172715 July, 1727 (four sheets written at intervals). 5. Dr Mead to Conduitt, 7 July, 1727. 6. Wm. Stukeley to Conduitt, 15 July, 1727. 7. Wm. Stukeley to Conduitt, 22 July, 1727. 8. Memoranda of Newton, given by A. Demoivre to Conduitt, Nov. 1727 (in Conduct's hand). 9. Draft of a letter from Conduitt to A. Pope, 8 Nov. 1727, enclosing 10. The dedication to the Queen of Sir I. N.'s chronology, and 11. An account of the chief events of Newton's life. 12. A. Pope to Conduitt, 10 Nov. 1727, printed by Brewster, ii. 521. 13. Nicholas Wickins to Prof. Smith, 16 Jan. 1727-8, printed by Brewster, ii. 88. 14. W. Stukeley to Conduitt, 16 Jan. 1727-8. 15. Humphrey Newton to Conduitt, 17 Jan. 1727-8, printed by Brewster, ii. 91. 16. J. Conduitt to - , 6 Feb. 1727-8, printed by Brewster, i. viii. 17. W. Stukeley to Conduitt, 13 Feb. 1727-8. 18. Humphrey Newton to Conduitt, 14 Feb. 1727-8, printed by Brewster, ii. 95. 19. W. Stukeley to Conduitt, 29 Feb. 1727-8. 20. J. Conduitt to , 4 June, 1729 ; see Brewster i. x. n 1 . 21. Bp. Sherlock to - ,10 June, 1731. 22. Note of Newton's elections at the Royal Society. 23. Nevil Maskelyne to Dr Horsley, with remarks on Horsley's ed. of Newton, by one Robison, 8 May, 1782. 24. Seward to Horsley, s. d. 25. W. Derham's account of conversations with Newton. 26. Account of Newton's mother, "given me [Conduitt] by Mrs Hutton, whose maiden name was Aiscough." * SECTION XIII. PAPERS ON NEWTON'S FAMILY MATTERS, AND ON THE MINT. 1. Statement of Lord Halifax's legacy to Mrs Barton, and of the transfer from the Executor George Lord Halifax, giving the date of the trust, 26 October, 1706. With some notes on Miracles. 2. An account of what his majesty may lose by renewing for seven years the contract with Cornwall and Devonshire for Tynn. 3. An account of the gold and silver coined at the Mint, from 1713 to 1715, with some notes on Repentance at the back. 4. Draft of a letter to the Lords Commissioners of the Treasury with this account, some notes on the Controversy on Fluxions at the back. 5. The accounts of Mr Ambrose Warren, Agent for the Trustees, &c., of the charity of his Grace Thomas Archbishop of Canterbury, founded at the Tabernacle by Golden Square, for the quarter ending Christmas, 1700. 6. Paper of calculations, apparently for the Mint. 7. Proposal for a medal to commemorate the Union of England and Scotland. 8. Various letters and fragments on family matters. 9. Pedigree and papers relating to his family, all in Newton's hand excepting the pedigree, which is a copy. * SECTION XIV. BOOKS AND PAPERS NOT BY NEWTON. 1. Essaies and Meditations concerning morality and religion. The first part. A folio, with no author's name, written in the same hand throughout. 2. Sir C. Wren's cipher, describing three instruments proper for discovering the longitude at sea. In Halley's hand. Printed by Brewster, ii. p. 263. 56 CATALOGUE OF NEWTON PAPERS. 3. Drawing of the arms of the Swinfords of Swinford, with some notes. In Mrs Barton's hand. 4. Catherine Conduitt's will, 9 July, 1731. 5. Epitaph on F s Oh is (Charteris). 6. Epigrammes ecrites en vieux Gaulois en imitation de Clement Marot, per Mons. Rousseau. Copied at Geneva, 1709. 7. Problem in Spherical Trigonometry, in French. 8. A scheme of the Longitude, signed Laurans. 9. Several copies (printed) of Leibnitz's Charta volans. 29 July, 1713. 10. An abridgement of a Manuscript of Sir Robert Southwell's concerning travelling. Writt. 1658, Feb. 20. Written from the other end are " Chansons Frangoises." 11. A MS. of Cicero de Senectute, about 1480. 12. Treatise in French, on the Infinite Divisibility of Matter. No name ; handwriting unknown. 13. Metaphysical Speculations on Astronomy. No name ; hand unknown ; of no interest. 14. Viaticum Nautarum, or the Sailor's Vade Mecum, by Robert Wright, B.A., formerly of Jesus College in Cambridge. 15. CEdipus Sphingi, Auctore R. P. Nicolas Augustino Venetiis, 1709. (Incomplete.) 16. A MS. book on the Motions of the Secondary Planets, divided into six chapters. 17. Elementary calculations and figures relating to Spherical Trigonometry, possibly by St John Hare. * SECTION XV. Complimentary letters to Newton from distinguished foreigners. CAMBRIDGE : PRINTED BY C. J. CLAY, M.A. & SONS, AT THE UNIVERSITY PRESS. 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