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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.
Bernouilli'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, witḥ 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.
The references do not agree with the Principia.
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 probably 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 experiments, with Newton's deductions; chiefly rough notes.
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.
16. 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.
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.
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 Lunæ, 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 investigation 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 Observations.
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.
Notes on the Correspondence in Wallis's Works, Vol. 3. 4. Notæ ad Acta Eruditorum.
5. Rough drafts of the Leibnitz Scholium in the 2nd Edition of the Principia, and proposed additions to it.
6. Enarratio plenior Scholii præcedentis.
8. An account of the Commercium Epistolicum (several varying copies).
9. Papers relating to the origin of the Dispute.
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 Commercium 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. Bernouilli's problem in the Acta Eruditorum for Oct. 1698. 26. Historical Annotations on the Elogium of Leibnitz.
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 Abbé Conti.
29. Proposed addition to the “Remarks” on Leibnitz's second Letter to the Abbé Conti—after Leibnitz's death. (Des Maizeaux, Vol. 2, pp. 82–106.)
30. Drafts of a letter to a friend of Leibnitz (probably Chamberlayne), 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
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 Abbé Conti in reply to the Postscript 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 Epistolicum,” &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 Varignon and others, relating to Bernouilli's Letter of 7 June, 1713, which had been disavowed by the writer.