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II. ELEMENTARY MATHEMATICS. (Holograph.)
1. Observations on the Algebra of Kinckhuysen.
2. The first Ten Propositions of the 2nd book of Euclid, succinctly enunciated and demonstrated.
3. Theorem on the Area of a Triangle.
4. Trigonometria succinctè proposita et nova methodo demonstrata a St 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.
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 fuentes et eorum momenta.
10. Propositions in the Method of Fluxions (dotted letters employed).
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.
13. 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.
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 mistakes 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.
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 consist of but three terms.
PAPERS RELATING TO GEOMETRY. (Holograph.)
1. De Problematum resolutione Synthetica.
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 touching three given straight lines.
14. Fragments relating to the writings of the Ancients in general, but especially to the Porisms of Euclid, and the Loci of
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.
6. 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, 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.
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.
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,
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°, 12o 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. Notæ ad Acta Eruditorum.
5. Rough drafts of the Leibnitz Scholium in the 2nd Edition of the Principia, and proposed additions to it.